Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://chronos.msu.ru/old/RREPORTS/levichev-popitka_sinteza.pdf Äàòà èçìåíåíèÿ: Sat Dec 14 13:25:27 2013 Äàòà èíäåêñèðîâàíèÿ: Fri Feb 28 20:42:05 2014 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: trees

M ( "" "-" ). M, (= ) ­ (t,x,y,z). , = (0,0,0,0) ­ , t (x,y,z), (1) x2 + y2 + z2 = C2t
2

(1) ­ () (0,0,0) (x,y,z). . (1) , ( , ). , , .. , . (1) () .

, (. [-84]) [-50]:


, , ( ). , ( ) DLF-: ( ), , ? : ( ). D, L, F - DLF-. , , D U(2), F - U(1,1), . L "" , (2)
z ix1 z ix 4 ix1 z ix1 z ix1

,

z = x2 + ix3, x1, x2, x3, x4 . (2) [L-09], o, (2) D, - F. - , F L D, D\ F , D\ L . D, F, L ( ) . .


([Le-11a, Theorem 6]). F L L D, ( F). [Le-03]. . - . : ( ) «, », ? , , () (), , ( , .). (., , [PaSe-82]) D ( , DLF LF- ). DLF-, D, L, F «» . () , . , M , -, ­ ( ). , , .


. , , . . 57-71 [K-80] ( -) . (.70), . . - (., , [SaWu77, .77 ]). D, L, F , , - . D, L, F : , M, . : ( ) D , M. : In an extensive series of papers, Bernard Haisch and Alfonso Rueda have developed a hypothesis that matter resists acceleration not because it possesses some innate thing called mass as Newton proposed and we all believed, but because the zero-point field exerts a force whenever acceleration takes place. This assertion, that accelerated observers experience a force due to the zero-point field, and that this "electromagnetic reaction force" is responsible for the inertia of material objects, rests upon computations in [RuHa-98]. The hypothetical Unruh effect (or sometimes Fulling­Davies­ Unruh effect) is the prediction that an accelerating observer will


observe black-body radiation where an inertial observer would observe none. In [Un-76] Unruh demonstrated theoretically that the notion of vacuum depends on the path of the observer through space-time. From the viewpoint of the accelerating observer, the vacuum of the inertial observer will look like a state containing many particles in thermal equilibrium -- a warm gas... This is because two mutually accelerating observers may not be able to find a globally defined coordinate transformation relating their coordinate choices. An accelerating observer will perceive an event horizon. The existence of Unruh radiation could be linked to this apparent event horizon, putting it in the same conceptual framework as Hawking radiation. On the other hand, the theory of the Unruh effect explains that the definition of what constitutes a "particle" depends on the state of motion of the observer. In both cases (that is, Rueda-Haish and Unruh), the calculations are performed in the Minkowski space-time (the starting point being the world trajectory of the uniformly accelerated observer). Our goal is now to explore both cases in the background of the Einstein's static universe (which is the Segal's compact cosmos D, essentially), including the question of whether or not there is the event horizon. This explains why one has to determine the world trajectory of the uniformly accelerated observer first. [RuHa-98] Rueda, A. and Haisch, B. Contribution to inertial mass by reaction of the vacuum to accelerated motion, Foundations of Physics, 28 (1998), pp. 1057-1108 [Un-76] W.G.Unruh, Notes on black-hole evaporation, Phys. Rev. D, vol.14, n.4 (1976).


(1967 ­ 2011) ­ . () (Tom Branson, 1953-2006). Levichev A. V., O. S. Sviderskiy. Contractions of certain Lie algebras in the context of the DLF-theory. Levichev A. V., O. S. Sviderskiy. U(p,q) p+q , - : I. p+q= 2, 3. U(p,q) p, q ( ). , U(p,q) (p+q)2. - (. [LeSv-09]). U(2,1) U(3), ( SU(2,2) SU(3,3)) «» . : () - U(3). ( «» D) . Embedding of U(1,1) into U(2) and generalizations to higher dimensions: the Sviderskiy formula Given nonnegative integers p and q, we define the Lie algebra u(p,q) as the totality of all p+q by p+q matrices m (complex entries allowed) which satisfy

ms + sm* = 0,

(3.1)

The above s is the diagonal matrix with p ones and q negative ones on the principal diagonal. Formula n = sm (3.2a)


defines a linear bijection between vector spaces of Lie algebras u(p,q) and u(p+q): (3.2a) is mentioned on p.219 of [2]. Obviously, m = sn (3.2b)

is the formula for the inverse mapping from u(p+q) onto u(p,q). Formulas (3.2a, b) might be viewed as giving canonical linear correspondence between u(p,q) and u(p+q) but how about correspondence between Lie groups U(p,q) and U(p+q)? We have started research in this direction with Oleg Sviderskiy (31 July 1969 ­ 30 March 2011). As a tribute to Oleg, it is now suggested that the formula for the canonical correspondence between groups U(p,q) and U(p+q) be known as the Sviderskiy formula (Theorem 1 below). We define the Lie group U(p,q) as the totality of all p+q by p+q matrices Z (complex entries allowed) which satisfy Z*sZ=s (3.3)

with s introduced above. We now describe how U(1,1) sits in U(2). This is defined by the following function h from D=U(2): the image of a matrix Z =
z1 z 3 z2 z4

is the matrix V with entries

v1 = d/z4, v2 = z2/z4, v3 = - z3/z4, v4 = 1/ z4; (3.4) d is the determinant of Z; the determinant of V equals z1/z4. Proposition 1. The mapping (3.4) is only undefined for elements Z on the torus z1 = z4 = 0 in D=U(2). The image is the entire F=U(1,1). In terms of Lorentzian metrics (introduced in [5] on both D and F) the mapping (3.4) is conformal. The tangent


mapping (or the differential of h) at the neutral element of D is exactly our (3.2b). The Sviderskiy formula is defined as a fractional linear application of a certain 2n by 2n matrix W to (all) matrices in U(p,q); here n=p+q. The n by n blocks A, B, C, D of the matrix W are defined as follows: A=D=
I 0
p

0 0

B=C=

0 0

0 Iq

where Ip (respectively, Iq) stand for the unit matrix of size p (respectively, of size q). Theorem 1. (The Sviderskiy formula). The fractional linear application of the above introduced matrix W is defined for all matrices in U(p,q), and U(p,q) is in a one-to-one correspondence with its image. The inverse mapping is also defined as the fractional linear transformation (by this W). Remark. The above (3.4) is a special case of the Sviderskiy formula. On quarks as fermions in U(3) One can start with an imbedding of SU(2,2) into SU(3,3) (as well as of D into U(3)) which will be the most useful for the purpose of the classification of elementary particles, in particular as related to quarks viewed as fermions in U(3), with a bi-invariant Lorentzian metric on the latter group. As soon as a certain imbedding is chosen, one has to study composition factors of suitable induced representations of SU(2,2) acting on D imbedded into U(3). This simplest try (which goes along the lines suggested by Segal in [Se-91]) results, already, in six massive fermions grouped into three


generations. Also, there are three most natural ways of placing SU(2,2) within SU(3,3). Using this, one can try to model colors. (1926-1994), Turkish-American physicist. W.T.Grandy, Jr., A Nonstandard Model, Foundations of Physics, Vol.23, n.3, 1993, 439-460. An elementary-particle picture developed primarily by Barut as an alternative to the Standard Model is re-examined. The model is formulated on the basis of short-range magnetic interactions among the stable particles and at present is able to account qualitatively for most of the known phenomena. P.441: Is it possible that the electromagnetic unification provided by Maxwell has not been taken far enough, and there exists an already-unified theory of elementary particle interactions without introducing extraneous forces? Ockham's razor alone, or economy of theoretical constructs, suggests that what we call weak and strong forces may be "fictitious" in the same sense that we classify Coriolis, centrifugal, and chemical forces, and that things ought to be made of those entities into which they decay. P.444: It is our contention here, along with Barut, that magnetic interactions among the stable fermions might form the basis for a sound and transparent model of elementary particles. P.457: What we have reviewed here would seem to be, at the very least, the beginnings of a desirable description of how the world works; but at best it is a program, rather than a full-blown theory. ... To proceed further it is necessary to learn how to carry out detailed calculations involving few-body interactions... It is necessary here to consider localized wavefunctions, and to avoid the use of perturbation theory. ... This may not be the way it works, but until all the loopholes have been closed it is difficult to ignore, and surely worthy of continued effort. Herbert Jehle (1907 ­ 1983) made wide and deep contributions to physics. Early in his career (late '40s), he became known for


his work on the two-component field equations to allow for neutrinos with mass. Along with his study of field equations was his review and extension of the spinor description of particles on a curved space-time and curved internal gauge manifold (1953). In a series of publications (Phys. Rev. D and Physics Letters. B, 1971 ­ 1981) he developed a model for muon, electron, neutrinos, mesons, and baryons based on flux quantization. It was proposed that the lepton's magnetic field may be represented by the superposition of alternative forms which a quantized flux loop may adopt. These alternative loopforms should be superimposed with complex probability amplitudes in a manner similar to the superposition of alternative path histories in Feynman's space-time approach to quantum mechanics. The electric Coulomb field has been shown to result from the spinning of the loop. This is so particularly important result. It holds for muon and electron, and is not too astonishing. The Dirac electron theory starts with the charge e of the electron and yields a corresponding magnetic moment. Starting with the concept of flux loopforms, provided they reconstruct the same magnetic moment, we get the Coulomb field equivalent to an electric charge e. The sign depends on whether the magnetic moment vector and the spin angular velocity vector of the loopforms are parallel or antiparallel to each other. (Charge and current follow by Maxwell-Lorentz equations.) A representation of quarks in terms of linked quantized flux loops is suggested to describe a low-lying meson as a linkage of an elementary loop with an antiloop, and a low-lying baryon as three interlinked elementary loops. The quantum numbers of particle physics seem to relate directly to topological and other properties of linked loops and their probability amplitude distributions. Strong and weak interactions might be qualitatively understood in terms of interactions of quantized flux loops (say, weak interactions may be understood to occur


when the flux loops involved in the interaction have to cross over themselves or over each other).

- . - ( ). , Time, Space, Knowledge (1977), . «... , , - , , , , . , , , , . : , , . , ; . , , .» , L "" D (. 12 [-10]). () , .. L ( , L ). , DLF (.. )


. : [Vi-95] (" - - ­ ...-. ­ ") .-. , "... ... - ". , " , .-..-.- ". [RuHa-98] (" ") [Vi-95] : " , ". , L DLF-, .. (object's glow), (`') . . . 1. (1977).

. XXXI: " (, ), ... (vision) ". , (..) :


, . ( . ) . "T" , ( ). . XXXII: " - , . , `', `', `' (insights) , (appearances). `' `'(that are in effect); (levels) `' `' `' - `', `' (`encompasses') . `'(`take up residence') , - . (transcending) `', `' (restrictive) `' , ".

. XXXIII: "... , ... (, ) ". . XXXII: " ...


(a visionary path)... - ... ­ ... ..., () ..." (1977): 1 (), 1 ( ­ ). C. 4: " `' (`things') . , `' , ` ' (`focal setting'; : ­ `'). , , - , `', , ". [-10], [-10], [-11], [-08] ( ) ( ). `'. ( , DLF-) , , 7 [Le-11]. .4 : "..., , , ;


. , , . , , , , ..." C. 5: " , ­ . , . ( - , , ) , , , . « », ... `' , , . ... ­ ­ , . , `' , ".


C.8: "... : , `', ?... , ­ `' (`nothing') , ". .10: "... , , ". ( .11) , " ( ) ­ ... (open up) `', . , ( ) `', `' `' ". , ( ) , (. 9: tracking with our `mind's eye'), « ». ( .11) : `space' projecting `space' into `space'. ( ), , ( ) . , , , . (


8 9 , . http://math.bu.edu/people/levit/sk-04-f.pdf) . . , (: ) ­ . . , , , , () U(p,q), . [09], [-09a]. ( ) [-09a]: «... 2008 , " " [-95, .88]: "... . , , . , , , , , , . , ... " , . [09a] DLF-. , L , () (


1, . [-09a], [-09]). , , D, L, F ( F , D ­ ). ( U(3)), 8. ( ) ­ U(2,1), ( 4 5 ­ ). . -, ( ) . ... U(p,q) p, q ( ). , U(p,q) (p+q)2. - (. [LeSv-09])» - [09a] . , D = U(2), F= U(1,1), U(3) . , U(3) ( «») ?

, Dynamics of Time and Space ­ transcending Limits on Knowledge (book published in 1992). c.XXXVI: , `' (`recover') . ,


. ­ . , () . c.XXXVII: , . (-1977: (object's glow), (`') . " " . ­ ? Conventional quantum mechanics uses representations of the PoincarÈ group, which are induced from its Lorentz subgroup as in Wigner's seminal work [Wi-39]. The underlying space­time is the Minkowski world M (the one of special relativity). There was no formal parallelization involved since it was unthinkable of a better group than M's vector group (flat parallelization, or Mparallelization, according to the current chronometric terminology). Almost always in the literature, physicists merely start with sections having values in a fixed spin space. In general, the parallelization procedure is essentially defined by parallelizing (4D but not necessarily commutative) subgroup of SU(2,2). c. XXXIX: (conducting on our own) , .


? (c.16): field. , (. 38), (. Weeler, H. Jehle). , , . , S (inward, " ") , . . . 39 ("eknosis"), : GS S ( fi) Gm (m ­ mind, ). fo ( ­ knowing capacity). , ( ) (fi, fo) ( ). , . 5 ( « »), .41: () , ­ , , , . . ( ), ... , (records of the


past) . , , ... 81: Rather than accepting this sharp division between subjective and objective time (A.L.- . ), let us see if there is a view that encompasses both. ... 82: This `past as totality' is a construct: the hypothetical point of reference for the hypothesized entity `all that there is'. ... The present as we experience it takes form quite differently: Not as a constructed totality, but as a concrete circumstance with its own defining lineage or lineages. 91: We can all recall occasions when time's power becomes almost tangible (= , ` '). ... Such times of vitality reveal the momentum of time as a thrusting, driving presence. 96: (..: ?) The future `keeps going on': first, in always coming toward us; second, in `stretching' on beyond, so that there is always `more' future available. The "Giant Body Exercise" (. 1 TSK 1977) . ­ («»). (. !), 1977. , ( !) , " " ( forum.roerich.info).

1. Conducting the Vision ( ?)


As thoughts and sensations come up, look within each arising moment for the quality of awareness it carries. «» , «» (), , ( ) «». : « » - ( ). Be sensitive to the way that awareness transfers from one experience to the next. () « », « » . A perception or thought goes forward, carrying awareness, then a second perception or thought recollects and passes that awareness on. What is the quality of this experience? , () ; . ? .1 ( - ). MOST IMPORTANT (?) 123: We find ourselves awash in social structures, technologies, personal concerns, and cultural artifacts ­ adrift in a sea of words and images, sense impressions, ideas, fantasies, and


emotions. ... Our attempts at solutions play out rhythms that activate anew the prevailing patterns, calling us forward to conduct the conducted once again. ... The process is selfdefeating and painfully self-destructive. , , , () ­ , , , , ... , . ( ) , ... , .

127 ( ?): Once the temporal order is identified as a construct, it can in principle be differently constructed. For instance, we might be able (128) to discern beneath the shifting patterns of temporality an `inward' dimension of time: an unchanging continuum available `behind' the shifting scenery of the temporal order. ("" -?) , () , , , . , `' : , `' .


However, for any such alternative to make itself available, we would have to activate a different way of knowing: one that does not trace its lineage to the presupposed constructs of the temporal order. , , : , . 129: ... mind establishes a temporal order. Yet mind also depends on the functioning of such an order. Mind has a design `in mind', and the design requires a surface `on' which it can be executed. Linear time is established as this `on'. ... . . ` ' , , `' . `'. 130: When time itself is seen as a part of the conducted, the ways that we conduct the temporal order no longer set absolute limits. ... Is there a knowledge that will make available more directly what remains unformed in the temporal dynamic? ( 13 Conducting Temporal Sameness) , , , . ... ,


, ? Can we trace the secret workings of an appearing not shaped by the claim of being real? () , `'? Exercise 2 Time of Thinking A.Sit comfortably and let thoughts arise in the mind. Instead of depending on the content of the thoughts for knowledge of what is happening, let yourself in the activity of thinking. At this level, there is no need to report back on what is thought or to craft the content of thoughts into new and ongoing stories. Just stay with the thinking of each thought. As you grow accustomed to looking with this attitude, you will find that thoughts calm down. The thinking mind is no longer obligated to construct a reality, and thoughts are no longer structured by the need to arrive at a specified destination. Thought residues seem less solid, their power less strong. B.To deepen the quality evoked in the first part of this exercise, practice seeing without relying on the eyes. In interacting with others, practice understanding what is being said without relying on the words. p.252: Exercise 3=Playfulness of Thoughts A. Settle into the activity of mind, not making any special efforts of changing anything about what is happening. Look for a particular flavor within experience or within your thoughts: old and heavy, fuzzy, or lazy and cloudy. Perhaps there is a time of day when this pattern often comes up for


you; if so, this would be a good time to conduct this practice. 253: Take some time to acknowledge the qualities of this state of mind. Surface indications may include lack of motivation and enthusiasm. See if you can notice how energy drains away even as it arises. Within this dullness, just covered over by it, there may be a painful feeling that goes toward agitation or toward `lostness vastness'. The emotional tone may be one of hopelessness, linked to the sense that energy is being squandered in thought patterns that lead nowhere. A characteristic of this state is that the embodied qualities of experience, together with the spiritual dimension that communicates meaning and value, have completely vanished. With just a little practice, it is fairly easy to tell when thoughts have started to go in this direction There may be a gloominess, but there may also be a rather pleasant, comfortable feeling. A characteristic of this stage is that we play without being playful: play in a way that is incomplete, even grim. We may seek various diversions, for instance, in reading or music. We may taste a sweet sadness. Dull and weak, wrapped in clouds of thought, we pass the time like children given toys to amuse them so that they will not bother the grownups. Time goes by unnoticed, perception is blurry. When we glance at our thoughts, we may not be sure whether we are hearing words or seeing images. There are no clear distinctions, nothing sharp or specific. We are lost in heaviness, and are not even concerned with finding a way out. If you can find a certain balance within this state, there is the opportunity not to play thoughts out or


254: accept their claims or conclusions. Playfully regarded, thoughts come to seem more like random events. The structure they compose, impose, and witness has no substance: It arises as they do. The gravity they generate operates only within their own domain. See if you can lightly shift experience toward this more playful mode. Pay particular attention to thoughts that arise in polar terms of like or dislike, good or bad, and so forth. Such thoughts confirm the truth of the `thought-out' ( ?) order and the underlying `no new knowledge' message that thoughts proclaim. Without making a strong effort, you may find that this relaxed way of investigating lets you break away from the role you play in the stories you conduct. Exploring the heaviness of thinking in this playful way, you can gradually learn to cultivate a quality of inquiry even within dullness. As you grow more skilled in the play of mind, each new thought, sensation, or emotion can be your teacher and guide, opening to a knowledge that is more objective and complete. You may find that the energy that pervades each experience shifts of its own accord. One benefit can be a heightened ability to solve difficulties as they arise. B. Once you are familiar with this way of shifting the energy of thoughts to a lighter way of being, practice releasing the energy of thoughts into knowledge. Playful and relaxed in each situation, practice taking immediate action, responding instantly and without reflection as mental events arise ­ like a fighter countering an opponent's move (: !).


255: The following gestures can encourage this light responsiveness at times when feelings of dullness are strong: Sit with a straight back, the mouth open, breathing lightly through both nose and mouth. Look up sharply and strongly several times with the eyes. Each time you do this, let the eyes return to their usual position in a gentle, relaxed way. Move the head from side to side very slowly and openly, three or nine times. Sitting in a relaxed way, with the back straight, open the chest and bring energy higher in the body. COMMENT 3 As appearance arises, we catch hold of it and make it make sense. We react to what we present (? ­ , `we present' - .. appearance? ­ `we... make it make sense' ­ , `appearance '); then we respond emotionally to our reaction. As we play each condition, each chapter or stage, we play it out; as we identify it, we identify with it. We are caught in a shaping of our own making. Tangled in the emerging story, the conductor cannot conduct it to its fulfillment. Knowledge remains incomplete, for it arises only within the emerging whole. Whatever we do, we can never gain mastery. The heaviness of thoughts that we often experience is linked to this structure. Thoughts bear responsibility for the whole, and must guarantee and witness what arises. The gravity of thinking


is the force that anchors (p.256:) substance and reality; if we were not gravely single-minded in our thinking, things would just `fall apart'. , . , . , ; , `' . To cultivate playfulness of mind is to move from this selfimposed gravity toward light, from the grave to the lighthearted. There is nothing mysterious in this movement; on the conventional level, it comes about simply through relaxing the rigid structures we normally accept as essential. Since this relaxation is itself nourishing, there are immediate practical benefits. , . ; ­ , . , . It can help to lighten thoughts if we reflect quite specifically on the changes that have taken place in our views over time. Right now we maintain that things are a particular way: We hold to certain beliefs, we accept certain values, we honor a particular


range of explanations. But tomorrow things may look different. Last year or twenty years ago our views were very likely not the same... , . , : -, , . , , -. ( 20 ) ( ) , ... ... appreciation for how views change over time can help us let go of the tight positions we hold. When we can see beyond our own immediate views, we have already weakened the gravity of thoughts. Once we can be playful with our thoughts, we can discover within them a fundamental clarity that expresses a knowledge not bound to content ( ! ?). The fullness of this knowledge can sustain and guide us. It becomes (p.257:) natural for thoughts to loosen their grip on reality, for we realize that we do not have to rely on thoughts to structure our responses to experience. In the openness of this emerging freedom, knowledge can conduct itself into being. When it is no longer molded by the unrelenting gravity of thoughts and the distortions of emotionality that thoughts conduct, our commitment to our own highest values may actually intensify. Now, however, our actions will grow out of harmony rather than conflict, fullness rather than limitation,


availability rather than restriction. We could speak of `harmony knowledge' or `rightfulness knowledge', of knowledge based on natural balance. While this approach supports no particular views, it does encourage solutions to our problems. The focus is no longer based on asserting our claim in opposition to someone else's, but on speaking to mutual concerns. We think less in terms of `I' and more in terms of `I and you', of `we' or 'you and they together'. (End of Chapter 25)

(338, 339) :

Like heroes of knowledge, we can enact a self-illuminating model of mastery. Inhabiting the world of unknown knowledgeability, we draw near the livelihood of those who have carried knowledge forward in the past, preserving its presence for the future. This is no trick of the imagination. Dwelling in knowledge, we allow time to reveal a truth beyond possessing, a joy that cannot be lost, a wonder that is always close at hand. , , , . . , , ; , ; , .


If we worry that we are not the ones to go forward, we only undermine the power of knowledge. We may doubt our own strength, but still we can act. Open to knowledge, we can go forward together with others. , " ." , , . , . Perhaps it is not that difficult as we imagine. The light of knowledge is available in each perception, each appearance, each moment. Right now, we can live in the vastness of openness and the presence of perfect knowledge. We can engage a golden time ­ a holy time ­ and enact the treasured embodiment of livelihood. , , . , , () . . "" ­ ­ . If we insist on maintaining conventional views, all this will be just talk: idle speculation and unconfirmed hypotheses, fairy tales for the child who longs for something more than the routine of daily life. But why should we accept such customary judgments? We are all experts in negativity; we all know what does not work. Which of us is familiar with the alternative? Should we let our not-knowing bar the path before we even begin? What would be the point?


, : , , , . , , ? ; , " ." - ? - , ? ? There is no danger in seeking to enact knowledge. We are not being asked to take on someone else's doctrine on faith or give up our own values. The path of knowledge is a path of independence. It is our way we develop; our knowledge we rely on; our awareness we respect. The only teacher we need is here; the light of inquiry and realization is available. What prevents us from setting forth? . - . ­ . ; , ; , . When we cherish the soul and heart and mind ( , 5 ­ forum.roerich.info) ... , we support our greatest treasure as human beings. Alive and intelligent, we have capacities that separate us from rocks and trees, from animals and other forms of life. We can open more widely, encompassing treasures of knowledge. We can allow for


knowledge itself to open vastly, dynamic, and unique. , ­ . , , , . . , ­ , , . The knowledge our inquiry discloses does not belong to someone else. It does not belong to us either, and it may not be accessible as `our' knowledge. Yet we can be partners with knowledge, friends with knowledge, lovers of knowledge. Drawing on our own mind and senses and feelings, we can open the heart of space and enter the depth of time. What starts as an idea discloses its availability at the center of all that is. As the magnitude of the positive is amplified, the wholeness of experience steps into the light. Freely and easily, knowledge walks forward to greet us, inviting our participation with a gentle smile. , , . , `' . , , . , . ; , . , () . , , .


, , , . ( )

D ( ) U(2), . - D , . " " ("conformal infinity") , D f(); f - . F U(1,1), . L ­ () . . [Ja-11a, pp.1,2] (c ), ( [Pe-64]) . , , " ­ ", . [Da-2005], "2- " ( . 23 ,


( 6 [Da-2005]) . ). () : M F, F L, L D. , D F () T, D L T . [Da-2005] A. Daigneault, Irving Segal's Axiomatization of Spacetime and its Cosmological Consequences, arxiv.org/abs/gr-qc/0512059 [Ja-2011a] A. Jadczyk, Geometry and Shape of Minkowski's Space Conformal Infinity, arXiv:1107.0933v1[math-ph] 5 Jul 2011 [Ja-2011b] A. Jadczyk, Conformally Compactified Minkowski Space: Myths and Facts, 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics, K.Gurlebeck (ed.), Weimar, Germany, 1520 July 2011 [Pe-1964] Roger Penrose, The Light Cone at Infinity, in Relativistic Theories of Gravitation, ed. L.Infeld, Pergamon Press, Oxford, 1964, pp. 369-373 1. Levichev A. V., J. Feng. More on the Mathematics of the DLF Theory: Embedding of the Oscillator World L into Segal's Compact Cosmos D. American Journal of Undergraduate Research, Vol.11, NOS 3&4, 29-33 (201213)


2. Akopyan A.A., Levichev A. V. The Sviderskiy formula and a contribution to Segal's chronometry. Mathematical Structures and Modeling (2012), 25: 44-51. 3. .., ... (-) . (2011), 2(49), 41-51. 4. Levichev A. V. Pseudo-Hermitian realization of the Minkowski world through DLF theory. Physica Scripta, vol. 83 (2011), N. 1, pp.1-9

5. Levichev A. V. Algebro-geometric transition from Special Relativity to the DLF theory. IIId "Knowledge-OntologyTheory" Conference Proceedings (2011), 3-5 October, Vol.2, 51-58, Novosibirsk, Sobolev Institute of Mathematics of the Russian Academy of Sciences, 2011. 6. Levichev A. V. Segal's chronometry: emergence of the theory and its application to physics of particles and interactions. In: The Search for Mathematical Laws of the Universe: Physical Ideas, Approaches and Concepts, eds. M.M.Lavrentiev and V.N.Samoilov (Novosibirsk: Academic Publishing House), pp. 69-99, 2010. 7. Akopyan A.A., Levichev A. V. On SO(3,3) as the projective group of the space SO(3), 2013, accepted for publication 8. Levichev A. V., O. Simpson, B. Vadala-Roth. On hyperbolic motion in two homogeneous space-times (2013, submitted to the Mathematical Structures and Modeling)


. , ( ) 2009 2010 . (1967 ­ 2011) ­ . () (Tom Branson, 1953-2006). 9. Levichev A. V., O. S. Sviderskiy. Contractions of certain Lie algebras in the context of the DLF-theory, 16 pages. 10. Levichev A. V., O. S. Sviderskiy. U(p,q) p+q , - : I. p+q = 2, 3 (22 pages).


: [2] .., .., .., . , , 1979. [5] Levichev A.V., Pseudo-Hermitian realization of the Minkowski world through the DLF-theory, Physica Scripta, vol.83 (2011), issue 1, 1-9 [-95] . , . [-84] .., .., , 277(1984), 253-257 [-50] , .. , , 1950, .5, .3, .187. [L-09] A. Levichev, Oscillator Lie algebra and algebras u(2), u(1,1), as a single matrix system in u(2,1). In: "Lie algebras, algebraic groups, and the theory of invariants"/Proceedings of the Summer School-Conference, Samara, Russia, June 8-15 2009, pp.32-34 [Le-11a] = [Le-11] Levichev A.V., Pseudo-Hermitian realization of the Minkowski world through the DLF-theory, Physica Scripta, vol.83 (2011), issue 1, 1-9 [Le-03] Levichev, .V. Three symmetric worlds instead of the Minkowski space-time, Trans.RANS, ser. &C, 7 (2003), n.3-4, 87-93 [LeSv-09] Levichev, .V., O.S.Svidersky) Lie groups U(p,q) of matrices of size p+q as a single system based on linear-fractional transformations: I. General consideration and cases p+q = 2,3. Proceedings of the International Conference "Contemporary problems in Analysis and Geometry", pp.68-69, Sobolev Institute of Mathematics SD RAS, Novosibirsk, Russia, 2009. [-10] A.Levichev, J. Feng) More on the mathematics of the 3-Fold Model: embedding of the oscillator world L into Segal's compact cosmos D. http://grani.agni-age.net/pdf/5013.pdf


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