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Cover Stavraki G.L. Model of Space-Time as a Field  Noncommutative Causal  Structure
Id: 86925
13.9 EUR

Model of Space-Time as a Field Noncommutative Causal Structure

URSS. 128 pp. (English). Paperback. ISBN 978-5-396-00012-4.


The book presents a detailed description of the space-time model as a causal virtual-field physical structure. Under certain conditions this model leads to fixation of the symmetry group and field representations and also to the representation of reversible local times in the world of virtual events as chains of local T-reflections.

The book is intended for experts in quantum field theory and elementary particle physics and for all those interested in the problems of submicroworld physics.


Section I

 Quantum virtual nature of geometric extension
Section II

 Lagrangian quantum fields on light-like hyperplanes as approximations to the fields of the model
Section III

 Calculation of the field-bilinear part (I.6) of the fundamental equation of nearness (I.3) in u- and V- Lagrangian formalisms
Section IV

 Necessity of T-symmetry of the closed algebra equation (I.3), its realization in the calculation via identification of the fields of u- and V-formalisms, connection with the space-time curvature and "current-field" duality; explicit formulas of the corresponding approximation
Section V

 Derivation of equations for unimatrix parameters from the closedness condition of algebra (I.3) within the adopted approximation
Section VI

 Calculation of parameters of the unimatrix, the matrices S1, S2 and the eigenvalues of the Casimir operator for field representations in the charge group omega from the closedness condition of algebra (I.3). Fixation thereby of the charge group as group E6 together with the corresponding representations for fields. Necessity of non-Hermiticity of scalar fields in the model. Explicit notation of the field U-matrix, abstracted from the correspondence principle, with calculated parameters and of the exact algebraic equation defining it at two points
Section VII

 Possible approach to the description of space-time in the large as an algebraic causal network and the corresponding continuous approximation
 Appendix I
 Appendix II


The present study is an attempt to formulate the notion of quantum causal nearness of possible local events in the virtual word described by a specially organized complex of physical quantum fields assumed to be primary. The fundamental element of extension, or the space-time "cell", is described in the model by the equation of a commutator algebra closed at two such "nearest" local complexes. The corresponding causal relationship is visually interpreted as a light line closed as a "figure-of-eight" loop. The symmetry of this local construction under -reflection allows representation of a -reversible flow of local time by a discrete chain of local -reflections instead of a continuous time shift. The fundamental causal interval thus constructed is then an indivisible time step of such symmetric time.

The structural charge symmetry group in such a model turns out to be fixed as group with non-standard representations of fermion and scalar fields. It is assumed that fields of geometric type in the model can appear as effective fields-connectednesses owing to the model covariance supergroup localization in the global algebraic space-time network of "linked" chains.

Under certain conditions this argument allows us to interpret the superinvariant expression, quadratic in the found complex of physical fields, as a renormalized approximate Lagrangian averaged over geometric fields and corresponding to sub-Planck energies. The degree of model reality could in principle be verified by calculating the low-energy limit of such a Lagrangian scheme.

The work was concluded thanks to the boundless devotion and tolerance of my wife, I. V. Karpenko. I would like to express sincere gratitude to my friends and colleagues P. Singh, R. N. Faustov, V. O. Galkin, R. F. Polishchuk, and G. A. Vilkovyskii for their permanent support.

I am grateful to M. Tsaplina for the English translation of the book.

G. Stavraki
Moscow, 8 June 2008.

 About the Author


The author is a theoretical physicist, a research worker of the Computation Center of the Russian Academy of Sciences. In 1966, in his talk at the International High-Energy Physics School (Yalta) he suggested the possibility of a joint description of boson and fermion degrees of freedom of quantum fields within the framework of a unified closed algebra and was the first to define the concept of Lie superalgebras (referred to as K-algebras) and to construct an example of a simple Lie superalgebra. In 1990 the "Theoretical and mathematical physics" journal published his first version of the operator-field model of space-time as a virtual causal structure. In 2003, in the note in "Concise encyclopedia of supersymmetry" (Cluwer Academic Publishers, Dordrecht) he suggested the introduction of the concept of quantum causal light-like nearness in space-time and in 2006 realized it (in his work published in "Gravitation and Cosmology") using a special construction within the framework of quantum field theory. The present book offers the extended version of the construction.

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