G. L. Stavraki

128 páginas

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.