The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube II.Simple Cases of Symmetry Breakdown and Restoration

TL;DR

This paper explores how deforming a nonuniform lattice in a finite hypercube can induce and control symmetry breaking and restoration in simple quantum field theories, revealing new phenomena and constraints.

Contribution

It demonstrates that lattice deformation parameters can facilitate symmetry phenomena and provide physical constraints, extending understanding of quantum field theories on discrete structures.

Findings

Deformation enables symmetry breakdown and restoration at different energy scales.

The approach reproduces known results at low energies with high accuracy.

Identifies critical points associated with symmetry restoration in the lattice.

Abstract

This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and restoration of symmetry in simple quantum-field theories with scalar fields. It is demonstrated that an appropriate deformation opens up new possibilities for symmetry breakdown and restoration. To illustrate, at low energies it offers high-accuracy reproducibility of the same results as with a nondeformed theory. In case of transition from low to higher energies and vice versa it gives description for new types of symmetry breakdown and restoration depending on the rate of the deformation parameter variation in time, and indicates the critical points of the previously described lattice associated with a symmetry restoration. Besides, such a deformation enables one to find important constraints on the initial model parameters having an explicit physical meaning.