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Bulletin of the Russian Academy of Sciences Physics

Field-Theoretical Form of the Molecular Dynamics Method in Condensed Matter Physics

Anatoly Yu. Zakharov

Published Aug 1, 2026• 0 citations
Publisher

Abstract

Abstract We presented a relativistic quantum generalization of the nonrelativistic classical Hamiltonian dynamics of a system of interacting atoms. The interaction between atoms is considered within the concept of a covariant auxiliary field. It is established that the auxiliary field is a superposition of elementary fields of the Klein–Gordon type. The field contribution to the thermodynamics of a system of interacting atoms is investigated.

DOI
10.1134/s1062873826701273

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Abstract We presented a relativistic quantum generalization of the nonrelativistic classical Hamiltonian dynamics of a system of interacting atoms. The interaction between atoms is considered within the concept of a covariant auxiliary field. It is established that the auxiliary field is a superposition of elementary fields of the Klein–Gordon type. The field contribution to the thermodynamics of a system of interacting atoms is investigated.
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general form only in the non-relativistic approximation. It is shown that the auxiliary field is a superposition of Klein-Gordon fields, the parameters of which are related to singular points of the Fourier transform of the corresponding interatomic potential. The general form of the relativistic Hamiltonian system of interacting atoms is established. It is shown that the exact calculation of the relativistic partition function of a system of interacting atoms, taking into account the field degrees of freedom, reduces to renormalizing the parameters of the auxiliary field. It is established that the field degrees of freedom lead to a divergence in the total energy of a classical relativistic system - an analogue of the ultraviolet catastrophe. Quantization of the auxiliary field eliminates this divergence. The existence of a phase transition within the framework of relativistic quantum statistical thermodynamics has been proven.
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a generalized Hamiltonian dynamics and to a covariant Schrödinger type equation is shown. Examples for relativistic potential problems are solved. Mathematically and physically acceptable probability densities for the Klein-Gordon equation and for the Dirac equation are derived, and a new continuity equation for each case is given. The quantum distribution for mass is discussed, and unambiguous representations of four-velocity and four-acceleration operators are given.
The Hamilton-Jacobi method is generalized, both, in classical and relativistic mechanics. The implications in quantum mechanics are considered in the case of Klein-Gordon equation. We find that the wave functions of Klein-Gordon theory can be considered as describing the motion of an ensemble of particles that move under the action of the electromagnetic field alone, without quantum potentials, hidden uninterpreted variables, or zero point fields. The number of particles is not locally conserved.