Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/0610153 · International Journal of Modern Physics A

NEW APPROACH TO N-BODY RELATIVISTIC QUANTUM MECHANICS

YING-QIU GU

Published Apr 30, 2007• 7 citations
arXivHTMLPDF

Abstract

In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schrödinger equation for many-body.

DOI
10.1142/s0217751x07036233

Related papers

New Approach to NNN-body Relativistic Quantum Mechanics

Gu, Y Q

In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schr\\"odinger equation for many-body.

•Oct 13, 2006•21 citations

RELATIVISTIC QUANTUM DYNAMICS OF MANY-BODY SYSTEMS

F. Coester, Wayne Nicholas Polyzou

Relativistic quantum dynamics requires a unitary representation of the Poincare group on the Hilbert space of states. The dynamics of many-body systems must satisfy cluster separability requirements. In this paper we formulate an abstract framework of four dimensional Euclidean Green functions that can be used to construct relativistic quantum dynamics of N-particle systems consistent with these requirements. This approach should be useful in bridging the gap between few-body dynamics based on phenomenological mass operators and on quantum field theory.

arXiv:nucl-th/0102050•Sep 1, 2001•2 citations

RELATIVISTIC HAMILTONIAN SYSTEM OF A PARTICLE AND RELATIVISTIC HEISENBERG'S EQUATION

K.H. Tzou, 浙江大学物理系

In this paper, as suggested by the classical canonical equations, a new set of the corresponding relativistic equations is set up. Therefrom a relativistic form of Heisenberg's equation is deduced. The rclalivistic Hamiltonian system of a particle according to the formulation here established has been fully discussed and by following it, however, Diracs equation appears naturally as a necessary form of relativistic wave equation tor electron in quantum mechanics. The process of taking square root in Dirac's theory is seen to have its classical analogy. Finally, some applications of the relativistic Heisenberg's equation to Dirac's theory have been discussed and it has thereby been pointed out that this equation brings some quantities to being more symmetrical in the relativity sense and also some more general than those the non-relativistic equation can introduce.

Acta Physica Sinica•Jan 1, 1947•1 citation

Classical approximations of relativistic quantum physics

G.E. Johnson

A correspondence of classical to quantum physics studied by Schrö\-dinger and Ehrenfest applies without the necessity of technical conjecture that classical observables are associated with Hermitian Hilbert space operators. This correspondence provides appropriate nonrelativistic classical interpretations to realizations of relativistic quantum physics that are incompatible with the canonical formalism. Using this correspondence, Newtonian mechanics for a $1/r$ potential provides approximations for the dynamics of nonrelativistic classical particle states within unconstrained quantum field theory (UQFT).

arXiv:1604.07654•Apr 25, 2016•1 citation

The Dirac Equation

Kenneth G. Dyall, Knut Fægri

The purpose of this chapter is to introduce the Dirac equation, which will provide us with a basis for developing the relativistic quantum mechanics of electronic systems. Thus far we have reviewed some basic features of the classical relativistic theory, which is the foundation of relativistic quantum theory. As in the nonrelativistic case, quantum mechanical equations may be obtained from the classical relativistic particle equations by use of the correspondence principle, where we replace classical variables by operators. Of particular interest are the substitutions In terms of the momentum four-vector introduced earlier, this yields In going from a classical relativistic description to relativistic quantum mechanics, we require that the equations obtained are invariant under Lorentz transformations. Other basic requirements, such as gauge invariance, must also apply to the equations of relativistic quantum mechanics. We start this chapter by reexamining the quantization of the nonrelativistic Hamiltonian and draw out some features that will be useful in the quantization of the relativistic Hamiltonian. We then turn to the Dirac equation and sketch its derivation. We discuss some properties of the equation and its solutions, and show how going to the nonrelativistic limit reduces it to a Schrödinger-type equation containing spin.

Oxford University Press eBooks•Jul 5, 2007•0 citations

N-electrons Dirac equation in Minkowski space

Ophelliam Loiselet

Quantum mechanics describes multi-electronic system by using non-relativistic probabilistic theories (non-relativistic many-body Hamiltonian, Bethe-Salpeter equation, Breit equation, density functional theory and so on).All of these theories are approximations and provide a probabilistic conception of quantum mechanics, which prevents it to be compatible with general relativity (or "macro scale" physics).Indeed, the real observable world (or Minkowski space) is for us a 3D+time space but quantum mechanics is expressed in multi-dimensional Hilbert space, which is not physical but purely mathematical.In this article we try to make a relativistic equation that gives a correct description of atomic physics in the real three-dimensional space for N ≥ 2 electrons systems: i.e a N-electrons Dirac equation.The starting point is to use the wave mechanics concept of De Broglie and Schrödinger: considering the electron as a mini oscillating cloud or matter-wave.For this we start from the Hartree equation, which gives already a 3D space description of each electron wave function.Then we jump into Hartree-Fock theory, that takes into account the electron exchange and can be also expressed in 3D, thanks to Slater-Condon rules.By extending the concept of exchange potential to a relativistic 4-exchange potential, and doing the same for the electron-electron repulsion potential, we have obtained a relativistic N electrons Dirac equation, in 3D+time space, including new relativistic interactions.The non-relativistic equivalence to Hartree-Fock equations will be demonstrated, which shows that the equation is already correct to describe light atoms.

•Jul 3, 2024•0 citations
In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schrödinger equation for many-body.
Relativistic quantum dynamics requires a unitary representation of the Poincare group on the Hilbert space of states. The dynamics of many-body systems must satisfy cluster separability requirements. In this paper we formulate an abstract framework of four dimensional Euclidean Green functions that can be used to construct relativistic quantum dynamics of N-particle systems consistent with these requirements. This approach should be useful in bridging the gap between few-body dynamics based on phenomenological mass operators and on quantum field theory.
In this paper, as suggested by the classical canonical equations, a new set of the corresponding relativistic equations is set up. Therefrom a relativistic form of Heisenberg's equation is deduced. The rclalivistic Hamiltonian system of a particle according to the formulation here established has been fully discussed and by following it, however, Diracs equation appears naturally as a necessary form of relativistic wave equation tor electron in quantum mechanics. The process of taking square root in Dirac's theory is seen to have its classical analogy. Finally, some applications of the relativistic Heisenberg's equation to Dirac's theory have been discussed and it has thereby been pointed out that this equation brings some quantities to being more symmetrical in the relativity sense and also some more general than those the non-relativistic equation can introduce.
A correspondence of classical to quantum physics studied by Schrö\-dinger and Ehrenfest applies without the necessity of technical conjecture that classical observables are associated with Hermitian Hilbert space operators. This correspondence provides appropriate nonrelativistic classical interpretations to realizations of relativistic quantum physics that are incompatible with the canonical formalism. Using this correspondence, Newtonian mechanics for a 1/r1/r1/r potential provides approximations for the dynamics of nonrelativistic classical particle states within unconstrained quantum field theory (UQFT).
The purpose of this chapter is to introduce the Dirac equation, which will provide us with a basis for developing the relativistic quantum mechanics of electronic systems. Thus far we have reviewed some basic features of the classical relativistic theory, which is the foundation of relativistic quantum theory. As in the nonrelativistic case, quantum mechanical equations may be obtained from the classical relativistic particle equations by use of the correspondence principle, where we replace classical variables by operators. Of particular interest are the substitutions In terms of the momentum four-vector introduced earlier, this yields In going from a classical relativistic description to relativistic quantum mechanics, we require that the equations obtained are invariant under Lorentz transformations. Other basic requirements, such as gauge invariance, must also apply to the equations of relativistic quantum mechanics. We start this chapter by reexamining the quantization of the nonrelativistic Hamiltonian and draw out some features that will be useful in the quantization of the relativistic Hamiltonian. We then turn to the Dirac equation and sketch its derivation. We discuss some properties of the equation and its solutions, and show how going to the nonrelativistic limit reduces it to a Schrödinger-type equation containing spin.
Quantum mechanics describes multi-electronic system by using non-relativistic probabilistic theories (non-relativistic many-body Hamiltonian, Bethe-Salpeter equation, Breit equation, density functional theory and so on).All of these theories are approximations and provide a probabilistic conception of quantum mechanics, which prevents it to be compatible with general relativity (or "macro scale" physics).Indeed, the real observable world (or Minkowski space) is for us a 3D+time space but quantum mechanics is expressed in multi-dimensional Hilbert space, which is not physical but purely mathematical.In this article we try to make a relativistic equation that gives a correct description of atomic physics in the real three-dimensional space for N ≥ 2 electrons systems: i.e a N-electrons Dirac equation.The starting point is to use the wave mechanics concept of De Broglie and Schrödinger: considering the electron as a mini oscillating cloud or matter-wave.For this we start from the Hartree equation, which gives already a 3D space description of each electron wave function.Then we jump into Hartree-Fock theory, that takes into account the electron exchange and can be also expressed in 3D, thanks to Slater-Condon rules.By extending the concept of exchange potential to a relativistic 4-exchange potential, and doing the same for the electron-electron repulsion potential, we have obtained a relativistic N electrons Dirac equation, in 3D+time space, including new relativistic interactions.The non-relativistic equivalence to Hartree-Fock equations will be demonstrated, which shows that the equation is already correct to describe light atoms.