scholarly journals On the description of subsystems in relativistic hypersurface Bohmian mechanics

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140181 ◽  
Author(s):  
Detlef Dürr ◽  
Matthias Lienert
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Density Matrix ◽  
Relativistic Quantum ◽  
Bohmian Mechanics ◽  
Conditional Density ◽  
Relativistic Quantum Theory ◽  
Relativistic Case ◽  
Usual Quantum ◽  
Effective Wave

A candidate for a realistic relativistic quantum theory is the hypersurface Bohm–Dirac model. Its formulation uses a foliation of space–time into space-like hypersurfaces. In order to apply the theory and to make contact with the usual quantum formalism, one needs a framework for the description of subsystems. The presence of spin together with the foliation renders the subsystem description more complicated than in the non-relativistic case with spin. In this paper, we provide such a framework in terms of an appropriate conditional density matrix and an effective wave function as well as clarify their relation, thereby generalizing previous subsystem descriptions in the non-relativistic case.

The non-relativistic and relativistic quantum theory with temperature

2020 ◽  
Author(s):  
Wu Xiang-Yao ◽  
Ben-Shan Wu ◽  
Han Liu
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Hydrogen Atom ◽  
Energy Level ◽  
Relativistic Quantum ◽  
Temperature Correction ◽  
Quantum Thermodynamics ◽  
Relativistic Quantum Theory ◽  
Energy Principle ◽  
Entropy Principle

Abstract In this paper, we have proposed the principle of quantum thermodynamics, including energy principle and microcosmic entropy principle, and given the quantum thermodynamics of non-relativistic and relativistic quantum theory, i.e., the temperature-dependent schrodinger equation, Dirac equation and photon equation. We given the solution for wave function and energy level with temperature. Taking the hydrogen atom as an example, we given the temperature correction to hydrogen atom energy level and wave function.

scholarly journals A minimalist pilot-wave model for quantum electrodynamics

2007 ◽  
Vol 463 (2088) ◽  
pp. 3115-3129 ◽  
Author(s):  
W Struyve ◽  
H Westman
Keyword(s):  
Wave Function ◽  
Electromagnetic Field ◽  
Quantum Theory ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Wave Model ◽  
Relativistic Quantum Theory ◽  
Pilot Wave ◽  
Free Electromagnetic Field

We present a way to construct a pilot-wave model for quantum electrodynamics. The idea is to introduce beables corresponding only to the bosonic and not to the fermionic degrees of freedom of the quantum state. We show that this is sufficient to reproduce the quantum predictions. The beables will be field beables corresponding to the electromagnetic field and will be introduced in a way similar to that of Bohm's model for the free electromagnetic field. Our approach is analogous to the situation in non-relativistic quantum theory, where Bell treated spin not as a beable but only as a property of the wave function. After presenting this model, we also discuss a simple way for introducing additional beables that represent the fermionic degrees of freedom.

scholarly journals Semi-classical approximations based on Bohmian mechanics

2020 ◽  
Vol 35 (14) ◽  
pp. 2050070 ◽  
Author(s):  
Ward Struyve
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Expectation Values ◽  
Usual Approach ◽  
Classical Approximation

Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which evolves according to some Schrödinger equation with a Hamiltonian that depends on the classical degrees of freedom. The classical degrees of freedom satisfy classical equations that depend on the expectation values of quantum operators. In this paper, we study an alternative approach based on Bohmian mechanics. In Bohmian mechanics the quantum system is not only described by the wave function, but also with additional variables such as particle positions or fields. By letting the classical equations of motion depend on these variables, rather than the quantum expectation values, a semi-classical approximation is obtained that is closer to the exact quantum results than the usual approach. We discuss the Bohmian semi-classical approximation in various contexts, such as nonrelativistic quantum mechanics, quantum electrodynamics and quantum gravity. The main motivation comes from quantum gravity. The quest for a quantum theory for gravity is still going on. Therefore a semi-classical approach where gravity is treated classically may be an approximation that already captures some quantum gravitational aspects. The Bohmian semi-classical theories will be derived from the full Bohmian theories. In the case there are gauge symmetries, like in quantum electrodynamics or quantum gravity, special care is required. In order to derive a consistent semi-classical theory it will be necessary to isolate gauge-independent dependent degrees of freedom from gauge degrees of freedom and consider the approximation where some of the former are considered classical.

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