Quantization of Electromagnetic Field and Potential in Rindler Space-Time

The article treats quantization of electromagnetic field that is defined in Rindler space-time. Likely the electromagnetic field, the potential did quantizated in inertial frame, the electromagnetic field, the potential can quantizate by the transformation of electromagnetic field or the transformation of the potential in the accelerated frame. We treat Lorentz gauge condition in quantization of electromagnetic potential.

Motion of Charged Spinning Particles in a Unified Field

Using a geometry wider than Riemannian one, the parameterized absolute parallelism (PAP) geometry, we derived a new curve containing two parameters. In the context of the geometrization philosophy, this new curve can be used as a trajectory of charged spinning test particle in any unified field theory constructed in the PAP space. We show that imposing certain conditions on the two parameters, the new curve can be reduced to a geodesic curve giving the motion of a scalar test particle or/and a modified geodesic giving the motion of neutral spinning test particle in a gravitational field. The new method used for derivation, the Bazanski method, shows a new feature in the new curve equation. This feature is that the equation contains the electromagnetic potential term together with the Lorentz term. We show the importance of this feature in physical applications.

Effects of Linear Central Potential Induced by Lorentz Symmetry Violation framework and Cornell-type Non-electromagnetic Potential on Spin-0 Scalar Particles

The relativistic quantum dynamics of a spin-0 scalar particle under the effects of the violation of Lorentz symmetry in the presence of a non-electromagnetic potential is analyzed. The central potential induced by the Lorentz symmetry violation is a linear electric and constant magnetic field and, analyze the effects on the eigenvalues and the wave function. We see there is a dependence of the linear charge density on the quantum numbers of the system

Linear Central Potential Effects Induced by Lorentz Symmetry Violation on Spin-0 Particle Under Coulomb-type scalar Potential

In this work, quantum dynamics of a spin-0 particle under the effects of Lorentz symmetry violation in the presence of Coulombtype non-electromagnetic potential $(S(r) ∝ \frac{1}{r})$ is investigated. The non-electromagnetic (or scalar) potential is introduced by modifying the mass term via transformation $M → M + \frac{η_c}{r}$ in the relativistic wave equation. The linear central potential induced by the Lorentz symmetry violation is a linear radial electric and constant magnetic field and, analyze the effects on the spectrum of energy and the wave function

Hölder estimates for magnetic Schrödinger semigroups in $${\mathbb {R}}^{d}$$ from mirror coupling

We use the mirror coupling of Brownian motion to show that under a $$\beta \in (0,1)$$ β ∈ ( 0 , 1 ) -dependent Kato-type assumption on the possibly nonsmooth electromagnetic potential, the corresponding magnetic Schrödinger semigroup in $${\mathbb {R}}^d$$ R d has a global $$L^{p}$$ L p -to-$$C^{0,\beta }$$ C 0 , β Hölder smoothing property for all $$p\in [1,\infty ]$$ p ∈ [ 1 , ∞ ] ; in particular, his all eigenfunctions are uniformly $$\beta $$ β -Hölder continuous. This result shows that the eigenfunctions of the Hamilton operator of a molecule in a magnetic field are uniformly $$\beta $$ β -Hölder continuous under weak $$L^q$$ L q -assumptions on the magnetic potential.

On the Equivalence Principle and Relativistic Quantum Mechanics

Einstein’s Equivalence Principle implies that the Lorentz force equation can be derived from a geodesic equation by imposing a certain (necessary) condition on the electromagnetic potential (Trzetrzelewski, EPL 120:4, 2018). We analyze the quantization of that constraint and find the corresponding differential equations for the phase of the wave function. We investigate these equations in the case of Coulomb potential and show that physically acceptable solutions do not exist. This result signals an inconsistency between Einstein’s Equivalence Principle and Relativistic Quantum Mechanics at an atomic level.

The Smoothness of Schrodinger Operator with Electromagnetic Potential

In this paper, we prove that the Feynman-Kac It^o formula of the Schrodinger operator with electromagnetic (t; x) in equation (1) in [8] is dierentiable of the variable t, and so establish that the innitely dierentiable in a region, therefore, investigate smoothness of this function.

On the Feynman path integral for the magnetic Schrödinger equation with a polynomially growing electromagnetic potential

The Feynman path integrals for the magnetic Schrödinger equations are defined mathematically, in particular, with polynomially growing potentials in the spatial direction. For example, we can handle electromagnetic potentials [Formula: see text] such that [Formula: see text] “a polynomial of degree [Formula: see text] in [Formula: see text]” [Formula: see text] and [Formula: see text] are polynomials of degree [Formula: see text] in [Formula: see text]. The Feynman path integrals are defined as [Formula: see text]-valued continuous functions with respect to the time variable.