Growth of Sobolev norms for the Maxwell–Dirac and Dirac–Klein–Gordon systems in R 1 + 1

2021 ◽  
pp. 1-9
Author(s):  
Hyungjin Huh
Keyword(s):  
Energy Conservation ◽  
Local Energy ◽  
Dirac Equations ◽  
Sobolev Norms ◽  
Similar Idea ◽  
Klein Gordon

We obtain the growth of Sobolev norms of the solution to the Maxwell–Dirac equations in R 1 + 1 by applying elementary techniques. In particular, we estimate L ∞ bound of the solution by making use of a local energy conservation. The similar idea can be applied to the Dirac–Klein–Gordon equations.

scholarly journals QUANTUM SINGULARITIES IN STATIC SPACETIMES

2011 ◽  
Vol 20 (05) ◽  
pp. 729-743 ◽  
Author(s):  
JOÃO PAULO M. PITELLI ◽  
PATRICIO S. LETELIER
Keyword(s):  
Quantum Mechanics ◽  
Wave Operator ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Mathematical Framework ◽  
Physical Content ◽  
Dirac Equations ◽  
Quantum Particles ◽  
Klein Gordon ◽  
Quantum Singularities

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein–Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator to be self-adjoint and emphasize their importance to the interpretation of quantum singularities.

scholarly journals Local energy conservation law for a spatially-discretized Hamiltonian Vlasov-Maxwell system

2017 ◽  
Vol 24 (6) ◽  
pp. 062112 ◽  
Author(s):  
Jianyuan Xiao ◽  
Hong Qin ◽  
Jian Liu ◽  
Ruili Zhang
Keyword(s):  
Energy Conservation ◽  
Conservation Law ◽  
Local Energy ◽  
Maxwell System ◽  
Energy Conservation Law

Relativistic quantum bouncing particles in a homogeneous gravitational field

2021 ◽  
pp. 2150098
Author(s):  
Ar Rohim ◽  
Kazushige Ueda ◽  
Kazuhiro Yamamoto ◽  
Shih-Yuin Lin
Keyword(s):  
Gravitational Field ◽  
Relativistic Effect ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Dirac Equations ◽  
Rindler Coordinates ◽  
Klein Gordon ◽  
Homogeneous Gravitational Field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

scholarly journals Hawking radiation from cubic and quartic black holes via tunneling of GUP corrected scalar and fermion particles

2019 ◽  
Vol 34 (09) ◽  
pp. 1950057 ◽  
Author(s):  
Wajiha Javed ◽  
Rimsha Babar ◽  
Ali Övgün
Keyword(s):  
Black Holes ◽  
Hawking Radiation ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
Jacobi Method ◽  
Dirac Equations ◽  
Tensor Theory ◽  
Klein Gordon ◽  
The Given ◽  
Do So

We analyze the effect of the generalized uncertainty principle (GUP) on the Hawking radiation from the hairy black hole in U(1) gauge-invariant scalar–vector–tensor theory by utilizing the semiclassical Hamilton–Jacobi method. To do so, we evaluate the tunneling probabilities and Hawking temperature for scalar and fermion particles for the given spacetime of the black holes with cubic and quartic interactions. For this purpose, we utilize the modified Klein–Gordon equation for the Boson particles and then Dirac equations for the fermion particles, respectively. Next, we examine that the Hawking temperature of the black holes do not depend on the properties of tunneling particles. Moreover, we present the corrected Hawking temperature of scalar and fermion particles which look similar in both interactions, but there are different mass and momentum relationships for scalar and fermion particles in cubic and quartic interactions.

scholarly journals Relativistic particle in a box: Klein–Gordon versus Dirac equations

2018 ◽  
Vol 39 (2) ◽  
pp. 025401 ◽  
Author(s):  
Pedro Alberto ◽  
Saurya Das ◽  
Elias C Vagenas
Keyword(s):  
Relativistic Particle ◽  
Dirac Equations ◽  
Klein Gordon
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