Relativistic free fermions in spiral dislocation space–time with a distortion of a radial line into a spiral

2021 ◽  
Author(s):  
S. Zare ◽  
H. Hassanabadi ◽  
G. Junker
Keyword(s):  
Relativistic Quantum ◽  
Geometric Approach ◽  
Bound State ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Coupling Constant ◽  
Radial Line ◽  
Defect Parameter ◽  
Free Fermions ◽  
Closed Form Solutions

Relativistic quantum mechanics of free fermions in the presence of the spiral dislocation of space–time with a distortion of a radial line into a spiral is studied within the Katanaev–Volovich geometric approach. The generalized Dirac equation in this background is constructed. Exact closed-form solutions are found by reducing the problem to that of a nonrelativistic two-dimensional [Formula: see text]-problem with a complex coupling constant. The influence of the defect parameter related to the spiral dislocation on these solutions is investigated. We also study the charge density of free fermions in the presence of such a spiral dislocation in space–time. Based on the Bender–Boettcher approach for non-Hermitian Hamiltonians we study, in addition, bound-state solutions of the system.

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

scholarly journals LORENTZ BOOSTED NN POTENTIAL FOR FEW-BODY SYSTEMS: APPLICATION TO THE THREE-NUCLEON BOUND STATE

2003 ◽  
Vol 18 (02n06) ◽  
pp. 124-127 ◽  
Author(s):  
H. KAMADA ◽  
W. GLÖCKLE ◽  
J. GOLAK ◽  
CH. ELSTER
Keyword(s):  
Quantum Mechanics ◽  
Binding Energy ◽  
Schrodinger Equation ◽  
Relativistic Quantum ◽  
Bound State ◽  
Nucleon Nucleon ◽  
Relativistic Quantum Mechanics ◽  
Equal Time ◽  
Momentum Change ◽  
Approximate Scheme

In the context of equal time relativistic quantum mechanics we introduce a Lorentz boosted potential. The dynamical input are nonrelativistic realistic nucleon-nucleon (NN) potentials, which by a suitable momentum change are analytically transformed into NN potentials fulfilling the relativistic two-nucleon Schrödinger equation in the c.m. system. The binding energy of the three nucleon (3N) bound state is calculated and we find that the boost effects for the two-body subsystems are repulsive and lower the binding energy. In addition we compare to a recently proposed approximate scheme.

THE MASSLESS BOUND STATE FORMALISM IN TWO-PARTICLE RELATIVISTIC QUANTUM MECHANICS

1988 ◽  
Vol 03 (05) ◽  
pp. 1235-1261 ◽  
Author(s):  
H. SAZDJIAN
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Bound State ◽  
Relativistic Quantum Mechanics ◽  
Composite Systems ◽  
Bound State Case ◽  
State Case

We develop, in the framework of two-particle relativistic quantum mechanics, the formalism needed to describe massless bound state systems and their internal dynamics. It turns out that the dynamics here is two-dimensional, besides the contribution of the spin degrees of freedom, provided by the two space-like transverse components of the relative coordinate four-vector, decomposed in an appropriate light cone basis. This is in contrast with the massive bound state case, where the dynamics is three-dimensional. We also construct the scalar product of the theory. We apply this formalism to several types of composite systems, involving spin-0 bosons and/or spin-1/2 fermions, which produce massless bound states.

scholarly journals Non-inertial frames in Minkowski space-time, accelerated either mathematical or dynamical observers and comments on non-inertial relativistic quantum mechanics

2014 ◽  
Vol 11 (10) ◽  
pp. 1450086 ◽  
Author(s):  
Horace W. Crater ◽  
Luca Lusanna
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Minkowski Space Time ◽  
Accelerated Observers ◽  
Inertial Frames ◽  
Locality Principle

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and how to define Unruh–DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.

What Entanglement Might Be Telling Us: Space, Quantum Mechanics, and Bohm’s Fish Tank

2020 ◽  
pp. 139-153
Author(s):  
Jenann Ismael
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
The Difference ◽  
Emergent Structure ◽  
Pass Through ◽  
Quantum Phenomena ◽  
Fish Tank ◽  
Low Dimensional

There are pressures that are coming from a number of quarters in quantum cosmology to view space or space-time as an emergent structure. But in recent years in the foundations of standard, non-relativistic quantum mechanics, interpretations have emerged that treat space as emergent. My primary purpose is (i) to make explicit the considerations stemming from quantum mechanics alone, that are pushing in the direction of viewing space (or space-time) as an emergent structure, and (ii)to clarify exactly what it means to say that space is emergent in the sense that this chapter is interested inhere. Itdoes that by presenting some simple low-dimensional models that reproduce central features of quantum phenomena, and analyzing the examples with attention to the difference between two different kinds of explanation: one in which the correlations emerge from a more fundamental (and not ultimately spatial) description and one in which correlations are explained by influences that pass through the space in which the correlated events are situated.

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