scholarly journals Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

2017 ◽  
Vol 2017 ◽  
pp. 1-49 ◽  
Author(s):  
Alexei A. Deriglazov ◽  
Walberto Guzmán Ramírez
Keyword(s):  
General Relativity ◽  
Relativistic Quantum ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Theoretical Description ◽  
Vector Model ◽  
Relativistic Quantum Mechanics ◽  
Spinning Particle ◽  
Rotating Body ◽  
Relativistic Spin

We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D) paradoxical behavior of the Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.

scholarly journals Ultrarelativistic Spinning Particle and a Rotating Body in External Fields

2016 ◽  
Vol 2016 ◽  
pp. 1-27 ◽  
Author(s):  
Alexei A. Deriglazov ◽  
Walberto Guzmán Ramírez
Keyword(s):  
Electromagnetic Field ◽  
Three Dimensional ◽  
Vector Model ◽  
Maximum Speed ◽  
Field Interaction ◽  
Spinning Particle ◽  
Spin Field ◽  
Field Coupling ◽  
Rotating Body ◽  
Ultrarelativistic Limit

We use the vector model of spinning particle to analyze the influence of spin-field coupling on the particle’s trajectory in ultrarelativistic regime. The Lagrangian with minimal spin-gravity interaction yields the equations equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations of a rotating body. We show that they have unsatisfactory behavior in the ultrarelativistic limit. In particular, three-dimensional acceleration of the particle becomes infinite in the limit. Therefore, we examine the nonminimal interaction through the gravimagnetic momentκand show that the theory withκ=1is free of the problems detected in MPTD equations. Hence, the nonminimally interacting theory seems a more promising candidate for description of a relativistic rotating body in general relativity. Vector model in an arbitrary electromagnetic field leads to generalized Frenkel and BMT equations. If we use the usual special-relativity notions for time and distance, the maximum speed of the particle with anomalous magnetic moment in an electromagnetic field is different from the speed of light. This can be corrected assuming that the three-dimensional geometry should be defined with respect to an effective metric induced by spin-field interaction.

Massive particles, Kerr–Minkowski fields and singularity removal in relativistic quantum mechanics

2007 ◽  
Vol 463 (2083) ◽  
pp. 1815-1826
Author(s):  
Brian Bramson
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Radial Distance ◽  
Unitary Representations ◽  
Relativistic Quantum Mechanics ◽  
Twistor Theory ◽  
Kerr Field ◽  
Singularity Removal ◽  
Bounded Below

This paper concerns the spacetime locations of massive spinning particles in relativistic quantum mechanics. Using techniques from twistor theory and the unitary representations of the Lorentz group, it is shown that, for a particle of mass m and spin j , the radial distance from the particle to the observer is bounded below by . If the particle is the source of a Kerr–Minkowski field, the analogue of a Kerr field in general relativity, it is further shown that quantization removes the ring singularity if j is Fermionic or zero.

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 de Broglie clock, electron channeling, and time in quantum mechanics

2019 ◽  
Vol 97 (1) ◽  
pp. 37-41 ◽  
Author(s):  
M. Bauer
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Resonance Energy ◽  
Intrinsic Property ◽  
Theoretical Description ◽  
Time Operator ◽  
Relativistic Quantum Mechanics ◽  
Electron Channeling ◽  
Quantum Mechanical Description ◽  
Dynamical Time

De Broglie’s association of a wave to particles is a fundamental concept in the quantum mechanical description of nature. The wave oscillation is referred to alternatively as the “de Broglie clock”, the “Compton clock”, or the “de Broglie periodic phenomenon”. In the present paper it is shown that Dirac’s relativistic quantum mechanics, complemented with the dynamical time operator recently introduced, provides a consistent theoretical description of: (i) the generation of the de Broglie wave through Lorentz boosts; and (ii) the characteristics of the resonance observed in electron channeling through thin crystals as responding to both the periodicity derived from the adjustment of the de Broglie period to the crystal interatomic distance (resonance energy) and the periodicity of the predicted trembling motion (Zitterbewegung). One can conclude that the channeling experiments provide the first direct evidence of the electron Zitterbewegung, and that the de Broglie period is an intrinsic property of matter arising from a self-adjoint dynamical time operator.

Exact solution of the relativistic finite-difference equation for the Coulomb plus a ring-shaped-like potential

2019 ◽  
Vol 34 (17) ◽  
pp. 1950089 ◽  
Author(s):  
Sh. M. Nagiyev ◽  
A. I. Ahmadov
Keyword(s):  
Energy Spectrum ◽  
Finite Difference ◽  
Jacobi Polynomials ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Dynamical Symmetry ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Radial Part ◽  
Radial Wave

In this paper, a three-dimensional problem of the motion of a charged relativistic particle in a noncentral Coulomb plus ring-shaped potential is studied. Our investigation is based on a finite-difference version of relativistic quantum mechanics. The energy eigenvalues and the corresponding wave functions are obtained analytically. It is shown that radial part and the angular part of the wave functions are expressed through the Meixner–Pollaczek polynomials and Jacobi polynomials, respectively. All relativistic expressions, for example, radial wave functions and energy spectrum, have the correct nonrelativistic limit. We also build a dynamical symmetry group for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

scholarly journals SUPERSYMMETRIC RELATIVISTIC QUANTUM MECHANICS

2006 ◽  
Vol 21 (06) ◽  
pp. 1333-1340 ◽  
Author(s):  
YOSHINOBU HABARA ◽  
HOLGER B. NIELSEN ◽  
MASAO NINOMIYA
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Equations Of Motion ◽  
Relativistic Quantum Mechanics ◽  
Chiral Multiplet ◽  
Second Quantization ◽  
Matrix Formulation ◽  
The Matrix ◽  
Particle Level ◽  
Dirac Sea

We present an attempt to formulate the supersymmetric and relativistic quantum mechanics in the sense of realizing supersymmetry on the single particle level, by utilizing the equations of motion which is equivalent to the ordinary second quantization of the chiral multiplet. The matrix formulation is used to express the operators such as supersymmetry generators and fields of the chiral multiplets. We realize supersymmetry prior to filling the Dirac sea.

scholarly journals Derivation of the Local Lorentz Gauge Transformation of a Dirac Spinor Field in Quantum Einstein-Cartan Theory

2019 ◽  
Author(s):  
Rainer Kühne
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Relativistic Quantum Mechanics ◽  
Dirac Spinor ◽  
Dirac Algebra ◽  
Gauge Transformations ◽  
Cartan Theory

I examine the groups which underly classical mechanics, non-relativistic quantum mechanics, special relativity, relativistic quantum mechanics, quantum electrodynamics, quantum flavourdynamics, quantum chromodynamics, and general relativity. This examination includes the rotations SO(2) and SO(3), the Pauli algebra, the Lorentz transformations, the Dirac algebra, and the U(1), SU(2), and SU(3) gauge transformations. I argue that general relativity must be generalized to Einstein-Cartan theory, so that Dirac spinors can be described within the framework of gravitation theory.

Dirac Systems with Discrete Spectra

1987 ◽  
Vol 39 (1) ◽  
pp. 100-122 ◽  
Author(s):  
D. B. Hinton ◽  
J. K. Shaw
Keyword(s):  
Separation Of Variables ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Relativistic Quantum Mechanics ◽  
Radial Wave ◽  
One Dimensional ◽  
The One ◽  
Image Position ◽  
Discrete Spectra ◽  
Radial Wave Equation

In this paper we consider the one dimensional Dirac system1.1where αk(x) < 0, λ is a complex spectral parameter, and the remaining coefficients are suitably smooth and real valued. We regard (1.1) as regular at x = a but singular at x = b; in Section 4 we extend our result to problems having two singular endpoints.Equation (1.1) arises from the three dimensional Dirac equation with spherically symmetric potential, following a separation of variables. For the choices p(x) = k/x, αk(x) = 1,p2(x) = (z/x) + c, p1(x) = (z/x) – c, and appropriate values of the constants, (1.1) is the radial wave equation in relativistic quantum mechanics for a particle in a field of potential V = z/x [17]. Such an equation was studied by Kalf [11] in the context of limit point-limit circle criteria, which is one of the matters we consider here.

New Exact Solution of the Bound States for the Potential Family V(r)=A/r2-B/r+Crk (k=0,-1,-2) in both Noncommutative Three Dimensional Spaces and Phases: Non Relativistic Quantum Mechanics

2015 ◽  
Vol 58 ◽  
pp. 164-176 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Zeeman Effect ◽  
Three Dimensional ◽  
Energy Spectra ◽  
Relativistic Quantum Mechanics ◽  
Quantum Numbers ◽  
New States ◽  
Ordinary Quantum

In present work we obtain the modified bound-states solutions for central family V(r)=A/r2-B/r+Crk (k=0,-1,-2) in both noncommutative three dimensional spaces and phases. It has been observed that the energy spectra in ordinary quantum mechanics was changed, and replaced degenerate new states, depending on two infinitesimals parameters Θ and θ corresponding the noncommutativity of space and phase, in addition to the discrete atomic quantum numbers: j, l, sz=+-1/2 and corresponding to the two spins states of electron by (up and down) and non polarized electron. The deformed anisotropic Hamiltonian formed by three operators: the first describes usual the usual family potential, the second describe spin-orbit interaction while the last one describes the modified Zeeman effect (containing ordinary Zeeman effect).

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