scholarly journals QUANTIZATION OF A PSEUDOCLASSICAL MODEL OF THE SPIN 1 RELATIVISTIC PARTICLE

1995 ◽  
Vol 10 (05) ◽  
pp. 701-718 ◽  
Author(s):  
D. M. GITMAN ◽  
A. E. GONÇALVES ◽  
I. V. TYUTIN
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Particle ◽  
Canonical Quantization ◽  
Maxwell Theory ◽  
Massless Case

A consistent procedure for canonical quantization of a pseudoclassical model of the spin 1 relativistic particle is considered. Two approaches to treating quantization for the massless case are discussed — the limit of the massive case and independent quantization of a modified action. The quantum mechanics constructed for the massive case proves to be equivalent to the Proca theory; and for massless case, to the Maxwell theory. Results obtained are compared with ones for the case of the spinning (spin 1/2) particle.

SUSY coherent states and enhanced canonical quantizations for Pauli model

2021 ◽  
pp. 2150105
Author(s):  
Jean Vignon Hounguevou ◽  
Daniel Sabi Takou ◽  
Gabriel Y. H. Avossevou
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coherent States ◽  
Differential Operators ◽  
Canonical Quantization ◽  
Point Of View ◽  
Supersymmetric Quantum Mechanics ◽  
Geometric Properties

In this paper, we study coherent states for a quantum Pauli model through supersymmetric quantum mechanics (SUSYQM) method. From the point of view of canonical quantization, the construction of these coherent states is based on the very important differential operators in SUSYQM call factorization operators. The connection between classical and quantum theory is given by using the geometric properties of these states.

QUANTUM SUPERSPACE, q-EXTENDED SUPERSYMMETRY AND PARASUPERSYMMETRIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (28) ◽  
pp. 2657-2670 ◽  
Author(s):  
K. N. ILINSKI ◽  
V. M. UZDIN
Keyword(s):  
Quantum Mechanics ◽  
Extended Supersymmetry ◽  
Harmonic Oscillator ◽  
Unit Circle ◽  
Canonical Quantization ◽  
Matrix Representations ◽  
Dimensional Matrix ◽  
Continuous Parameter ◽  
Superspace Formalism

We describe q-deformation of the extended supersymmetry and construct q-extended supersymmetric Hamiltonian. For this purpose we formulate q-superspace formalism and construct q-supertransformation group. On this basis q-extended supersymmetric Lagrangian is built. The canonical quantization of this system is considered. The connection with multi-dimensional matrix representations of the parasupersymmetric quantum mechanics is discussed and q-extended supersymmetric harmonic oscillator is considered as a simplest example of the described constructions. We show that extended supersymmetric Hamiltonians obey not only extended SUSY but also the whole family of symmetries (q-extended supersymmetry) which is parametrized by continuous parameter q on the unit circle.

scholarly journals Quantum backflow in solutions to the Dirac equation of the spin-1 2 free particle

2018 ◽  
Vol 33 (32) ◽  
pp. 1850186 ◽  
Author(s):  
Hong-Yi Su ◽  
Jing-Ling Chen
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Negative Energy ◽  
Dirac Particle ◽  
Relativistic Quantum Mechanics ◽  
Probability Current ◽  
Negative Probability

It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.

Conditional interpretation of time in quantum gravity and a time operator in relativistic quantum mechanics

2020 ◽  
Vol 35 (21) ◽  
pp. 2050114
Author(s):  
M. Bauer ◽  
C. A. Aguillón ◽  
G. E. García
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Relativistic Quantum ◽  
Canonical Quantization ◽  
Time Operator ◽  
Relativistic Quantum Mechanics ◽  
Problem Of Time ◽  
Quantization Of Gravity ◽  
Dynamical Time ◽  
Spatial Coordinates

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.

scholarly journals INDEX THEOREMS ON TORSIONAL GEOMETRIES

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2260-2261
Author(s):  
TETSUJI KIMURA
Keyword(s):  
Quantum Mechanics ◽  
Canonical Quantization ◽  
Quantization Condition ◽  
Euler Characteristics ◽  
Flux Compactification ◽  
Index Theorems ◽  
Fundamental Information ◽  
Canonical Quantization Condition ◽  
Background Fields ◽  
Effective Theories

We investigate the Atiyah-Singer index theorems with torsion given by Neveu-Schwarz three-form flux H under the condition d H = 0 in flux compactification scenarios with non-trivial background fields in string theories. Using an identification between the Clifford algebra on the geometry and the canonical quantization condition in [Formula: see text] quantum mechanics, we explicitly reformulate the Dirac index on manifolds with torsion, which will provides a fundamental information to effective theories derived from string theory. In the same analogy we also reformulate the Euler characteristics and the Hirzebruch signatures in the framework of [Formula: see text] quantum mechanics.

scholarly journals Devepment of the Incompatibility between Einstein's General Relativity and Heisenberg's Uncertainty Principle

2018 ◽  
Author(s):  
Alexandre GEORGES
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Scientific Community ◽  
Relativistic Particle ◽  
Mathematical Proof ◽  
Werner Heisenberg ◽  
Time Dilatation ◽  
Heisenberg's Uncertainty Principle ◽  
Einstein’S General Relativity

Are General Relativity and Quantum Mechanics incompatible? Each in their world, that of the infinitely large and that of the infinitely small, they did not seem to interfere as long as they avoided each other. However, it is their fundamental oppositions that prevent the scientific community from achieving a unification of physics. The proposal of this paper is to provide a mathematical proof of incompatibility, beyond the fact that they have fundamentally different principles, between the foundations of General Relativity and Quantum Mechanics, namely the deformation of the space-time geometry and the Uncertainty Principle. It will thus be possible to provide an absolute limitation in establishing a unifying theory of physics, if any. Moreover, while respecting the conditions fixed by the Uncertainty Principle, it will be tempted to determine with accuracy and simultaneity, the position and the speed of a non-relativistic particle, by application of relativistic principles and bypassing the problems raised by such an operation. The Uncertainty Principle as stated by Werner Heisenberg will be then, in the light of observations made on the measurement of the time dilatation and in accordance with its own terms, refuted by the present. - Physics Essays, Volume 31, Issue 3 (September 2018), Article 12 - https://physicsessays.org/browse-journal-2/product/1667-12-alexandre-georges-incompatibility-between-einstein-s-general-relativity-and-heisenberg-s-uncertainty-principle.html

scholarly journals p-ADIC AND ADELIC FREE RELATIVISTIC PARTICLE

1999 ◽  
Vol 14 (05) ◽  
pp. 317-325 ◽  
Author(s):  
G. S. DJORDJEVIĆ ◽  
L. J. NEŠIĆ ◽  
B. DRAGOVICH
Keyword(s):  
Quantum Mechanics ◽  
Spectral Problem ◽  
Relativistic Particle ◽  
Planck Scale ◽  
Space Time ◽  
Quantum States ◽  
Discrete Structure ◽  
Adelic Quantum Mechanics

We consider spectral problem for a free relativistic particle in p-adic and adelic quantum mechanics. In particular, we found p-adic and adelic eigenfunctions. Within adelic approach there exist quantum states that exhibit discrete structure of space–time at the Planck scale.

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