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.

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 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.

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.

The Schrödinger Equation

2020 ◽  
pp. 265-288
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Quantum Tunneling ◽  
Schrodinger Equation ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Particle Dynamics ◽  
Quantization Condition ◽  
De Broglie Waves ◽  
Macroscopic Objects

In this chapter, the Schrödinger equation is “derived” for particles that can be described by de Broglie waves. The Schrödinger equation is very different from the corresponding equation of motion in classical mechanics. In order to illustrate the fundamental differences between the two theories, one of the simplest problems of particle dynamics is solved in both Newtonian and quantum mechanics. This simple example also helps to show that quantum mechanics is the fundamental theory and classical mechanics is an approximation, a remarkably good approximation, when considering macroscopic objects. The solution of the Schrödinger equation is presented for a particle inside a box and the quantization condition is derived. The amazing possibility of quantum tunneling when a particle is incident on a barrier of height larger than the energy of the incident particle is also discussed. Finally the three-dimensional Schrödinger equation is solved for the hydrogen atom.

Structure of the anomaly in the canonical quantization of bosonic strings in background fields

1996 ◽  
Vol 108 (2) ◽  
pp. 1083-1092
Author(s):  
I. L. Buchbinder ◽  
E. I. Buchbinder ◽  
B. R. Mishchuk ◽  
V. D. Pershin
Keyword(s):  
Bosonic Strings ◽  
Canonical Quantization ◽  
Background Fields

SPECTRAL INVERSE PROBLEM IN SUPERSYMMETRIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (23) ◽  
pp. 4123-4129 ◽  
Author(s):  
P.K. BERA ◽  
S. BHATTACHARYYA ◽  
B. TALUKDAR
Keyword(s):  
Inverse Problem ◽  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
State Energy ◽  
Bound State ◽  
Quantization Condition ◽  
Energy Spectra ◽  
Conventional Theory ◽  
Bound State Energy ◽  
Spectral Inverse Problem

The supersymmetric WKB quantization condition is used to study the so-called spectral inverse problem. Wavefunctions for the harmonic oscillator and hydrogen atom are obtained from the knowledge of their bound-state energy spectra. The analysis presented is based essentially on a repackaging of the conventional theory of integral equations.

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