scholarly journals Generalized Deformed Commutation Relations with Nonzero Minimal Uncertainties in Position and/or Momentum and Applications to Quantum Mechanics

2007 ◽  
Author(s):  
Christiane Quesne
Keyword(s):  
Quantum Mechanics ◽  
Commutation Relations ◽  
Deformed Commutation Relations

scholarly journals Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics

1997 ◽  
Vol 11 (10) ◽  
pp. 1281-1296 ◽  
Author(s):  
V. I. Man'ko ◽  
G. Marmo ◽  
F. Zaccaria ◽  
E. C. G. Sudarshan
Keyword(s):  
Quantum Mechanics ◽  
Vector Field ◽  
Equations Of Motion ◽  
Quantum Systems ◽  
Heisenberg Picture ◽  
Commutation Relations

It is shown that for quantum systems the vector field associated with the equations of motion may admit alternative Hamiltonian descriptions, both in the Schrödinger and Heisenberg picture. We illustrate these ambiguities in terms of simple examples.

scholarly journals Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

2020 ◽  
Vol 35 (13) ◽  
pp. 2050096
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Kinetic Energy ◽  
Energy Dependence ◽  
Uncertainty Principle ◽  
Equivalence Principle ◽  
Generalized Uncertainty Principle ◽  
Weak Equivalence ◽  
Weak Equivalence Principle ◽  
Deformation Function ◽  
Commutation Relations ◽  
Deformed Commutation Relations

A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.

Multiple Quantization

1953 ◽  
Vol 5 ◽  
pp. 26-36
Author(s):  
A. E. Scheidegger
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Physical Science ◽  
Commutation Relations ◽  
Vast Amount ◽  
Physical Evidence

The efforts of most theoretical physicists of this century have been directed towards that branch of the physical science which is commonly called “Quantum Theory.” Physically, Quantum Theory was postulated because of a vast amount of physical evidence which led to the postulates of states, observables, superposition, and commutation relations. From these four postulates, all quantum mechanics follows.

scholarly journals q-OSCILLATORS, NON-KÄHLER MANIFOLDS AND CONSTRAINED DYNAMICS

1995 ◽  
Vol 10 (12) ◽  
pp. 941-948 ◽  
Author(s):  
SERGEI V. SHABANOV
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Constrained Dynamics ◽  
Commutation Relations ◽  
Ordinary Quantum

It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kähler manifolds, or as a quantum theory with second- (or first-) class constraints.

scholarly journals Fock representations of Q-deformed commutation relations

2017 ◽  
Vol 58 (7) ◽  
pp. 073501 ◽  
Author(s):  
Marek Bożejko ◽  
Eugene Lytvynov ◽  
Janusz Wysoczański
Keyword(s):  
Commutation Relations ◽  
Deformed Commutation Relations ◽  
Fock Representations

scholarly journals A NOTE ON GAUSSIAN INTEGRALS OVER PARA-GRASSMANN VARIABLES

2004 ◽  
Vol 19 (11) ◽  
pp. 1705-1714 ◽  
Author(s):  
LETICIA F. CUGLIANDOLO ◽  
G. S. LOZANO ◽  
E. F. MORENO ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quadratic Form ◽  
Path Integral ◽  
Quadratic Forms ◽  
Disordered Systems ◽  
Commutation Relations ◽  
Deformed Commutation Relations ◽  
Grassmann Variables

We discuss the generalization of the connection between the determinant of an operator entering a quadratic form and the associated Gaussian path-integral valid for Grassmann variables to the para-Grassmann case [θp+1=0 with p=1(p>1) for Grassmann (para-Grassmann) variables]. We show that the q-deformed commutation relations of the para-Grassmann variables lead naturally to consider q-deformed quadratic forms related to multiparametric deformations of GL (n) and their corresponding q-determinants. We suggest a possible application to the study of disordered systems.

scholarly journals From quantum field theory to quantum mechanics

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Nuno Barros e Sá ◽  
Cláudio Gomes
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Localized States ◽  
Relativistic Quantum Mechanics ◽  
Position Operator ◽  
Quantum Field ◽  
Commutation Relations ◽  
Klein Gordon ◽  
Explicit Relation

AbstractThe purpose of this article is to construct an explicit relation between the field operators in Quantum Field Theory and the relevant operators in Quantum Mechanics for a system of N identical particles, which are the symmetrised functions of the canonical operators of position and momentum, thus providing a clear relation between Quantum Field Theory and Quantum Mechanics. This is achieved in the context of the non-interacting Klein–Gordon field. Though this procedure may not be extendible to interacting field theories, since it relies crucially on particle number conservation, we find it nevertheless important that such an explicit relation can be found at least for free fields. It also comes out that whatever statistics the field operators obey (either commuting or anticommuting), the position and momentum operators obey commutation relations. The construction of position operators raises the issue of localizability of particles in Relativistic Quantum Mechanics, as the position operator for a single particle turns out to be the Newton–Wigner position operator. We make some clarifications on the interpretation of Newton–Wigner localized states and we consider the transformation properties of position operators under Lorentz transformations, showing that they do not transform as tensors, rather in a manner that preserves the canonical commutation relations. From a complex Klein–Gordon field, position and momentum operators can be constructed for both particles and antiparticles.

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