On the Heisenberg algebra in Bargmann–Fock space with natural cutoffs

2016 ◽  
Vol 13 (05) ◽  
pp. 1650054 ◽  
Author(s):  
K. Nozari ◽  
M. Roushan
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
General Framework ◽  
Fock Space ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Space Representation ◽  
Maximal Momentum

We construct a generalized Hilbert space representation of quantum mechanics in [Formula: see text]-dimensions based on Bargmann–Fock space with natural cutoffs as a minimal length, minimal momentum and maximal momentum in order to have a general framework for Heisenberg algebra in Bargmann–Fock space.

scholarly journals Heisenberg Algebra in the Bargmann-Fock Space with Natural Cutoffs

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Maryam Roushan ◽  
Kourosh Nozari
Keyword(s):  
Uncertainty Principle ◽  
Fock Space ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Maximal Momentum

We construct a Heisenberg algebra in Bargmann-Fock space in the presence of natural cutoffs encoded as minimal length, minimal momentum, and maximal momentum through a generalized uncertainty principle.

scholarly journals Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Kourosh Nozari ◽  
F. Moafi ◽  
F. Rezaee Balef
Keyword(s):  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Field Theories ◽  
Majorana Fermion ◽  
Fermion Field ◽  
Free Fermion ◽  
Supersymmetric Field Theories ◽  
Fermion Fields ◽  
Maximal Momentum

We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra[x,p] = iℏ(1−βp+2β2p2), whereβis a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.

scholarly journals Nonrelativistic anti-Snyder model and some applications

2017 ◽  
Vol 32 (02n03) ◽  
pp. 1750009 ◽  
Author(s):  
C. L. Ching ◽  
C. X. Yeo ◽  
W. K. Ng
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Bound States ◽  
Homogeneous Magnetic Field ◽  
Maximum Energy ◽  
Minimal Length ◽  
Landau Levels ◽  
Space Representation ◽  
Free Particles ◽  
Ordinary Quantum

In this paper, we examine the (2[Formula: see text]+[Formula: see text]1)-dimensional Dirac equation in a homogeneous magnetic field under the nonrelativistic anti-Snyder model which is relevant to doubly/deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigensolutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states [Formula: see text] due to the orthogonality of the polynomials and the maximum energy is truncated at [Formula: see text]. Similar to the minimal length case, the degeneracy of the Dirac–Landau levels in anti-Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit [Formula: see text]. By taking [Formula: see text], we explore the motion of effective massless charged fermions in graphene-like material and obtained a maximum bound of deformed parameter [Formula: see text]. Furthermore, we consider the modified energy dispersion relations and its application in describing the behavior of neutrinos oscillation under modified commutation relations.

scholarly journals Differential representations of dynamical oscillator symmetries in discrete Hilbert space

2000 ◽  
Vol 5 (2) ◽  
pp. 97-106
Author(s):  
Andreas Ruffing
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Discrete Spectrum ◽  
Classical Limit ◽  
Heisenberg Algebra ◽  
Space Structure ◽  
Hermite Functions ◽  
Dynamical Symmetries ◽  
Creation And Annihilation Operators

As a very important example for dynamical symmetries in the context ofq-generalized quantum mechanics the algebraaa†−q−2a†a=1is investigated. It represents the oscillator symmetrySUq(1,1)and is regarded as a commutation phenomenon of theq-Heisenberg algebra which provides a discrete spectrum of momentum and space,i.e., a discrete Hilbert space structure. Generalizedq-Hermite functions and systems of creation and annihilation operators are derived. The classical limitq→1is investigated. Finally theSUq(1,1)algebra is represented by the dynamical variables of theq-Heisenberg algebra.

scholarly journals On the Relativistic Quantum Mechanics of a Particle in Space with Minimal Length

2012 ◽  
Vol 57 (9) ◽  
pp. 942
Author(s):  
Ch.M. Scherbakov
Keyword(s):  
Quantum Mechanics ◽  
Commutation Relation ◽  
Relativistic Quantum ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Group Symmetry ◽  
Relativistic Quantum Mechanics ◽  
Noncommutative Space ◽  
Quantum Mechanical

A noncommutative space and the deformed Heisenberg algebra [X,P] = iħ{1 – βP2}1/2 are investigated. The quantum mechanical structures underlying this commutation relation are studied. The rotational group symmetry is discussed in detail.

scholarly journals A general framework for quantum splines

2018 ◽  
Vol 15 (09) ◽  
pp. 1850147 ◽  
Author(s):  
L. Abrunheiro ◽  
M. Camarinha ◽  
J. Clemente-Gallardo ◽  
J. C. Cuchí ◽  
P. Santos
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Nonlinear System ◽  
General Framework ◽  
Hamiltonian Approach ◽  
Density Matrices ◽  
Quantum Domain ◽  
Riemannian Cubic ◽  
Geometrical Formulation

Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this concept to general density matrices with a Hamiltonian approach and using a geometrical formulation of quantum mechanics. Our main goal is to formulate an optimal control problem for a nonlinear system on [Formula: see text] which corresponds to the variational problem of quantum splines. The corresponding Hamiltonian equations and interpolation conditions are derived. The results are illustrated with some examples and the corresponding quantum splines are computed with the implementation of a suitable iterative algorithm.

scholarly journals Hilbert space representation of the minimal length uncertainty relation

1995 ◽  
Vol 52 (2) ◽  
pp. 1108-1118 ◽  
Author(s):  
Achim Kempf ◽  
Gianpiero Mangano ◽  
Robert B. Mann
Keyword(s):  
Hilbert Space ◽  
Uncertainty Relation ◽  
Minimal Length ◽  
Space Representation
Sign in / Sign up

Export Citation Format

Share Document