Letters in Mathematical Physics, ISSN 0377-9017, 4/2017, Volume 107, Issue 4, pp. 659 - 671

The standard uncertainty relations (UR) in quantum mechanics are typically used for unbounded operators (like the canonical pair). This implies the need for...

Geometry | 47N50 | 47B15 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | 81Q10 | Commutation relations | Physics | Uncertainty relations | Quantum theory | PHYSICS, MATHEMATICAL | Usage

Geometry | 47N50 | 47B15 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | 81Q10 | Commutation relations | Physics | Uncertainty relations | Quantum theory | PHYSICS, MATHEMATICAL | Usage

Journal Article

Annals of Physics, ISSN 0003-4916, 08/2017, Volume 383, pp. 92 - 100

We derive suitable uncertainty relations for characteristics functions of phase and number of a single-mode field obtained from the Weyl form of commutation...

Uncertainty relations | Quantum phase | Weyl commutators | STATES | DIFFERENCE | PHYSICS, MULTIDISCIPLINARY | ANGLE | OPERATORS | Physics - Quantum Physics | COMMUTATION RELATIONS | COMMUTATORS | CORRELATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Uncertainty relations | Quantum phase | Weyl commutators | STATES | DIFFERENCE | PHYSICS, MULTIDISCIPLINARY | ANGLE | OPERATORS | Physics - Quantum Physics | COMMUTATION RELATIONS | COMMUTATORS | CORRELATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 07/2017, Volume 58, Issue 7, p. 73501

We consider Fock representations of the Q-deformed commutation relations ∂ s ∂ t † = Q ( s , t ) ∂ t † ∂ s + δ ( s , t ) for s , t ∈ T . Here T : = R d (or...

VON-NEUMANN-ALGEBRAS | SPACE | OPERATOR | GENERALIZED STATISTICS | ANYON FIELDS | PHYSICS, MATHEMATICAL | COXETER GROUPS | FACTORIALITY | Operators | Deformation | Representations | Commutation | Statistics

VON-NEUMANN-ALGEBRAS | SPACE | OPERATOR | GENERALIZED STATISTICS | ANYON FIELDS | PHYSICS, MATHEMATICAL | COXETER GROUPS | FACTORIALITY | Operators | Deformation | Representations | Commutation | Statistics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 08/2018, Volume 341, Issue 8, pp. 2308 - 2325

We derive combinatorial identities for variables satisfying specific systems of commutation relations, in particular elliptic commutation relations. The...

Elliptic weights | Normal ordering | Rook theory | Basic hypergeometric series | Commutation relations | Weyl algebra | MATHEMATICS

Elliptic weights | Normal ordering | Rook theory | Basic hypergeometric series | Commutation relations | Weyl algebra | MATHEMATICS

Journal Article

INDIANA UNIVERSITY MATHEMATICS JOURNAL, ISSN 0022-2518, 2019, Volume 68, Issue 6, pp. 1849 - 1883

We define noncommutative spheres with partial commutation relations for the coordinates. We investigate the quantum groups acting maximally on them, which...

Coxeter groups | AUTOMORPHISM-GROUPS | Noncommutative sphere | de Finetti theorem | GRAPHS | MATHEMATICS | quantum automorphism group | distributional symmetries | compact quantum group | PRODUCTS | quantum sphere | partial commutation relation | DUALITY | MANIFOLDS | orthogonal group

Coxeter groups | AUTOMORPHISM-GROUPS | Noncommutative sphere | de Finetti theorem | GRAPHS | MATHEMATICS | quantum automorphism group | distributional symmetries | compact quantum group | PRODUCTS | quantum sphere | partial commutation relation | DUALITY | MANIFOLDS | orthogonal group

Journal Article

Journal of Algebra, ISSN 0021-8693, 04/2018, Volume 500, pp. 193 - 220

We study the phenomenon in which commutation relations for sequences of elements in a ring are implied by similar relations for subsequences involving at most...

Dehn diagram | Commutation relations | Elementary symmetric function | Rule of Three | Noncommutative symmetric function | MATHEMATICS

Dehn diagram | Commutation relations | Elementary symmetric function | Rule of Three | Noncommutative symmetric function | MATHEMATICS

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 11/2016, Volume 189, Issue 2, pp. 1624 - 1644

We consider quantum integrable models with the gl(2|1) symmetry and derive a set of multiple commutation relations between the monodromy matrix elements. These...

Bethe ansatz | monodromy matrix | Applications of Mathematics | Theoretical, Mathematical and Computational Physics | Physics | commutation relation | ONE-DIMENSION | CHAIN | PHYSICS, MULTIDISCIPLINARY | T-J MODEL | PHYSICS, MATHEMATICAL | BETHE-ANSATZ

Bethe ansatz | monodromy matrix | Applications of Mathematics | Theoretical, Mathematical and Computational Physics | Physics | commutation relation | ONE-DIMENSION | CHAIN | PHYSICS, MULTIDISCIPLINARY | T-J MODEL | PHYSICS, MATHEMATICAL | BETHE-ANSATZ

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2013, Volume 46, Issue 3, pp. 35304 - 11

In this short paper, the commutator of monomials of operators obeying constant commutation relations is expressed in terms of anti-commutators. The formula...

ANALOG | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUANTUM | Operators | Theorems | Commutation | Mathematical analysis | Constants | Polynomials | Commutators | Order disorder

ANALOG | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUANTUM | Operators | Theorems | Commutation | Mathematical analysis | Constants | Polynomials | Commutators | Order disorder

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 09/2019, Volume 31, Issue 8, p. 1950026

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations...

Singular Bogoliubov transformation | boson Fock space | canonical commutation relations | inequivalent representation | PHYSICS, MATHEMATICAL

Singular Bogoliubov transformation | boson Fock space | canonical commutation relations | inequivalent representation | PHYSICS, MATHEMATICAL

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 2017, Volume 30, Issue 10, p. 587

The proof of the main theorem of the paper [1] contains an error. We are grateful to Professor Ralf Meyer (Mathematisches Institut, Georg-August Universität...

Algebra

Algebra

Journal Article

Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 06/2015, Volume 24, Issue 7, pp. 1550034 - 1-1550034-19

We give elementary proofs of certain relations in the mapping class group of a closed surface of genus 2, MCG(F2, 0). We generalize portions of these to...

communication relations | knot colorings via quandles | Quandle homology | MATHEMATICS | Construction | Commutation | Proving | Homology | Mapping | Knot theory | Racks

communication relations | knot colorings via quandles | Quandle homology | MATHEMATICS | Construction | Commutation | Proving | Homology | Mapping | Knot theory | Racks

Journal Article

12.
Full Text
Representations of Canonical Commutation Relations Describing Infinite Coherent States

Communications in Mathematical Physics, ISSN 0010-3616, 10/2016, Volume 347, Issue 2, pp. 421 - 448

We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent...

DECOHERENCE | PHYSICS, MATHEMATICAL | Mathematical Physics | Physics

DECOHERENCE | PHYSICS, MATHEMATICAL | Mathematical Physics | Physics

Journal Article

Bernoulli, ISSN 1350-7265, 11/2013, Volume 19, Issue 5A, pp. 1855 - 1879

Given a birth-death process on N with semigroup (Pt)t ≥0 and a discrete gradient ∂u depending on a positive weight w, we establish intertwining relations of...

Sentence commutation | Ergodic theory | Interpolation | Markov processes | Semigroups | Mathematical independent variables | Mathematical inequalities | Random variables | Convexity | Curvature | Functional inequalities | Feynman-Kac semigroup | Intertwining relation | Discrete gradients | Birth-death process | STEINS METHOD | LOGARITHMIC SOBOLEV INEQUALITIES | POISSON | APPROXIMATION | DECAY | TRANSPORTATION-INFORMATION INEQUALITIES | intertwining relation | STATISTICS & PROBABILITY | birth-death process | SPECTRAL GAP | discrete gradients | POINCARE | functional inequalities | Probability | Mathematics | Feynman–Kac semigroup | birth–death process

Sentence commutation | Ergodic theory | Interpolation | Markov processes | Semigroups | Mathematical independent variables | Mathematical inequalities | Random variables | Convexity | Curvature | Functional inequalities | Feynman-Kac semigroup | Intertwining relation | Discrete gradients | Birth-death process | STEINS METHOD | LOGARITHMIC SOBOLEV INEQUALITIES | POISSON | APPROXIMATION | DECAY | TRANSPORTATION-INFORMATION INEQUALITIES | intertwining relation | STATISTICS & PROBABILITY | birth-death process | SPECTRAL GAP | discrete gradients | POINCARE | functional inequalities | Probability | Mathematics | Feynman–Kac semigroup | birth–death process

Journal Article

Annals of Physics, ISSN 0003-4916, 07/2017, Volume 382, pp. 170 - 180

Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated...

Generalized uncertainty principle | Minimal observable length | Rényi entropy | Tsallis entropy | PHYSICS, MULTIDISCIPLINARY | HEISENBERG ALGEBRA | OBSERVABLES | PLANCK-SCALE PHYSICS | SPACETIME | PRINCIPLE | GAMMA-RAY BURSTS | QUANTUM-GRAVITY | Renyi entropy | Physics - Quantum Physics | WAVE PACKETS | PROBABILITY DENSITY FUNCTIONS | UNCERTAINTY PRINCIPLE | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | COMMUTATION RELATIONS | ENTROPY | FOURIER TRANSFORMATION | WAVE FUNCTIONS

Generalized uncertainty principle | Minimal observable length | Rényi entropy | Tsallis entropy | PHYSICS, MULTIDISCIPLINARY | HEISENBERG ALGEBRA | OBSERVABLES | PLANCK-SCALE PHYSICS | SPACETIME | PRINCIPLE | GAMMA-RAY BURSTS | QUANTUM-GRAVITY | Renyi entropy | Physics - Quantum Physics | WAVE PACKETS | PROBABILITY DENSITY FUNCTIONS | UNCERTAINTY PRINCIPLE | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | COMMUTATION RELATIONS | ENTROPY | FOURIER TRANSFORMATION | WAVE FUNCTIONS

Journal Article

15.
Full Text
Quantum symmetries on noncommutative complex spheres with partial commutation relations

Infinite Dimensional Analysis, Quantum Probability and Related Topics, ISSN 0219-0257, 12/2018, Volume 21, Issue 4

We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry...

partial commutation relation | Noncommutative complex sphere | quantum automorphism group | compact quantum group | orthogonal group | MATHEMATICS, APPLIED | QUANTUM SCIENCE & TECHNOLOGY | DUALITY | STATISTICS & PROBABILITY | MANIFOLDS | PHYSICS, MATHEMATICAL | ISOMETRIES

partial commutation relation | Noncommutative complex sphere | quantum automorphism group | compact quantum group | orthogonal group | MATHEMATICS, APPLIED | QUANTUM SCIENCE & TECHNOLOGY | DUALITY | STATISTICS & PROBABILITY | MANIFOLDS | PHYSICS, MATHEMATICAL | ISOMETRIES

Journal Article

International Journal of Modern Physics B, ISSN 0217-9792, 04/2017, Volume 31, Issue 9, p. 1750061

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a...

rectangular lattices | relativistic energy-dispersion relations | Finite-depth potential wells | lattice alignment equation | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | GERMANIUM | CONDUCTIVITY | ELECTRONS | SILICON | HOLES | PHYSICS, MATHEMATICAL

rectangular lattices | relativistic energy-dispersion relations | Finite-depth potential wells | lattice alignment equation | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | GERMANIUM | CONDUCTIVITY | ELECTRONS | SILICON | HOLES | PHYSICS, MATHEMATICAL

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 10/2018, Volume 19, Issue 10, pp. 3179 - 3196

We exhibit a Hamel basis for the concrete $$*$$ ∗ -algebra $${\mathfrak {M}}_o$$ Mo associated to monotone commutation relations realised on the monotone Fock...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | THEOREM | PHYSICS, PARTICLES & FIELDS | Stochastic processes | Algebra

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | THEOREM | PHYSICS, PARTICLES & FIELDS | Stochastic processes | Algebra

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 04/2013, Volume 264, Issue 8, pp. 1975 - 2004

In the theory of C⁎-algebras, interesting noncommutative structures arise as deformations of the tensor product, e.g. the rotation algebra Aϑ as a deformation...

Twist | Rotation algebra | Commutation relations | Universal [formula omitted]-algebra | Isometries | Noncommutative torus | Universal C | algebra | TENSOR-PRODUCTS | CSTAR-ALGEBRAS | AUTOMORPHISMS | CROSSED-PRODUCTS | MATHEMATICS | STAR-ALGEBRAS | COMMUTING ISOMETRIES | Universal C-algebra | Algebra

Twist | Rotation algebra | Commutation relations | Universal [formula omitted]-algebra | Isometries | Noncommutative torus | Universal C | algebra | TENSOR-PRODUCTS | CSTAR-ALGEBRAS | AUTOMORPHISMS | CROSSED-PRODUCTS | MATHEMATICS | STAR-ALGEBRAS | COMMUTING ISOMETRIES | Universal C-algebra | Algebra

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 4/2017, Volume 351, Issue 2, pp. 653 - 687

Let $${X=\mathbb{R}^2}$$ X = R 2 and let $${q\in\mathbb{C}}$$ q ∈ C , $${|q|=1}$$ | q | = 1 . For $${x=(x^1,x^2)}$$ x = ( x 1 , x 2 ) and $${y=(y^1,y^2)}$$ y =...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | BOSONIZATION | POLYNOMIALS | FOCK REPRESENTATIONS | LEVY PROCESSES | GENERALIZED STATISTICS | SPACES | INFINITE DIMENSIONS | WHITE-NOISE | PHYSICS, MATHEMATICAL | OPERATORS | QUANTUM-FIELDS | Algebra

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | BOSONIZATION | POLYNOMIALS | FOCK REPRESENTATIONS | LEVY PROCESSES | GENERALIZED STATISTICS | SPACES | INFINITE DIMENSIONS | WHITE-NOISE | PHYSICS, MATHEMATICAL | OPERATORS | QUANTUM-FIELDS | Algebra

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 12/2012, Volume 53, Issue 12, p. 123510

We continue our analysis of the consequences of the commutation relation \documentclass[12pt]{minimal}\begin{document}$[S, T]\break = {\bb 1}$\end{document} [...

PHYSICS, MATHEMATICAL | WEYL RELATION | Operators | Terminology | Commutation | Mathematical analysis | Nonlinearity | Hilbert space | Commutators

PHYSICS, MATHEMATICAL | WEYL RELATION | Operators | Terminology | Commutation | Mathematical analysis | Nonlinearity | Hilbert space | Commutators

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.