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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
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
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
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
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
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
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
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
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
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
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
Journal Article
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
Journal Article
Annals of Physics, ISSN 0003-4916, 07/2017, Volume 382, pp. 170 - 180
Journal Article
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
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
Journal Article
Annales Henri Poincaré, ISSN 1424-0637, 10/2018, Volume 19, Issue 10, pp. 3179 - 3196
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
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
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
Journal Article
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