Letters in Mathematical Physics, ISSN 0377-9017, 12/2003, Volume 66, Issue 3, pp. 157 - 216

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes...

Geometry | Mathematical and Computational Physics | deformation quantization | Group Theory and Generalizations | homotopy Lie algebras | Physics | Statistical Physics | Deformation quantization | Homotopy Lie algebras | KONTSEVICH FORMALITY | FORMULA | PHYSICS, MATHEMATICAL | LIE-ALGEBRA HOMOLOGY | GEOMETRY

Geometry | Mathematical and Computational Physics | deformation quantization | Group Theory and Generalizations | homotopy Lie algebras | Physics | Statistical Physics | Deformation quantization | Homotopy Lie algebras | KONTSEVICH FORMALITY | FORMULA | PHYSICS, MATHEMATICAL | LIE-ALGEBRA HOMOLOGY | GEOMETRY

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 2/2018, Volume 2018, Issue 2, pp. 1 - 34

We discuss the relation between the cluster integrable systems and q-difference Painlevé equations. The Newton polygons corresponding to these integrable...

Topological Strings | Integrable Hierarchies | Supersymmetric Gauge Theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | SYMMETRIES | FIELD-THEORIES | QUANTUM GROUPS | 5-DIMENSIONAL GAUGE-THEORIES | TAU-FUNCTIONS | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Measurement | Permutations | Gauge theory | Deformation | Mathematical analysis | Clusters | Mutation | Polygons | Mathematical Physics | Nuclear and particle physics. Atomic energy. Radioactivity | Nonlinear Sciences | Exactly Solvable and Integrable Systems | High Energy Physics - Theory | Nonlinear Sciences - Exactly Solvable and Integrable Systems

Topological Strings | Integrable Hierarchies | Supersymmetric Gauge Theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | SYMMETRIES | FIELD-THEORIES | QUANTUM GROUPS | 5-DIMENSIONAL GAUGE-THEORIES | TAU-FUNCTIONS | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Measurement | Permutations | Gauge theory | Deformation | Mathematical analysis | Clusters | Mutation | Polygons | Mathematical Physics | Nuclear and particle physics. Atomic energy. Radioactivity | Nonlinear Sciences | Exactly Solvable and Integrable Systems | High Energy Physics - Theory | Nonlinear Sciences - Exactly Solvable and Integrable Systems

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 10/2018, Volume 108, Issue 10, pp. 2293 - 2301

We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not...

Geometry | Nongeometric string backgrounds | Deformation quantization | 17A20 | Theoretical, Mathematical and Computational Physics | Complex Systems | 81S99 | Nonassociative algebras | Group Theory and Generalizations | Physics | PHYSICS, MATHEMATICAL | Algebra

Geometry | Nongeometric string backgrounds | Deformation quantization | 17A20 | Theoretical, Mathematical and Computational Physics | Complex Systems | 81S99 | Nonassociative algebras | Group Theory and Generalizations | Physics | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 10/2019, Volume 277, Issue 8, pp. 2815 - 2838

We introduce a novel commutative C*-algebra CR(X) of functions on a symplectic vector space (X,σ) admitting a complex structure, along with a strict...

Fock space | Gelfand spectrum | Deformation quantization | C-algebra | MATHEMATICS | Analysis | Algebra | Mathematics - Functional Analysis

Fock space | Gelfand spectrum | Deformation quantization | C-algebra | MATHEMATICS | Analysis | Algebra | Mathematics - Functional Analysis

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 02/2015, Volume 30, Issue 4n05, p. 1550016

Emergent gravity is based on a novel form of the equivalence principle known as the Darboux theorem or the Moser lemma in symplectic geometry stating that the...

gauge-gravity correspondence | noncommutative geometry | Models of quantum gravity | SEIBERG-WITTEN MAP | SYMPLECTIC GROUPOIDS | YANG-MILLS | TOPOLOGICAL STRINGS | INSTANTONS | PHYSICS, NUCLEAR | QUANTUM-GRAVITY | STAR PRODUCTS | EQUIVALENCE | NONCOMMUTATIVE GAUGE-THEORY | DEFORMATION QUANTIZATION | PHYSICS, PARTICLES & FIELDS

gauge-gravity correspondence | noncommutative geometry | Models of quantum gravity | SEIBERG-WITTEN MAP | SYMPLECTIC GROUPOIDS | YANG-MILLS | TOPOLOGICAL STRINGS | INSTANTONS | PHYSICS, NUCLEAR | QUANTUM-GRAVITY | STAR PRODUCTS | EQUIVALENCE | NONCOMMUTATIVE GAUGE-THEORY | DEFORMATION QUANTIZATION | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of High Energy Physics, ISSN 1029-8479, 10/2019, Volume 2019, Issue 10, pp. 1 - 96

We develop an approach to the study of Coulomb branch operators in 3D N $$ \mathcal{N} $$ = 4 gauge theories and the associated quantization structure of their...

Extended Supersymmetry | Supersymmetric Gauge Theory | Solitons Monopoles and Instantons | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Supersymmetry and Duality | Physics | Elementary Particles, Quantum Field Theory | 3-DIMENSIONAL GAUGE-THEORIES | MATHEMATICAL DEFINITION | DEFORMATION QUANTIZATION | DUALITY | MIRROR SYMMETRY | PHYSICS, PARTICLES & FIELDS | Measurement | Operators (mathematics) | Bubbling | Boundary conditions | Algebra | Monopoles

Extended Supersymmetry | Supersymmetric Gauge Theory | Solitons Monopoles and Instantons | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Supersymmetry and Duality | Physics | Elementary Particles, Quantum Field Theory | 3-DIMENSIONAL GAUGE-THEORIES | MATHEMATICAL DEFINITION | DEFORMATION QUANTIZATION | DUALITY | MIRROR SYMMETRY | PHYSICS, PARTICLES & FIELDS | Measurement | Operators (mathematics) | Bubbling | Boundary conditions | Algebra | Monopoles

Journal Article

Advances in Mathematics, ISSN 0001-8708, 09/2017, Volume 317, pp. 575 - 639

Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a...

Quantum observables | Deformation quantization | Batalin–Vilkovisky (BV) quantization | Renormalization group flow | Algebraic index theorem | MATHEMATICS | Batalin-Vilkovisky (BV) quantization | SUPERSYMMETRY | ATIYAH-SINGER INDEX | THEOREM | POISSON MANIFOLDS | CHAINS | GEOMETRY | Analysis | Algebra

Quantum observables | Deformation quantization | Batalin–Vilkovisky (BV) quantization | Renormalization group flow | Algebraic index theorem | MATHEMATICS | Batalin-Vilkovisky (BV) quantization | SUPERSYMMETRY | ATIYAH-SINGER INDEX | THEOREM | POISSON MANIFOLDS | CHAINS | GEOMETRY | Analysis | Algebra

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 06/2018, Volume 274, Issue 12, pp. 3531 - 3551

For Toeplitz operators Tf(t) acting on the weighted Fock space Ht2, we consider the semi-commutator Tf(t)Tg(t)−Tfg(t), where t>0 is a certain weight parameter...

Vanishing mean oscillation | Semi-classical limit | Heat transform | Semi-commutator | MATHEMATICS | DEFORMATION QUANTIZATION | VANISHING MEAN-OSCILLATION | MANIFOLDS | DOMAINS

Vanishing mean oscillation | Semi-classical limit | Heat transform | Semi-commutator | MATHEMATICS | DEFORMATION QUANTIZATION | VANISHING MEAN-OSCILLATION | MANIFOLDS | DOMAINS

Journal Article

Journal fur die Reine und Angewandte Mathematik, ISSN 0075-4102, 01/2012, Volume 662, Issue 662, pp. 1 - 56

We study Berezin-Toeplitz quantization on Kahler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute...

MATHEMATICS | BERGMAN-KERNEL | THEOREM | ASYMPTOTIC-EXPANSION | METRICS | DEFORMATION QUANTIZATION | SYMPLECTIC-MANIFOLDS | OPERATORS | COMPLEX DIFFERENTIAL GEOMETRY | VECTOR-BUNDLES

MATHEMATICS | BERGMAN-KERNEL | THEOREM | ASYMPTOTIC-EXPANSION | METRICS | DEFORMATION QUANTIZATION | SYMPLECTIC-MANIFOLDS | OPERATORS | COMPLEX DIFFERENTIAL GEOMETRY | VECTOR-BUNDLES

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 01/2019, Volume 36, Issue 2, p. 25001

We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and...

generalized uncertainty principle | star-product | loop quantum cosmology | deformation quantization | polymer quantum mechanics | BLACK-HOLE ENTROPY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | HILBERT-SPACE | PHYSICS, PARTICLES & FIELDS

generalized uncertainty principle | star-product | loop quantum cosmology | deformation quantization | polymer quantum mechanics | BLACK-HOLE ENTROPY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | HILBERT-SPACE | PHYSICS, PARTICLES & FIELDS

Journal Article

Fortschritte der Physik, ISSN 0015-8208, 2019, Volume 67, Issue 8-9, p. 1910022

We describe three perspectives on higher quantization, using the example of magnetic Poisson structures which embody recent discussions of nonassociativity in...

bundle gerbes | higher quantization | nonassociative geometry | non-geometric strings | magnetic monopoles | STRINGS | INTEGRATION | PHYSICS, MULTIDISCIPLINARY | DEFORMATION QUANTIZATION | MONOPOLES | Conferences, meetings and seminars | Conferences and conventions

bundle gerbes | higher quantization | nonassociative geometry | non-geometric strings | magnetic monopoles | STRINGS | INTEGRATION | PHYSICS, MULTIDISCIPLINARY | DEFORMATION QUANTIZATION | MONOPOLES | Conferences, meetings and seminars | Conferences and conventions

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 9/2012, Volume 2012, Issue 9, pp. 1 - 55

We develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M . Starting...

String Duality | Flux compactifications | Non-Commutative Geometry | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Differential and algebraic geometry | Non-commutative geometry | String duality | POISSON | T-DUALITY | GRAVITY | STAR PRODUCT | NONCOMMUTATIVE GAUGE-THEORY | DEFORMATION QUANTIZATION | COMPACTIFICATIONS | D-BRANES | GEOMETRY | PHYSICS, PARTICLES & FIELDS

String Duality | Flux compactifications | Non-Commutative Geometry | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Differential and algebraic geometry | Non-commutative geometry | String duality | POISSON | T-DUALITY | GRAVITY | STAR PRODUCT | NONCOMMUTATIVE GAUGE-THEORY | DEFORMATION QUANTIZATION | COMPACTIFICATIONS | D-BRANES | GEOMETRY | PHYSICS, PARTICLES & FIELDS

Journal Article

Annals of Physics, ISSN 0003-4916, 03/2014, Volume 342, pp. 83 - 102

We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. The algebra would be large enough to capture...

Quantum resurgence | Quantisation deformation | Complex WKB method | Complex analysis | Complex topology | Zinn-Justin conjectures | PHYSICS, MULTIDISCIPLINARY | Zinn-justin conjectures | Algebra | Quantum physics | Deformation | Construction | Mathematical analysis | HYPERGEOMETRIC FUNCTIONS | QUANTUM COMPUTERS | QUANTIZATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DEFORMATION | ALGEBRA

Quantum resurgence | Quantisation deformation | Complex WKB method | Complex analysis | Complex topology | Zinn-Justin conjectures | PHYSICS, MULTIDISCIPLINARY | Zinn-justin conjectures | Algebra | Quantum physics | Deformation | Construction | Mathematical analysis | HYPERGEOMETRIC FUNCTIONS | QUANTUM COMPUTERS | QUANTIZATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DEFORMATION | ALGEBRA

Journal Article

Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, 2009, Volume 13, Issue 5, pp. 1445 - 1518

The problem of quantizing a symplectic manifold (M, omega) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting...

GEOMETRIC-QUANTIZATION | DEFORMATION QUANTIZATION | NILPOTENT ORBITS | EQUATIONS | PHYSICS, MATHEMATICAL | SIMONS GAUGE-THEORY | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

GEOMETRIC-QUANTIZATION | DEFORMATION QUANTIZATION | NILPOTENT ORBITS | EQUATIONS | PHYSICS, MATHEMATICAL | SIMONS GAUGE-THEORY | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 4/2018, Volume 2018, Issue 4, pp. 1 - 24

We formulate the worldline quantization (a.k.a. deformation quantization) of a massive fermion model coupled to external higher spin sources. We use the...

Higher Spin Gravity | Non-Commutative Geometry | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Models of Quantum Gravity | Elementary Particles, Quantum Field Theory | Measurement | Field theory | Deformation | Nuclear and particle physics. Atomic energy. Radioactivity

Higher Spin Gravity | Non-Commutative Geometry | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Models of Quantum Gravity | Elementary Particles, Quantum Field Theory | Measurement | Field theory | Deformation | Nuclear and particle physics. Atomic energy. Radioactivity

Journal Article

Nature Physics, ISSN 1745-2473, 04/2019, Volume 15, Issue 4, pp. 352 - 356

Many intriguing phenomena occur for electrons under strong magnetic fields(1,2). Recently, it was shown that an appropriate strain texture in graphene could...

CONDUCTANCE | ELECTRONIC-PROPERTIES | FIELDS | PHASE | DIRAC FERMIONS | PHYSICS, MULTIDISCIPLINARY | INSULATOR | GRAPHENE | SOUND | Stability | Deformation | Graphene | Lattices | Controllability | Acoustics | Electrons

CONDUCTANCE | ELECTRONIC-PROPERTIES | FIELDS | PHASE | DIRAC FERMIONS | PHYSICS, MULTIDISCIPLINARY | INSULATOR | GRAPHENE | SOUND | Stability | Deformation | Graphene | Lattices | Controllability | Acoustics | Electrons

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 08/2017, Volume 354, Issue 1, pp. 345 - 392

We investigate the structure of certain protected operator algebras that arise in three-dimensional superconformal field theories. We find that these algebras...

PHYSICS, MATHEMATICAL | OPERATORS | ALGEBRA | Algebra | Physics

PHYSICS, MATHEMATICAL | OPERATORS | ALGEBRA | Algebra | Physics

Journal Article

Selecta Mathematica, ISSN 1022-1824, 9/2018, Volume 24, Issue 4, pp. 3529 - 3617

Let $$\mathsf {k}$$ k be a field of characteristic zero. Etingof and Kazhdan (Sel. Math. (N.S.) 2:1–41, 1996) construct a quantisation $$U_\hbar \mathfrak b$$...

81R50 | Mathematics, general | Mathematics | 17B62 | 17B37 | MATHEMATICS | MATHEMATICS, APPLIED | LIE BIALGEBRAS

81R50 | Mathematics, general | Mathematics | 17B62 | 17B37 | MATHEMATICS | MATHEMATICS, APPLIED | LIE BIALGEBRAS

Journal Article