Selecta Mathematica, New Series, ISSN 1022-1824, 04/2018, Volume 24, Issue 2, pp. 1247 - 1313

We study linear Batalin-Vilkovisky (BV) quantization, which is a derived and shifted version of the Weyl quantization of symplectic vector spaces. Using a...

17B55 | 55U99 | 58J52 | 18D50 | 81Q99 | 53D55 | 81T70 | 14D23 | 17B81 | 13D10 | 18G55 | 14D15 | INFINITY-CATEGORIES | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | GAUGE ALGEBRA | THEOREM | COMPLEXES | N-ALGEBRAS | STACKS | MODEL | SHIFTED SYMPLECTIC STRUCTURES | Machinery | Algebra | Magneto-electric machines

17B55 | 55U99 | 58J52 | 18D50 | 81Q99 | 53D55 | 81T70 | 14D23 | 17B81 | 13D10 | 18G55 | 14D15 | INFINITY-CATEGORIES | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | GAUGE ALGEBRA | THEOREM | COMPLEXES | N-ALGEBRAS | STACKS | MODEL | SHIFTED SYMPLECTIC STRUCTURES | Machinery | Algebra | Magneto-electric machines

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 06/2017, Volume 29, Issue 5, p. 1750015

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension 4 ℓ + 3 endowed with a Wu structure...

algebraic topology | topological quantum field theory | Anomalies | QUADRATIC-FUNCTIONS | PHYSICS, MATHEMATICAL

algebraic topology | topological quantum field theory | Anomalies | QUADRATIC-FUNCTIONS | PHYSICS, MATHEMATICAL

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 2/2017, Volume 107, Issue 2, pp. 375 - 408

This note describes the restoration of time in one-dimensional parameterization-invariant (hence timeless) models, namely, the classically equivalent Jacobi...

Supersymmetry | Spinning particle | Theoretical, Mathematical and Computational Physics | Complex Systems | 83C47 | Physics | One-dimensional gravity | AKSZ | Geometry | 81T45 | Jacobi action | Secondary 70805 | Parametrization invariant Lagrangian | BFV | Group Theory and Generalizations | Primary 81T70

Supersymmetry | Spinning particle | Theoretical, Mathematical and Computational Physics | Complex Systems | 83C47 | Physics | One-dimensional gravity | AKSZ | Geometry | 81T45 | Jacobi action | Secondary 70805 | Parametrization invariant Lagrangian | BFV | Group Theory and Generalizations | Primary 81T70

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2015, Volume 105, Issue 12, pp. 1735 - 1783

A construction of gauge-invariant observables is suggested for a class of topological field theories, the AKSZ sigma models. The observables are associated to...

Geometry | Q-manifolds | observables | Batalin–Vilkovisky formalism | 57R56 | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Topological field theory | Physics

Geometry | Q-manifolds | observables | Batalin–Vilkovisky formalism | 57R56 | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Topological field theory | Physics

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 11/1995, Volume 174, Issue 1, pp. 57 - 91

Commun.Math.Phys.174:57-92,1995 We establish general theorems on the cohomology $H^*(s|d)$ of the BRST differential modulo the spacetime exterior derivative,...

Physics - High Energy Physics - Theory | 81T70 | 81T13 | 17B81

Physics - High Energy Physics - Theory | 81T70 | 81T13 | 17B81

Journal Article

Journal of Algebra, ISSN 0021-8693, 08/2015, Volume 435, pp. 1 - 32

The paper explores the indecomposable submodule structures of quantum divided power algebra Aq(n) defined in [23] and its truncated objects Aq(n,m). An...

Loewy filtration | Quantum divided power algebra | Rigidity | q-Differentials | Quantum Grassmann algebra | Quantum de Rham cohomology | LOCALIZATION | REPRESENTATIONS | UNITY | VARIETIES | WEYL ALGEBRAS | LIE-ALGEBRAS | MATHEMATICS | MODULES | ENVELOPING-ALGEBRAS | CATEGORY | ROOTS | Analysis | Algebra

Loewy filtration | Quantum divided power algebra | Rigidity | q-Differentials | Quantum Grassmann algebra | Quantum de Rham cohomology | LOCALIZATION | REPRESENTATIONS | UNITY | VARIETIES | WEYL ALGEBRAS | LIE-ALGEBRAS | MATHEMATICS | MODULES | ENVELOPING-ALGEBRAS | CATEGORY | ROOTS | Analysis | Algebra

Journal Article

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Perturbative N = 2 Supersymmetric Quantum Mechanics and L-Theory with Complex Coefficients

Letters in Mathematical Physics, ISSN 0377-9017, 1/2016, Volume 106, Issue 1, pp. 109 - 129

We construct L-theory with complex coefficients from the geometry of 1|2-dimensional perturbative mechanics. Methods of perturbative quantization lead to...

Theoretical, Mathematical and Computational Physics | 55N20 | supersymmetric field theories | Statistical Physics, Dynamical Systems and Complexity | quantization in field theory | cohomological methods | Physics | 57N65 | Geometry | 81T70 | generalized (extraordinary) homology and cohomology theories | 81T60 | Group Theory and Generalizations | algebraic topology of manifolds | PHYSICS, MATHEMATICAL | Quantum theory | Mathematics - Algebraic Topology

Theoretical, Mathematical and Computational Physics | 55N20 | supersymmetric field theories | Statistical Physics, Dynamical Systems and Complexity | quantization in field theory | cohomological methods | Physics | 57N65 | Geometry | 81T70 | generalized (extraordinary) homology and cohomology theories | 81T60 | Group Theory and Generalizations | algebraic topology of manifolds | PHYSICS, MATHEMATICAL | Quantum theory | Mathematics - Algebraic Topology

Journal Article

Communications in mathematical physics, ISSN 0010-3616, 1990, Volume 129, Issue 2, pp. 393 - 429

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 11/1995, Volume 174, Issue 1, pp. 93 - 116

Commun.Math.Phys.174:93-116,1995 Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion...

Physics - High Energy Physics - Theory | 81T70 | 81T13 | 17B81

Physics - High Energy Physics - Theory | 81T70 | 81T13 | 17B81

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 12/1993, Volume 158, Issue 3, pp. 569 - 644

We find a relation between the spectrum of solitons of massive N = 2 quantum field theories in d = 2 and the scaling dimensions of chiral fields at the...

FUSION | SOLITONS | LINEAR SIGMA-MODELS | RINGS | ISING-MODEL | PHYSICS, MATHEMATICAL | SCATTERING | GEOMETRY | Physics - High Energy Physics - Theory | 81T70 | 81T60 | 53C55 | 32G81

FUSION | SOLITONS | LINEAR SIGMA-MODELS | RINGS | ISING-MODEL | PHYSICS, MATHEMATICAL | SCATTERING | GEOMETRY | Physics - High Energy Physics - Theory | 81T70 | 81T60 | 53C55 | 32G81

Journal Article

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Boundary Coupling of Lie Algebroid Poisson Sigma Models and Representations up to Homotopy

Letters in Mathematical Physics, ISSN 0377-9017, 10/2012, Volume 102, Issue 1, pp. 31 - 64

A general form for the boundary coupling of a Lie algebroid Poisson sigma model is proposed. The approach involves using the Batalin–Vilkovisky formalism in...

Poisson sigma models | Lie algebroids | D-branes | Theoretical, Mathematical and Computational Physics | topological field theories | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | Secondary 81T70 | Batalin–Vilkovisky formalism | Primary 81T45 | 81T30 | Group Theory and Generalizations | Batalin-Vilkovisky formalism | BRANES | PHYSICS, MATHEMATICAL | GEOMETRY

Poisson sigma models | Lie algebroids | D-branes | Theoretical, Mathematical and Computational Physics | topological field theories | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | Secondary 81T70 | Batalin–Vilkovisky formalism | Primary 81T45 | 81T30 | Group Theory and Generalizations | Batalin-Vilkovisky formalism | BRANES | PHYSICS, MATHEMATICAL | GEOMETRY

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2010, Volume 94, Issue 3, pp. 243 - 261

An odd vector field Q on a supermanifold M is called homological, if Q 2 = 0. The operator of Lie derivative L Q makes the algebra of smooth tensor fields on M...

Geometry | Q -manifolds | gauge theories | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | 57R32 | characteristic classes | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Physics | Q-manifolds | LIE | PHYSICS, MATHEMATICAL | ALGEBRA

Geometry | Q -manifolds | gauge theories | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | 57R32 | characteristic classes | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Physics | Q-manifolds | LIE | PHYSICS, MATHEMATICAL | ALGEBRA

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 11/2010, Volume 94, Issue 2, pp. 197 - 228

We describe a canonical reduction of AKSZ–BV theories to the cohomology of the source manifold. We get a finite-dimensional BV theory that describes the...

Courant geometry | Theoretical, Mathematical and Computational Physics | topological quantum field theory | Statistical Physics, Dynamical Systems and Complexity | Physics | Poisson geometry | 53D17 | Geometry | 81T45 | Batalin–Vilkovisky quantization | 57R56 | 81T70 | Group Theory and Generalizations | Batalin-Vilkovisky quantization | QUANTIZATION | PHYSICS, MATHEMATICAL | GEOMETRY

Courant geometry | Theoretical, Mathematical and Computational Physics | topological quantum field theory | Statistical Physics, Dynamical Systems and Complexity | Physics | Poisson geometry | 53D17 | Geometry | 81T45 | Batalin–Vilkovisky quantization | 57R56 | 81T70 | Group Theory and Generalizations | Batalin-Vilkovisky quantization | QUANTIZATION | PHYSICS, MATHEMATICAL | GEOMETRY

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 9/2017, Volume 107, Issue 9, pp. 1649 - 1688

As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the...

Deformation quantization | Theoretical, Mathematical and Computational Physics | Complex Systems | Poisson sigma model | BV-BFV formalism | Primary 53D55 | Physics | Secondary 53D17 | Geometry | 57R56 | 81T70 | Group Theory and Generalizations | Symplectic groupoid | Formal geometry | MANIFOLDS | SIGMA-MODEL | PHYSICS, MATHEMATICAL | GEOMETRY

Deformation quantization | Theoretical, Mathematical and Computational Physics | Complex Systems | Poisson sigma model | BV-BFV formalism | Primary 53D55 | Physics | Secondary 53D17 | Geometry | 57R56 | 81T70 | Group Theory and Generalizations | Symplectic groupoid | Formal geometry | MANIFOLDS | SIGMA-MODEL | PHYSICS, MATHEMATICAL | GEOMETRY

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 07/2004, Volume 69, Issue 1, pp. 157 - 175

General boundary conditions (‘branes’) for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson...

Geometry | coisotropic submanifolds | branes | Mathematical and Computational Physics | deformation quantization | dual pairs | Group Theory and Generalizations | Physics | Statistical Physics | SYMPLECTIC GROUPOIDS | CLASSICAL PSEUDOGROUPS | QUANTUM | MANIFOLDS | PHYSICS, MATHEMATICAL

Geometry | coisotropic submanifolds | branes | Mathematical and Computational Physics | deformation quantization | dual pairs | Group Theory and Generalizations | Physics | Statistical Physics | SYMPLECTIC GROUPOIDS | CLASSICAL PSEUDOGROUPS | QUANTUM | MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 07/1993, Volume 155, Issue 2, pp. 249 - 260

The geometry of P-manifolds (odd symplectic manifolds) and SP-manifolds (P-manifolds provided with a volume element) is studied. A complete classification of...

PHYSICS, MATHEMATICAL | Physics - High Energy Physics - Theory | 58H99 | 81T70 | 81T60 | 58A50

PHYSICS, MATHEMATICAL | Physics - High Energy Physics - Theory | 58H99 | 81T70 | 81T60 | 58A50

Journal Article

Selecta Mathematica, ISSN 1022-1824, 4/2018, Volume 24, Issue 2, pp. 1247 - 1313

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 05/2005, Volume 257, Issue 1, pp. 193 - 225

We consider an intrinsic entropy associated with a local conformal net by the coefficients in the expansion of the logarithm of the trace of the “heat kernel”...

Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | Physics | Statistical Physics | DENSITY | LOCAL CONFORMAL NETS | 2ND LAW | STATISTICS | OBSERVABLES | SECTORS | SUBFACTORS | QUANTUM-FIELD THEORY | CLASSIFICATION | INDEX | PHYSICS, MATHEMATICAL

Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | Physics | Statistical Physics | DENSITY | LOCAL CONFORMAL NETS | 2ND LAW | STATISTICS | OBSERVABLES | SECTORS | SUBFACTORS | QUANTUM-FIELD THEORY | CLASSIFICATION | INDEX | PHYSICS, MATHEMATICAL

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 6/2012, Volume 6, Issue 3, pp. 775 - 780

The term “ $${\mathcal {A}}$$ -invariance” refers to the invariance of our results, with respect to the “arithmetic” employed, viz. to an appropriate algebra...

Fields interaction | Yang–Mills functional | {\mathcal {H}om-\otimes}$$ adjunction | {\mathcal {A}}$$ -invariance | {\mathcal {A}}$$ -connection Lagrangian | 83C45 | 81C45 | Mathematics | Noether’s perspective | Curvature Lagrangian | 58D29 | 81T13 | 46N50 | Operator Theory | 83V47 | Analysis | 81T10 | Self-interaction | 81T70 | Mathematics, general | Utiyama’s adjunction | Gauge invariant Action density | Hom - ⊗ adjunction | Noether's perspective | Utiyama's adjunction | Yang-Mills functional | A-invariance | A-connection Lagrangian | MATHEMATICS | MATHEMATICS, APPLIED | Hom - circle times adjunction

Fields interaction | Yang–Mills functional | {\mathcal {H}om-\otimes}$$ adjunction | {\mathcal {A}}$$ -invariance | {\mathcal {A}}$$ -connection Lagrangian | 83C45 | 81C45 | Mathematics | Noether’s perspective | Curvature Lagrangian | 58D29 | 81T13 | 46N50 | Operator Theory | 83V47 | Analysis | 81T10 | Self-interaction | 81T70 | Mathematics, general | Utiyama’s adjunction | Gauge invariant Action density | Hom - ⊗ adjunction | Noether's perspective | Utiyama's adjunction | Yang-Mills functional | A-invariance | A-connection Lagrangian | MATHEMATICS | MATHEMATICS, APPLIED | Hom - circle times adjunction

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 02/1992, Volume 144, Issue 1, pp. 189 - 212

It is shown how coupling to gauge fields can be used to explain the basic facts concerning holomorphic factorization of the WZW model of two dimensional...

CONFORMAL FIELD-THEORY | CONSTRUCTION | CURRENT-ALGEBRA | ZUMINO-WITTEN MODELS | QUANTIZATION | PHYSICS, MATHEMATICAL | 2 DIMENSIONS | 81T70 | 55N91 | 81T40 | 81R10

CONFORMAL FIELD-THEORY | CONSTRUCTION | CURRENT-ALGEBRA | ZUMINO-WITTEN MODELS | QUANTIZATION | PHYSICS, MATHEMATICAL | 2 DIMENSIONS | 81T70 | 55N91 | 81T40 | 81R10

Journal Article

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