scholarly journals SEIBERG–WITTEN EQUATIONS FROM FEDOSOV DEFORMATION QUANTIZATION OF ENDOMORPHISM BUNDLE

2011 ◽  
Vol 08 (02) ◽  
pp. 411-428 ◽  
Author(s):  
MICHAŁ DOBRSKI
Keyword(s):  
Gauge Group ◽  
Deformation Quantization ◽  
Star Products ◽  
Recursive Methods ◽  
Fedosov Construction ◽  
Arbitrary Gauge

It is shown how Seiberg–Witten equations can be obtained by means of Fedosov deformation quantization of endomorphism bundle and the corresponding theory of equivalences of star products. In such setting, Seiberg–Witten map can be iteratively computed for arbitrary gauge group up to any given degree with recursive methods of Fedosov construction. Presented approach can be also considered as a generalization of Seiberg–Witten equations to Fedosov type of noncommutativity.

scholarly journals Ashtekar's variables for arbitrary gauge group

1992 ◽  
Vol 46 (6) ◽  
pp. R2279-R2282 ◽  
Author(s):  
Peter Peldán
Keyword(s):  
Gauge Group ◽  
Ashtekar's Variables ◽  
Arbitrary Gauge

Anomalies of Arbitrary Gauge Group and its Reduction Group, Einstein and Lorentz Anomalies

1985 ◽  
Vol 4 (1) ◽  
pp. 91-101 ◽  
Author(s):  
Kuang-Chao Chou ◽  
Han-Ying Guo ◽  
Ke Wu
Keyword(s):  
Gauge Group ◽  
Reduction Group ◽  
Arbitrary Gauge

scholarly journals On partition functions of refined Chern-Simons theories on S3

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
M.Y. Avetisyan ◽  
R.L. Mkrtchyan
Keyword(s):  
Partition Function ◽  
Gauge Group ◽  
Topological Strings ◽  
Simons Theory ◽  
Partition Functions ◽  
Coupling Constant ◽  
Sine Functions ◽  
Chern Simons ◽  
Arbitrary Gauge ◽  
Chern Simons Theory

Abstract We present a new expression for the partition function of the refined Chern-Simons theory on S3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero. Using this form of the partition function we show that the previously known Krefl-Schwarz representation of the partition function of the refined Chern-Simons theory on S3 can be generalized to all simply laced algebras.For all non-simply laced gauge algebras, we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of duality with the refined topological strings.

scholarly journals DEFORMATION QUANTIZATION OF CLASSICAL FIELDS

2001 ◽  
Vol 16 (14) ◽  
pp. 2533-2558 ◽  
Author(s):  
H. GARCÍA-COMPEÁN ◽  
J. F. PLEBAŃSKI ◽  
M. PRZANOWSKI ◽  
F. J. TURRUBIATES
Keyword(s):  
Gauge Theory ◽  
Deformation Quantization ◽  
The Other ◽  
Star Products ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Quantization Formalism ◽  
Classical Fields ◽  
Free Fields ◽  
Nontrivial Topology

We study the deformation quantization of scalar and Abelian gauge classical free fields. Stratonovich–Weyl quantizer, star products and Wigner functionals are obtained in field and oscillator variables. The Abelian gauge theory is particularly intriguing since the Wigner functional is factorized into a physical part and the other one containing the constraints only. Some effects of nontrivial topology within the deformation quantization formalism are also considered.

scholarly journals ON RELATION BETWEEN WEYL AND KONTSEVICH QUANTUM PRODUCTS: DIRECT EVALUATION UP TO THE ℏ3-ORDER

2001 ◽  
Vol 16 (10) ◽  
pp. 615-625 ◽  
Author(s):  
A. ZOTOV
Keyword(s):  
Deformation Quantization ◽  
Jacobi Identity ◽  
Star Product ◽  
Star Products ◽  
Moyal Product ◽  
Third Order ◽  
Direct Evaluation ◽  
The Third ◽  
Arbitrary Change ◽  
Poisson Bivector

In his celebrated paper Kontsevich has proved a theorem which manifestly gives a quantum product (deformation quantization formula) and states that changing coordinates leads to gauge equivalent star products. To illuminate his procedure, we make an arbitrary change of coordinates in the Weyl (Moyal) product and obtain the deformation quantization formula up to the third order. In this way, the Poisson bivector is shown to depend on ℏ and not to satisfy the Jacobi identity. It is also shown that the values of coefficients in the formula obtained follow from associativity of the star product.

scholarly journals Subalgebras with converging star products in deformation quantization: An algebraic construction forCPn

1996 ◽  
Vol 37 (12) ◽  
pp. 6311-6323 ◽  
Author(s):  
M. Bordemann ◽  
M. Brischle ◽  
C. Emmrich ◽  
S. Waldmann
Keyword(s):  
Deformation Quantization ◽  
Star Products ◽  
Algebraic Construction

scholarly journals The SUSY Yang–Mills plasma in a T-matrix approach

2015 ◽  
Vol 30 (24) ◽  
pp. 1550145 ◽  
Author(s):  
Gwendolyn Lacroix ◽  
Claude Semay ◽  
Fabien Buisseret
Keyword(s):  
Gauge Group ◽  
Bound States ◽  
Bound State ◽  
Lattice Data ◽  
Superstring Theory ◽  
Matrix Formulation ◽  
Yang Mills ◽  
Bound State Spectrum ◽  
T Matrix ◽  
Arbitrary Gauge

In this paper, the thermodynamic properties of [Formula: see text] supersymmetric Yang–Mills theory with an arbitrary gauge group are investigated. In the confined range, we show that identifying the bound state spectrum with a Hagedorn one coming from noncritical closed superstring theory leads to a prediction for the value of the deconfining temperature [Formula: see text] that agrees with recent lattice data. The deconfined phase is studied by resorting to a [Formula: see text]-matrix formulation of statistical mechanics in which the medium under study is seen as a gas of quasigluons and quasigluinos interacting nonperturbatively. Emphasis is put on the temperature range (1–5) [Formula: see text], where the interactions are expected to be strong enough to generate bound states. Binary bound states of gluons and gluinos are indeed found to be bound up to 1.4 [Formula: see text] for any gauge group. The equation of state is then computed numerically for [Formula: see text] and [Formula: see text], and discussed in the case of an arbitrary gauge group. It is found to be nearly independent of the gauge group and very close to that of nonsupersymmetric Yang–Mills when normalized to the Stefan–Boltzmann pressure and expressed as a function of [Formula: see text].

scholarly journals GENERALIZED INVERSION OF THE HOCHSCHILD COBOUNDARY OPERATOR AND DEFORMATION QUANTIZATION

2011 ◽  
Vol 08 (01) ◽  
pp. 99-106 ◽  
Author(s):  
A. V. BRATCHIKOV
Keyword(s):  
Deformation Quantization ◽  
Generalized Inverse ◽  
Poisson Manifolds ◽  
Star Products ◽  
Generalized Inversion ◽  
Coboundary Operator ◽  
Differential Complex

Using a derivative decomposition of the Hochschild differential complex we define a generalized inverse of the Hochschild coboundary operator. It can be applied for systematic computations of star products on Poisson manifolds.

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