Quantum Abelian Yang-Mills Theory on Riemannian Manifolds with Boundary

被引：3

作者：

Diaz-Marin, Homero G. ^{[1
]}

Oeckl, Robert ^{[2
]}

机构：

[1] Univ Michoacana, Fac Ciencias Fis Matemat, Ciudad Univ, Morelia 58060, Michoacan, Mexico

[2] Univ Nacl Autonoma Mexico, Ctr Ciencias Matemat, Morelia 58190, Michoacan, Mexico

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷

关键词：

Yang-Mills theory; TQFT; Riemannian manifolds; FIELD THEORY; GAUGE-THEORIES; SURFACES; FORMULATION; SPACE;

D O I：

10.3842/SIGMA.2018.105

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We quantize abelian Yang-Mills theory on Riemannian manifolds with boundaries in any dimension. The quantization proceeds in two steps. First, the classical theory is encoded into an axiomatic form describing solution spaces associated to manifolds. Second, the quantum theory is constructed from the classical axiomatic data in a functorial manner. The target is general boundary quantum field theory, a TQFT-type axiomatic formulation of quantum field theory.

引用

页数：31

共 28 条

[1]

[Anonymous], 1992, Oxford Mathematical Monographs

[2]

[Anonymous], ADV THEOR MATH PHYS

[3] QUANTUM FIELDS IN CURVED SPACE-TIMES [J].

ASHTEKAR, A ;

MAGNON, A .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1975, 346 (1646) :375-394

[4]

Atiyah M., 1988, PUBL MATH-PARIS, V68, P175, DOI [DOI 10.1007/BF02698547, 10.1007/BF02698547]

[5] THE YANG-MILLS EQUATIONS OVER RIEMANN SURFACES [J].

ATIYAH, MF ;

BOTT, R .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1983, 308 (1505) :523-615

[6] QUANTUM YANG-MILLS THEORY ON ARBITRARY SURFACES [J].

BLAU, M ;

THOMPSON, G .

INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1992, 7 (16) :3781-3806

[7]

Cattaneo A. S., 2015, MATH PHYS STUDIES, P275

[8] Perturbative Quantum Gauge Theories on Manifolds with Boundary [J].

Cattaneo, Alberto S. ;

Mnev, Pavel ;

Reshetikhin, Nicolai .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2018, 357 (02) :631-730

[9] Dirichlet to Neumann operator for Abelian Yang-Mills gauge fields [J].

Diaz-Marin, Homero G. .

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2017, 14 (11)

[10] General Boundary Formulation for n-Dimensional Classical Abelian Theory with Corners [J].

Diaz-Marin, Homero G. .

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2015, 11

← 1 2 3 →