The Gauge Group of a Principal Bundle

1994 ◽  
pp. 79-86
Author(s):  
Dale Husemoller
Keyword(s):  
Gauge Group ◽  
Principal Bundle

scholarly journals CONTINUOUS TRACE C*-ALGEBRAS, GAUGE GROUPS AND RATIONALIZATION

2009 ◽  
Vol 01 (03) ◽  
pp. 261-288 ◽  
Author(s):  
JOHN R. KLEIN ◽  
CLAUDE L. SCHOCHET ◽  
SAMUEL B. SMITH
Keyword(s):  
Gauge Group ◽  
Metric Space ◽  
Principal Bundle ◽  
Rational Homotopy ◽  
Compact Metric Space ◽  
Gauge Groups ◽  
C Algebra ◽  
C Algebras ◽  
Rational Cohomology ◽  
Rational Homotopy Type

Let ζ be an n-dimensional complex matrix bundle over a compact metric space X and let Aζdenote the C*-algebra of sections of this bundle. We determine the rational homotopy type as an H-space of UAζ, the group of unitaries of Aζ. The answer turns out to be independent of the bundle ζ and depends only upon n and the rational cohomology of X. We prove analogous results for the gauge group and the projective gauge group of a principal bundle over a compact metric space X.

scholarly journals Gauge groups and bialgebroids

2021 ◽  
Vol 111 (6) ◽  
Author(s):  
Xiao Han ◽  
Giovanni Landi
Keyword(s):  
Gauge Group ◽  
Galois Extension ◽  
Principal Bundle ◽  
Module Structure ◽  
Crossed Module ◽  
Gauge Groups ◽  
Quantum Sphere ◽  
Hopf Algebroid ◽  
Commutative Algebras

AbstractWe study the Ehresmann–Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the gauge groupoid of a classical principal bundle. We show that the gauge group of the noncommutative bundle is isomorphic to the group of bisections of the bialgebroid, and we give a crossed module structure for the bisections and the automorphisms of the bialgebroid. Examples include: Galois objects of Taft algebras, a monopole bundle over a quantum sphere and a not faithfully flat Hopf–Galois extension of commutative algebras. For each of the latter two examples, there is in fact a suitable invertible antipode for the bialgebroid making it a Hopf algebroid.

On p-local homotopy types of gauge groups

2014 ◽  
Vol 144 (1) ◽  
pp. 149-160 ◽  
Author(s):  
Daisuke Kishimoto ◽  
Akira Kono ◽  
Mitsunobu Tsutaya
Keyword(s):  
Gauge Group ◽  
Homotopy Type ◽  
Principal Bundle ◽  
Dimensional Sphere ◽  
Gauge Groups ◽  
Homotopy Types

The aim of this paper is to show that the p-local homotopy type of the gauge group of a principal bundle over an even-dimensional sphere is completely determined by the divisibility of the classifying map by p. In particular, for gauge groups of principal SU(n)-bundles over S2d for 2 ≤ d ≤ p − 1 and n ≤ 2p − 1, we give a concrete classification of their p-local homotopy types.

scholarly journals SPHERICALLY SYMMETRIC SOLUTIONS IN MULTIDIMENSIONAL GRAVITY WITH THE SU(2) GAUGE GROUP AS THE EXTRA DIMENSIONS

2002 ◽  
Vol 11 (05) ◽  
pp. 685-701
Author(s):  
V. DZHUNUSHALIEV ◽  
H.-J. SCHMIDT ◽  
O. RURENKO
Keyword(s):  
Boundary Conditions ◽  
Gauge Group ◽  
Principal Bundle ◽  
Gauge Potential ◽  
Spherically Symmetric ◽  
Multidimensional Gravity ◽  
Symmetry Center ◽  
Symmetric Metrics ◽  
Gravitational Equations ◽  
Spacetime Foam

The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations depends on the boundary conditions of the "SU(2) gauge potential" (off-diagonal metric components) at the symmetry center and on the type of symmetry (symmetrical or antisymmetrical) of these potentials. In the chosen range of the boundary conditions it is shown that there are two types of solutions: wormhole-like and flux tube. The physical application of such kind of solutions as quantum handles in a spacetime foam is discussed.

GAUGE GROUP AND PHASES OF SUPERFLUID 3He

1978 ◽  
Vol 39 (C6) ◽  
pp. C6-50-C6-52
Author(s):  
V. L. Golo ◽  
M. I. Monastyrsky
Keyword(s):  
Gauge Group ◽  
Superfluid 3He

Phase space of mechanical systems with a gauge group

1991 ◽  
Vol 161 (2) ◽  
pp. 13-75 ◽  
Author(s):  
Lev V. Prokhorov ◽  
Sergei V. Shabanov
Keyword(s):  
Phase Space ◽  
Gauge Group ◽  
Mechanical Systems

scholarly journals Exploring the landscape of CHL strings on Td

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anamaría Font ◽  
Bernardo Fraiman ◽  
Mariana Graña ◽  
Carmen A. Núñez ◽  
Héctor Parra De Freitas
Keyword(s):  
Gauge Group ◽  
Moduli Space ◽  
Dynkin Diagram ◽  
Fundamental Groups ◽  
Computer Algorithms ◽  
Abelian Gauge ◽  
Reduced Rank ◽  
Systematic Exploration ◽  
String Models ◽  
Simply Connected

Abstract Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

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