Gauge theories in higher dimensions: Linear relations for gauge fields, integrability conditions, spherical symmetry in eight dimensions

2005 ◽  
pp. 306-310
Author(s):  
J. Nuyts
Keyword(s):  
Spherical Symmetry ◽  
Gauge Theories ◽  
Higher Dimensions ◽  
Gauge Fields ◽  
Linear Relations ◽  
Integrability Conditions

scholarly journals U(∞) GAUGE THEORY FROM HIGHER DIMENSIONS

1992 ◽  
Vol 07 (24) ◽  
pp. 6025-6037
Author(s):  
KIYOSHI SHIRAISHI
Keyword(s):  
Gauge Theory ◽  
Dimensional Reduction ◽  
Gauge Theories ◽  
Higher Dimensions ◽  
Gauge Fields ◽  
Degenerate Metric ◽  
Infinite Dimensional ◽  
Higher Derivative ◽  
Exact Symmetry

We show that classical U (∞) gauge theories can be obtained from the dimensional reduction of a certain class of higher-derivative theories. In general, the exact symmetry is attained in the limit of degenerate metric; otherwise, the infinite-dimensional symmetry can be taken as spontaneously broken. Monopole solutions are examined in the model for scalar and gauge fields. An extension to gravity is also discussed.

SPECTRAL FLOW OF HERMITIAN WILSON–DIRAC OPERATOR AND THE INDEX THEOREM IN ABELIAN GAUGE THEORIES ON FINITE LATTICES

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1943-1950 ◽  
Author(s):  
T. FUJIWARA
Keyword(s):  
Dirac Operator ◽  
Gauge Theories ◽  
Index Theorem ◽  
Two Dimensions ◽  
Gauge Fields ◽  
Continuous Family ◽  
Spectral Flow ◽  
Abelian Gauge ◽  
Characteristic Structure ◽  
Finite Lattices

The spectral flows of the hermitian Wilson-Dirac operator for a continuous family of abelian gauge fields connecting different topological sectors are shown to have a characteristic structure leading to the lattice index theorem. The index of the overlap Dirac operator is shown to coincide with the topological charge for a wide class of gauge field configurations. It is also argued that in two dimensions the eigenvalue spectra for some special but nontrivial background gauge fields can be described by a set of universal polynomials and the index can be found exactly.

STATISTICS OF 2D SOLITONS

1992 ◽  
Vol 07 (11) ◽  
pp. 2589-2600 ◽  
Author(s):  
LEE BREKKE ◽  
TOM D. IMBO
Keyword(s):  
Sigma Models ◽  
Gauge Theories ◽  
Higher Dimensions ◽  
Fractional Statistics ◽  
Topological Solitons ◽  
Multiply Connected ◽  
Target Manifold ◽  
Definition Of ◽  
Spin And Statistics ◽  
Nonlinear Sigma Models

We study the inequivalent quantizations of (1 + 1)-dimensional nonlinear sigma models with space manifold S1 and target manifold X. If X is multiply connected, these models possess topological solitons. After providing a definition of "spin" and "statistics" for these solitons and demonstrating a spin-statistics correlation, we give various exmples where the solitons can have exotic statistics. In some of these models, the solitons may obey a generalized version of fractional statistics called ambistatistics. The relevance of these 2D models to the statistics of vortices in (2 + 1)-dimensional spontaneously broken gauge theories is also discussed. We close with a discussion concerning the extension of our results to higher dimensions.

On the stability of gauge fields in higher dimensions

1990 ◽  
Vol 19 (3) ◽  
pp. 237-243 ◽  
Author(s):  
Zhong-Qi Ma ◽  
D. H. Tchrakian
Keyword(s):  
Higher Dimensions ◽  
Gauge Fields ◽  
The Stability

BLOCKSPIN AND MULTIGRID FOR STAGGERED FERMIONS IN NON-ABELIAN GAUGE FIELDS

1992 ◽  
Vol 03 (01) ◽  
pp. 121-147 ◽  
Author(s):  
T. KALKREUTER ◽  
G. MACK ◽  
M. SPEH
Keyword(s):  
Gauge Theories ◽  
Free Action ◽  
Real Space ◽  
Gauge Fields ◽  
Group Approach ◽  
Abelian Gauge ◽  
Staggered Fermions ◽  
Real Space Renormalization Group ◽  
Renormalization Group Approach ◽  
Definition Of

We discuss blockspins for staggered fermions, i. e. averaging and interpolation procedures which are needed in a real space renormalization group approach to gauge theories with staggered fermions and in a multigrid approach to the computation of gauge covariant propagators. The discussion starts from the requirement that the symmetries of the free action should be preserved by the blocking procedure in the limit of a pure gauge. A definition of an averaging kernel as a solution of a gauge covariant eigenvalue equation is proposed, and the properties of a corresponding interpolation kernel are examined in the light of general criteria for good choices of blockspins. Some results of multigrid computations of bosonic propagators in an SU(2) gauge field in 4 dimensions are also presented.

GAUGE-INVARIANT QUANTISATION OF CHIRAL GAUGE THEORIES

1990 ◽  
Vol 05 (03) ◽  
pp. 175-182 ◽  
Author(s):  
T. D. KIEU
Keyword(s):  
Path Integral ◽  
Gauge Theories ◽  
Berry Phase ◽  
Integral Functional ◽  
Gauge Fields ◽  
Quantum Mechanical ◽  
Gauge Invariant ◽  
Normal Ordering ◽  
Schwinger Model ◽  
Holomorphic Representation

The path-integral functional of chiral gauge theories with background gauge potentials are derived in the holomorphic representation. Justification is provided, from first quantum mechanical principles, for the appearance of a functional phase factor of the gauge fields in order to maintain the gauge invariance. This term is shown to originate either from the Berry phase of the first-quantized hamiltonians or from the normal ordering of the second-quantized hamiltonian with respect to the Dirac in-vacuum. The quantization of the chiral Schwinger model is taken as an example.

scholarly journals Finite field-dependent BRST–anti-BRST transformations: Jacobians and application to the Standard Model

2016 ◽  
Vol 31 (20n21) ◽  
pp. 1650111 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Standard Model ◽  
Gauge Theories ◽  
Landau Gauge ◽  
Gauge Fields ◽  
Nontrivial Solutions ◽  
Abelian Gauge ◽  
The Standard Model ◽  
Field Dependent ◽  
Quantum Action ◽  
General Gauge

We continue our research[Formula: see text] and extend the class of finite BRST–anti-BRST transformations with odd-valued parameters [Formula: see text], [Formula: see text], introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST–anti-BRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST–anti-BRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST–anti-BRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRST–anti-BRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters [Formula: see text] is obtained, providing the equivalence of path integrals in any 3-parameter [Formula: see text]-like gauges. The Gribov–Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in [Formula: see text]-like gauges, in a gauge-independent way using field-dependent BRST–anti-BRST transformations, and in [Formula: see text]-like gauges using transverse-like non-Abelian gauge fields.

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