Gauge group and gauge transformation in the continual theory of defects

1994 ◽  
Vol 71 (1) ◽  
pp. 2281-2287
Author(s):  
K. L. Malyshev
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Continual Theory

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

scholarly journals On the gauge symmetries of the spinning particle

2014 ◽  
Vol 92 (5) ◽  
pp. 411-414
Author(s):  
N. Kiriushcheva ◽  
S.V. Kuzmin ◽  
D.G.C. McKeon
Keyword(s):  
Simple Model ◽  
Gauge Group ◽  
Gauge Transformation ◽  
Group Structure ◽  
Simple Algebra ◽  
Direct Examination ◽  
Spinning Particle ◽  
Gauge Transformations ◽  
Gauge Symmetries ◽  
New Variables

We reconsider the gauge symmetries of the spinning particle by a direct examination of the Lagrangian using a systematic procedure based on the Noether identities. It proves possible to find a set of local bosonic and fermionic gauge transformations that have a simple gauge group structure, which is a true Lie algebra, both for the massless and massive case. This new fermionic gauge transformation of the “position” and “spin” variables in the action decouples from that of the “einbein” and “gravitino”. It is also possible to redefine the fields so that this simple algebra of commutators of the gauge transformations can be derived directly starting from the Lagrangian written in these new variables. We discuss a possible extension of our analysis of this simple model to more complicated cases.

scholarly journals VACUUM STRUCTURE OF GAUGE THEORY ON LATTICE WITH TWO PARALLEL PLAQUETTES ACTION

1999 ◽  
Vol 14 (25) ◽  
pp. 1753-1761 ◽  
Author(s):  
K. FARAKOS ◽  
G. K. SAVVIDY
Keyword(s):  
Monte Carlo ◽  
Gauge Theory ◽  
Monte Carlo Simulations ◽  
Gauge Group ◽  
Gauge Transformation ◽  
Spin System ◽  
Three Dimensional ◽  
Vacuum State ◽  
Lattice Gauge ◽  
Dimensional Cube

We perform Monte–Carlo simulations of a lattice gauge system with an action which contains two parallel plaquettes. The action is defined as a product of gauge group variables over two parallel plaquettes belonging to a given three-dimensional cube. The peculiar property of this system is that it has strong degeneracy of the vacuum state inherited from the corresponding gonihedric Z2 gauge spin system. These vacua are well separated and cannot be connected by a gauge transformation. We measure different observables in these vacua and compare their properties.

CLASSICAL YANG-MILLS-DIRAC SYSTEM WITH CONFORMAL SYMMETRY: A GEOMETRICAL ANALYSIS

1994 ◽  
Vol 09 (37) ◽  
pp. 3431-3444 ◽  
Author(s):  
J.-P. ANTOINE ◽  
L. DABROWSKI ◽  
I. MAHARA
Keyword(s):  
Minkowski Space ◽  
Gauge Group ◽  
Gauge Transformation ◽  
Conformal Symmetry ◽  
Conformal Group ◽  
Dirac System ◽  
Geometrical Analysis ◽  
Yang Mills ◽  
Dirac Equations

We consider classical Yang-Mills-Dirac equations on Minkowski space, with gauge group SU(2), and look for solutions invariant (up to a gauge transformation) under a four-dimensional subgroup of the conformal group. In each of the four different cases that we analyze, the equations admit non-Abelian solutions, but these cannot be obtained analytically. In addition, some cases admit solutions with chiral spinors that may be physically relevant. All these solutions are singular.

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 N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

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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