scholarly journals Stochastic modulation of non-Abelian gauge potential. Spin-rotational relaxation

1994 ◽  
Vol 222 (3) ◽  
pp. 309-312 ◽  
Author(s):  
Yu.A. Serebrennikov ◽  
U.E. Steiner
Keyword(s):  
Gauge Potential ◽  
Rotational Relaxation ◽  
Abelian Gauge ◽  
Stochastic Modulation

scholarly journals TOPOLOGICALLY MASSIVE GAUGE THEORY: A LORENTZIAN SOLUTION

2007 ◽  
Vol 22 (16n17) ◽  
pp. 2961-2976 ◽  
Author(s):  
K. SAYGILI
Keyword(s):  
Field Equation ◽  
Gauge Theory ◽  
Field Strength ◽  
Gauge Transformation ◽  
Global Section ◽  
Gauge Potential ◽  
Abelian Gauge ◽  
Abelian Field ◽  
Hopf Map ◽  
Topological Mass

We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space [Formula: see text] by means of an SU (1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng2. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map [Formula: see text] including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of [Formula: see text] as a trivial [Formula: see text] bundle over the upper portion of the pseudosphere [Formula: see text] which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto [Formula: see text] using a global section of the solution on [Formula: see text]. Then we discuss the integration of the field equation using the Archimedes map [Formula: see text]. We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on [Formula: see text].

scholarly journals Nuclear spin-rotation interaction and non-Abelian gauge potential

1995 ◽  
Vol 84 (3) ◽  
pp. 627-632 ◽  
Author(s):  
Yu.A. Serebrennikov ◽  
U.E. Steiner
Keyword(s):  
Nuclear Spin ◽  
Spin Rotation ◽  
Gauge Potential ◽  
Abelian Gauge

scholarly journals On Spinor Representations in the Weyl Gauge Theory

1997 ◽  
Vol 12 (26) ◽  
pp. 1957-1968 ◽  
Author(s):  
B. M. Barbashov ◽  
A. B. Pestov
Keyword(s):  
Gauge Theory ◽  
Differential Forms ◽  
Current Source ◽  
Gauge Potential ◽  
Spinor Representation ◽  
Abelian Gauge ◽  
Cartan Torsion ◽  
Gauge Space ◽  
Spinor Current ◽  
Spinor Representations

A spinor current-source is found in the Weyl non-Abelian gauge theory which does not contain the abstract gauge space. It is shown that the searched spinor representation can be constructed in the space of external differential forms and it is a 16-component quantity for which a gauge-invariant Lagrangian is determined. The connection between the Weyl non-Abelian gauge potential and the Cartan torsion field, and the problem of a possible manifestation of the considered interactions are considered.

scholarly journals Wilson loop and Wilczek-Zee phase from a non-Abelian gauge field

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Seiji Sugawa ◽  
Francisco Salces-Carcoba ◽  
Yuchen Yue ◽  
Andika Putra ◽  
I. B. Spielman
Keyword(s):  
Gauge Field ◽  
Wilson Loop ◽  
Berry Phase ◽  
Einstein Condensate ◽  
Gauge Potential ◽  
Abelian Gauge ◽  
Dimensional Parameter ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Aharonov Bohm

AbstractQuantum states can acquire a geometric phase called the Berry phase after adiabatically traversing a closed loop, which depends on the path not the rate of motion. The Berry phase is analogous to the Aharonov–Bohm phase derived from the electromagnetic vector potential, and can be expressed in terms of an Abelian gauge potential called the Berry connection. Wilczek and Zee extended this concept to include non-Abelian phases—characterized by the gauge-independent Wilson loop—resulting from non-Abelian gauge potentials. Using an atomic Bose–Einstein condensate, we quantum-engineered a non-Abelian SU(2) gauge field, generated by a Yang monopole located at the origin of a 5-dimensional parameter space. By slowly encircling the monopole, we characterized the Wilczek–Zee phase in terms of the Wilson loop, that depended on the solid-angle subtended by the encircling path: a generalization of Stokes’ theorem. This observation marks the observation of the Wilson loop resulting from a non-Abelian point source.

ANATOMY OF EINSTEIN'S THEORY: ABELIAN DECOMPOSITION OF GENERAL RELATIVITY

2012 ◽  
Vol 07 ◽  
pp. 116-147 ◽  
Author(s):  
Y. M. CHO
Keyword(s):  
Gauge Theory ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Gauge Potential ◽  
Abelian Gauge ◽  
Maximal Abelian Subgroup ◽  
Metric Tensor ◽  
Lorentz Gauge ◽  
Abelian Decomposition

Treating Einstein's theory as a gauge theory of Lorentz group, we decompose the gravitational connection (the gauge potential of Lorentz group) Γμ into the restricted connection of the maximal Abelian subgroup of Lorentz group and the valence connection which transforms covariantly under Lorentz gauge transformation. With this decomposition we show that the Einstein's theory can be decomposed into the restricted part made of the restricted connection which has the full Lorentz gauge invariance and the valence part made of the valence connection which plays the role of gravitational source of the restricted gravity. We show that there are two different Abelian decomposition of Einstein's theory, the light-like (or null) decomposition and the non light-like (or non-null) decomposition. In this decomposition the role of the metric gμν is replaced by a four-index metric tensor gμν which transforms covariantly under the Lorentz group, and the metric-compatibility condition ∇αgμν = 0 of the connection is replaced by the gauge and generally covariant condition [Formula: see text]. The decomposition shows the existence of a restricted theory of gravitation which has the full general invariance but is much simpler and has less physical degrees of freedom than Einstein's theory. Moreover, it tells that the restricted gravity can be written as an Abelian gauge theory, which implies that the graviton can be described by a massless spin-one field.

Topology of QCD vacuum and color confinement

2002 ◽  
Vol 80 (7) ◽  
pp. 745-754 ◽  
Author(s):  
H C Chandola ◽  
H C Pandey ◽  
H Nandan
Keyword(s):  
Unit Length ◽  
Cylindrical Symmetry ◽  
Gauge Potential ◽  
Dynamical Structure ◽  
Field Equations ◽  
Abelian Gauge ◽  
Qcd Vacuum ◽  
Color Confinement ◽  
Restricted Form ◽  
Magnetic Symmetry

Using the magnetic symmetry structure of non-Abelian gauge theories of the Yang–Mills type, the mathematical foundation of dual chromodynamics in fiber-bundle form is discussed. The dual gauge potential in its restricted form is constructed in terms of magnetic vectors on global sections, which has been shown to lead the dual dynamics between topological charges and color isocharges. Constructing the Lagrangian for such dual theory, the dynamical breaking of magnetic symmetry by an effective potential is shown to push the QCD vacuum in a confining phase. The dynamical structure of the theory is investigated by deriving the field equations associated with the confining phase. The associated flux-tube structure responsible for the confinement is analyzed by computing the asymptotic string solutions of the field equations under cylindrical symmetry. Using the confining part of the dual restricted Lagrangian, the finite string energy per unit length is calculated and its implications on color confinement are discussed. PACS Nos.: 11.38Aw, 14.80Hv, 11.30Jw

Topological Lifshitz Transition and Novel Edge States Induced by Non-Abelian SU(2) Gauge Field on Bilayer Honeycomb Lattice

2021 ◽  
Author(s):  
Wen-Xiang Guo ◽  
Wu-Ming Liu
Keyword(s):  
Secular Equation ◽  
Universality Class ◽  
Gauge Potential ◽  
Honeycomb Lattice ◽  
The Novel ◽  
Winding Number ◽  
Edge States ◽  
Abelian Gauge ◽  
Fermi Surfaces ◽  
Lifshitz Transition

Abstract We investigate the SU(2) gauge effects on bilayer honeycomb lattice thoroughly. We discover a topological Lifshitz transition induced by the non-Abelian gauge potential. Topological Lifshitz transitions are determined by topologies of Fermi surfaces in the momentum space. Fermi surface consists of N = 8 Dirac points at π-flux point instead of N = 4 in the trivial Abelian regimes. A local winding number is defined to classify the universality class of the gapless excitations. We also obtain the phase diagram of gauge fluxes by solving the secular equation. Furthermore, the novel edge states of biased bilayer nanoribbon with gauge fluxes are also investigated.

Sign in / Sign up

Export Citation Format

Share Document