Gauge fields on a lattice. II. Gauge-invariant Ising model

1975 ◽  
Vol 11 (8) ◽  
pp. 2098-2103 ◽  
Author(s):  
R. Balian ◽  
J. M. Drouffe ◽  
C. Itzykson
Keyword(s):  
Ising Model ◽  
Gauge Fields ◽  
Gauge Invariant

A BRST APPROACH TO MASSLESS GAUGE FIELDS OF INTEGER SPIN

1990 ◽  
Vol 05 (16) ◽  
pp. 3247-3264
Author(s):  
THOMAS DOMEIJ
Keyword(s):  
Wave Function ◽  
Symmetric Tensor ◽  
Flat Space ◽  
Gauge Fields ◽  
Arbitrary Integer ◽  
Massless Particles ◽  
Gauge Invariant ◽  
Function Representation ◽  
Integer Spin ◽  
Do So

We present a method based on BRST techniques for how to obtain the conventional equations for symmetric tensor gauge fields which describe free massless particles of arbitrary integer spin. We do so in a wave function representation in a flat space-time background of any dimension. A fairly straightforward way is also presented for how to obtain the equations from a gauge invariant Lagrangian of the form [Formula: see text].

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 ABELIAN PROJECTION AND STUDIES OF GAUGE-VARIANT QUANTITIES IN THE LATTICE QCD WITHOUT GAUGE FIXING

1996 ◽  
Vol 11 (13) ◽  
pp. 1081-1093 ◽  
Author(s):  
SERGEI V. SHABANOV
Keyword(s):  
Lattice Qcd ◽  
Continuum Limit ◽  
Gluon Propagator ◽  
Lorentz Invariance ◽  
Gauge Condition ◽  
Gauge Fields ◽  
Gauge Invariant ◽  
Dynamical Reduction ◽  
Gauge Fixing ◽  
The Continuum

We suggest a new (dynamical) Abelian projection of the lattice QCD. It contains no gauge condition imposed on gauge fields so that Gribov copying is avoided. Configurations of gauge fields that turn into monopoles in the Abelian projection can be classified in a gauge-invariant way. In the continuum limit, the theory respects the Lorentz invariance. A similar dynamical reduction of the gauge symmetry is proposed for studies of gauge-variant correlators (like a gluon propagator) in the lattice QCD. Though the procedure is harder for numerical simulations, it is free of gauge-fixing artifacts, like the Gribov horizon and copies.

scholarly journals Einstein–Yang–Mills theory: gauge invariant charges and linearization instability

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Emel Altas ◽  
Ercan Kilicarslan ◽  
Bayram Tekin
Keyword(s):  
General Relativity ◽  
Perturbation Theory ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Gauge Fields ◽  
Gauge Invariant ◽  
Yang Mills ◽  
First Order ◽  
Flat Spacetime ◽  
First Order Perturbation

AbstractWe construct the gauge-invariant electric and magnetic charges in Yang–Mills theory coupled to cosmological general relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser (Phys Lett B 116:259–263, 1982). For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part. In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.

scholarly journals Chern-Simons-Antoniadis-Savvidy Forms and Non-Abelian Anomaly

2019 ◽  
Vol 8 (1) ◽  
pp. 11-15
Author(s):  
Suhaivi Hamdan ◽  
Erwin Erwin ◽  
Saktioto Saktioto
Keyword(s):  
Field Strength ◽  
Gauge Transformation ◽  
Integral Form ◽  
Gauge Fields ◽  
Gauge Invariant ◽  
Time Coordinate ◽  
Form Analysis ◽  
Yang Mills ◽  
Chern Simons ◽  
Gauge Variation

Kuat medan tensor yang ditransformasikan secara homogen terhadap perluasan transformasi gauge memenuhi bentuk sifat invarian gauge. Analisa invarian gauge dalam bantuk integeralnya memperlihatkan hubungan dengan koordinat ruang-waktu yang menunjukan bentuk baru dari topologi Lagrangian. Sifat invarian dari bentuk Pontryagin-Chern terhadap kuat medan tensor non-Abelian dan lemma Poincare dapat digunakan untuk mengkontruksi bentuk ChSAS yang menunjukan sifat quasi-invarian dibawah transformasi gauge. Artikel ini bertujuan untuk membuktikan bahwa kuat medan tensor Yang-Mills dari bentuk ChSAS memilik variasi gauge anomali non-Abelian seperti pada bentuk Chern-Simons. Integrasi bentuk ChSAS menghasilkan dimensi-4, 6 dan 8 variasi gauge genap dan memperlihatkan hubungan dengan bentuk Chern-Simons dimensi-3 dan 5 untuk variasi gauge ganjil. Bentuk ChSAS memperlihatkan variabel lebih kompleks yang menujukan sifat berosilasi. Tensors field strength transformation homogeneously to extend gauge transformation fulfilling charateristic gauge invariant form. Analysis gauge invariant in integral form shows corresponding with space-time coordinate that prove new topology Lagrangians form. Furthermore invariant charateristic of Pontryagin-Chern to non-Abelian tensor gauge fields and lemma Poincare used to contruct ChSAS forms which shows quasi-inavriant under gauge transformation. This paper aims to prove Yang-Mills tensor gauge field of ChSAS forms has variation non-Abelian anomaly like Chern-Simons forms. The integration ChSAS forms resulted 4, 6 and 8-dimensional even gauge variation which also correspond 3 and 5-dimensional odd gauge variation Chern-Simons forms. The ChSAS forms also showed complex variable and osilation.  Keywords: Pontryagin-Chern, Kuat medan tensor non-Abelian, Chern-Simans-Antoniadis-Savvidy, Anomali Non-Abelian.

scholarly journals A scalable realization of local U(1) gauge invariance in cold atomic mixtures

Science ◽  
2020 ◽  
Vol 367 (6482) ◽  
pp. 1128-1130 ◽  
Author(s):  
Alexander Mil ◽  
Torsten V. Zache ◽  
Apoorva Hegde ◽  
Andy Xia ◽  
Rohit P. Bhatt ◽  
...  
Keyword(s):  
Large Scale ◽  
Gauge Theories ◽  
Spatial Dimension ◽  
Gauge Fields ◽  
Quantum Computers ◽  
Computational Techniques ◽  
Quantum Devices ◽  
Gauge Invariant ◽  
Quantum Simulator ◽  
Elementary Building

In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.

scholarly journals (Four) Dual Plaquette 3D Ising Models

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 633
Author(s):  
Desmond A. Johnston ◽  
Ranasinghe P. K. C. M. Ranasinghe
Keyword(s):  
Ising Model ◽  
High Temperature Phase ◽  
Transverse Spin ◽  
Global Symmetry ◽  
Temperature Phase ◽  
Gauge Invariant ◽  
Dual Formulation ◽  
Quantum Version ◽  
Ising Spins ◽  
Toric Code

A characteristic feature of the 3 d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3 d plaquette Ising and the X-Cube model is similar to that between the 2 d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2 d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3 d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3 d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin–Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.

scholarly journals EXTENSION OF CHERN–SIMONS FORMS AND NEW GAUGE ANOMALIES

2014 ◽  
Vol 29 (03n04) ◽  
pp. 1450027 ◽  
Author(s):  
IGNATIOS ANTONIADIS ◽  
GEORGE SAVVIDY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field ◽  
Gauge Invariant ◽  
Higher Rank ◽  
Gauge Anomalies ◽  
Chern Simons

We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher-rank field-strength tensors. The integrals of these forms over the corresponding space–time coordinates provides new topological Lagrangians. With these Lagrangians one can define gauge field theories which generalize the Chern–Simons quantum field theory. We also present explicit expressions for the potential gauge anomalies associated with the tensor gauge fields and classify all possible anomalies that can appear in lower dimensions.

The Collective Excitations in High-Tc Superconductors

2001 ◽  
Vol 15 (28n30) ◽  
pp. 4013-4016 ◽  
Author(s):  
I. Kanazawa
Keyword(s):  
Collective Excitations ◽  
Collective Modes ◽  
Gauge Fields ◽  
High Tc Superconductors ◽  
Gauge Invariant ◽  
High Tc ◽  
Underdoped Cuprates

It is proposed that the collective modes around the hole for k~(π,0) in underdoped cuprates might correspond to massive gauge fields [Formula: see text], which are introduced by the gauge-invariant carrieron (GIC) model.

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