scholarly journals Singularity-Free Canonical Theory of Gauge Fields in the Axial Gauge

1982 ◽  
Vol 67 (3) ◽  
pp. 965-976 ◽  
Author(s):  
N. Nakanishi
Keyword(s):  
Gauge Fields ◽  
Canonical Theory ◽  
Axial Gauge

scholarly journals Dirac, Majorana, Weyl in 4D

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 111
Author(s):  
Loriano Bonora ◽  
Roberto Soldati ◽  
Stav Zalel
Keyword(s):  
Feynman Diagram ◽  
The Other ◽  
Gauge Fields ◽  
Majorana Fermions ◽  
Diagram Method ◽  
Axial Gauge ◽  
Definition Of ◽  
Weyl Fermions

This is a review of some elementary properties of Dirac, Weyl and Majorana spinors in 4D. We focus in particular on the differences between massless Dirac and Majorana fermions, on one side, and Weyl fermions, on the other. We review in detail the definition of their effective actions, when coupled to (vector and axial) gauge fields, and revisit the corresponding anomalies using the Feynman diagram method with different regularisations. Among various well known results we stress in particular the regularisation independence in perturbative approaches, while not all the regularisations fit the non-perturbative ones. As for anomalies, we highlight in particular one perhaps not so well known feature: the rigid relation between chiral and trace anomalies.

scholarly journals Magnetism and anomalous transport in the Weyl semimetal PrAlGe: possible route to axial gauge fields

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Daniel Destraz ◽  
Lakshmi Das ◽  
Stepan S. Tsirkin ◽  
Yang Xu ◽  
Titus Neupert ◽  
...  
Keyword(s):  
Anomalous Transport ◽  
Gauge Fields ◽  
Axial Gauge ◽  
Weyl Semimetal

scholarly journals Fermionic dualities with axial gauge fields

2020 ◽  
Vol 102 (11) ◽  
Author(s):  
Adolfo G. Grushin ◽  
Giandomenico Palumbo
Keyword(s):  
Gauge Fields ◽  
Axial Gauge

scholarly journals Tunable axial gauge fields in engineered Weyl semimetals: semiclassical analysis and optical lattice implementations

2D Materials ◽  
2018 ◽  
Vol 5 (2) ◽  
pp. 024001 ◽  
Author(s):  
Sthitadhi Roy ◽  
Michael Kolodrubetz ◽  
Nathan Goldman ◽  
Adolfo G Grushin
Keyword(s):  
Optical Lattice ◽  
Gauge Fields ◽  
Semiclassical Analysis ◽  
Axial Gauge ◽  
Weyl Semimetals

Unification of Gauge Forces and Gravity using Tangled Vortex Knots and Entanglement Dynamics

2020 ◽  
Author(s):  
Mrittunjoy Guha Majumdar
Keyword(s):  
Field Theory ◽  
Short Range ◽  
Gauge Fields ◽  
Entanglement Dynamics ◽  
Unified Field Theory ◽  
Linear Dynamics ◽  
Unified Field ◽  
The Standard Model ◽  
Theory Of Everything ◽  
The Continuum

In this paper, the statistics of excitation-tangles in a postulated background ideal-superfluid field is studied. The structure of the Standard Model is derived in terms of tangle vortex-knots and soliton. Gravity is observed in terms of torsion and curvature in the continuum. In this way, non-linear dynamics and excitations give rise to a unified field theory as well as a Theory of Everything. As a result of this unification, spacetime and matter are shown to be fundamentally equivalent, while gauge fields arise from reorientation and excitations of the the fundamental underlying field. Finally, the equivalence of topological and quantum entanglement is explored to posit a theory of everything in terms of long- and short-range entanglement between fundamental quantum units (bits) of information.

scholarly journals Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Yi Yang ◽  
Bo Zhen ◽  
John D. Joannopoulos ◽  
Marin Soljačić
Keyword(s):  
Quantum Hall ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Spin Orbit ◽  
Abelian Gauge ◽  
Experimental Realization ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Necessary And Sufficient

Abstract The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin–orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

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