non-Abelian Quantum Field Theory Research Articles

The model for non-Abelian field topology for the multilayer fractional quantum anomalous Hall device

From the recent empirical discovery of the quantum anomalous Hall effect (QAHE), the interaction of the particle with spin–orbit coupling (SOC) plays an essential role in the cause of the QAHE, which includes three terms: external, internal, and chiral symmetric terms. Then, the non-Abelian quantum field theory was adopted to analyze and prove the conjecture on the causes that can lead to the fractional quantum Hall effect (FQHE). The spontaneously topological chiral symmetry breaking is the main contribution to the FQHE, which also includes two terms: the hopping of sublattice and Coulomb energy by the interaction of many-body particles. More generally, this exciton possesses an intermediate characteristic between the Wannier regimes and displays a peculiar two-dimensional wavefunction in the three-dimensional FQHE states. Finally, a bilayer three-dimensional model is proposed to implement the FQHE on the lattice by incorporating ferromagnetic dopants into three-dimensional topological insulative thin films. This study theoretically predicts the FQHE on the basis of other reports that have experimentally verified the rationality of the proposed model in magnetic topological insulators.

Quantum field theory in phase space

The tilde conjugation rule in thermofield dynamics, equivalent to the modular conjugation in a [Formula: see text]-algebra, is used to develop unitary representations of the Poincaré group, where the Hilbert space has the phase space content, a symplectic Hilbert space. The state is described by a quasi-amplitude of probability, which is a sort of wave function in phase space, associated with the Wigner function. The quantum field theory in phase space is then constructed, including the quantization rules for the Klein–Gordon and the Dirac fields, the derivation of the electrodynamics in phase space and elements of a relativistic quantum kinetic theory. Towards a physical interpretation of the theory, propagators are associated with the corresponding Wigner functions. The Feynman rules follow accordingly with vertices similar to those of usual non-Abelian quantum field theories.

Worldline colour fields and non-Abelian quantum field theory

In the worldline approach to non-Abelian field theory the colour degrees of freedom of the coupling to the gauge potential can be incorporated using worldline “colour” fields. The colour fields generate Wilson loop interactions whilst Chern-Simons terms project onto an irreducible representation of the gauge group. We analyse this augmented worldline theory in phase space focusing on its supersymmetry and constraint algebra, arriving at a locally supersymmetric theory in superspace. We demonstrate canonical quantisation and the path integral on S1for simple representations of SU(N).

Energy problem in the Einstein–Cartan theory

The Einstein–Cartan–Kibble–Sciama equations are presented in the following form: the codifferential of the differential of a tetrad is the tetrad current with the ordinary conservation law. This form is an analogue of the form for non-Abelian quantum field theory. A canonical gauge tetrad is proposed for six two-directions with extreme sectional Riemannian curvature. A nonlocal conservation law for the contracted Bianchi identities is presented. The physical and geometric meaning of the Gibbons-Hawking Lagrangian and surface term are proposed. Application of the tetrad current concept is illustrated for the Schwarzschild and de Sitter metrics.

Supersymmetry: Early Roots That Did Not Grow

This paper is about early roots of supersymmetry, as found in the literature from 1940s and early 1950s. There were models where the power of “partners” in alleviating divergences in quantum field theory was recognized. However, other currently known remarkable features of supersymmetry, such as its role in the extension of the Poincaré group, were not known. There were, of course, no supersymmetric nonabelian quantum field theories in those days.

Lattice QCD at finite temperature and density

QCD at finite temperature and density is becoming increasingly important for various experimental programmes, ranging from heavy ion physics to astro-particle physics. The non-perturbative nature of non-abelian quantum field theories at finite temperature leaves lattice QCD as the only tool by which we may hope to come to reliable predictions from first principles. This requires careful extrapolations to the thermodynamic, chiral and continuum limits in order to eliminate systematic effects introduced by the discretization procedure. After an introduction to lattice QCD at finite temperature and density, its possibilities and current systematic limitations, a review of present numerical results is given. In particular, plasma properties such as the equation of state, screening masses, static quark free energies and spectral functions are discussed, as well as the critical temperature and the QCD phase structure at zero and finite density.

CURRENT ALGEBRA IN THE PATH INTEGRAL FRAMEWORK

In this letter we describe an approach to the current algebra based on the path integral formalism. We use this method for Abelian and non-Abelian quantum field theories in (1+1) and (2+1) dimensions and the correct expressions are obtained. Our results show the independence of the regularization of the current algebras.

ANOMALIES AT FINITE TEMPERATURE AND DENSITY

Chiral anomalies for Abelian and non-Abelian quantum field theories at finite temperature and density (FTFD) are analyzed in detail in both imaginary and real time (IT and RT) formalisms. IT and RT triangle diagrams and IT functional methods (à la Fujikawa) are used at FTFD. The vector anomaly (the one regarding the lepton and baryon numbers) in the Weinberg–Salam theory, for an arbitrary number of fermion families, is also treated using IT functional methods at FTFD. In all cases, the expressions for the FTFD anomalies (as functions of the corresponding quantities) turn out to be identical to those at zero temperature and density, thereby extending previous results by various authors for the finite temperature and zero density case. Moreover, the independence of anomalies from temperature and density is shown to be consistent, at least in the Abelian case, with the analytic continuation from the IT formulation to the RT one.

Quantum holonomy and link invariants.

It is shown that, in a non-Abelian quantum field theory without an anomaly and broken symmetry, the set of all matrix-valued quantum holonomies $\ensuremath{\Psi}[\ensuremath{\gamma}]\ensuremath{\equiv}〈P\mathrm{exp}(i\ensuremath{\oint}\ensuremath{\int}{\ensuremath{\gamma}}^{}\mathrm{Adx})〉$ for closed contours $\ensuremath{\gamma}$ form a commutative semigroup, whereas $〈P\mathrm{exp}(i\ensuremath{\int}{\ensuremath{\alpha}}^{}\mathrm{Adx})〉=0$ for every open path $\ensuremath{\alpha}$. The eigenvalues $\ensuremath{\Phi}[\ensuremath{\gamma}]$ of $\ensuremath{\Psi}[\ensuremath{\gamma}]$ are classified according to the irreducible representations of the gauge group. In an irreducible representation $\ensuremath{\rho}$, $\mathrm{Tr}(\ensuremath{\Psi}[\ensuremath{\gamma}])=\ensuremath{\Phi}[\ensuremath{\gamma}]\mathrm{Tr}({1}_{\ensuremath{\rho}})$ is a Wilson loop. This equation solves a puzzle in the relation between link invariants and Wilson loops in the Chern-Simons theory in three dimensions when the gauge group is $\mathrm{SU}(N|N)$, and provides useful insight in understanding nonperturbative quantum chromodynamics as a string theory.