Exotic Yang–Mills Dilaton Gauge Theories

An exotic class of nonlinear p-form non-Abelian gauge theories is studied, arising from the most general allowed covariant deformation of linear Abelian gauge theory for a set of massless 1-form fields and 2-form fields in four dimensions. These theories combine a Chapline–Manton type coupling of the 1-forms and 2-forms, along with a Yang–Mills coupling of the 1-forms, a Freedman–Townsend coupling of the 2-forms, and an extended Freedman–Townsend type coupling between the 1-forms and 2-forms. It is shown that the resulting theories have a geometrically interesting dual formulation that is equivalent to an exotic Yang–Mills dilaton theory involving a nonlinear sigma field. In particular, the nonlinear sigma field couples to the Yang–Mills 1-form field through a generalized Chern class 4-form term.     

Chaotic Quantization of Classical Gauge Fields

We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges, and calculate Planck's constant from quantities defined in the underlying classical gauge theory.     

Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity

We analyze locally anisotropic configurations modeled by anholonomic frames with associated nonlinear connections in general relativity, affine–Poincarè and/or de Sitter gauge gravity and Kaluza–Klein theories. A suitable geometrical formalism for theories with higher order anisotropies and non compactified extra dimensions is introduced. We give a mostly self–containing review of some aspects of gauge models of gravity and discuss their anholonomic generalizations and the conditions of equivalence with the Einstein gravity in arbitrary dimensions. New classes of cosmological solutions describing Friedmann–Robertson–Walker like universes with resolution ellipsoid or torus symmetry.     

Classification of Gauge Orbit Types for SU(n)-Gauge Theories

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang–Mills theory with the Chern–Simons term proposed by Asorey et al. is discussed.     

Nonrelativistic Wave Equations with Gauge Fields

We illustrate a metric formulation of Galilean invariance by constructing wave equations with gauge fields. It consists of expressing nonrelativistic equations in a covariant form, but with a five-dimensional Riemannian manifold. First we use the tensorial expressions of electromagnetism to obtain the two Galilean limits of electromagnetism found previously by Le Bellac and Lévy-Leblond. Then we examine the nonrelativistic version of the linear Dirac wave equation. With an Abelian gauge field we find, in a weak field approximation, the Pauli equation as well as the spin—orbit interaction and a part reminiscent of the Darwin term. We also propose a generalized model involving the interaction of the Dirac field with a non-Abelian gauge field; the SU(2) Hamiltonian is given as an example.     

Gauge Theory Gravity with Geometric Calculus

A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein’s principles of equivalence and general relativity are replaced by gauge principles asserting, respectively, local rotation and global displacement gauge invariance. A new unitary formulation of Einstein’s tensor illuminates long-standing problems with energy–momentum conservation in general relativity. Geometric calculus provides many simplifications and fresh insights in theoretical formulation and physical applications of the theory.     

Vacuum-Induced Abelian and Non-Abelian Gauge Potentials in CavityQuantum Electrodynamics

Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems. In this paper, we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics. It is shown that a non-Abelian gauge potential is achieved only for a single atom, whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble. More importantly, two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted. The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes, which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.     

Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge Theory

In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.     

规范场和爱因斯坦

文章讨论的主题是现代非亚贝尔规范场的理论思想．文章说明了这个理论思想是承传、推广和拓展了爱因斯坦的物理思想、目标和原则．规范场理论把爱因斯坦后半生努力奋斗而未能达到的目标提到现实，更加迫近和部分地圆了爱因斯坦的梦想。     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of thevertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

Two-Particle Irreducible Effective Action in Gauge Theories

The goal of this paper is to develop the formalism of the two-particle irreducible (2PI) (G. Baym (1962). Physical Review 127, 1391; H. D. Dahmen and G. Jona Lasino (1962). Nuovo Cimento A 52, 807; C. de Dominicis and P. Martin (1964). Journal of Mathematical Physics 5, 14; J. Luttinger and J. Ward (1960). Physical Review 118, 1417; B. Vanderheyden and G. Baym (1998). Journal of Statistical Physics 98, 843; B. Vanderheyden and G. Baym (2000). In Progress in Nonequilibrium Green's Functions, World Scientific, Singapore). (or Cornwall–Jackiw–Tomboulis (CJT) (J. Cornwall, R. Jackiw, and E. Tomboulis (1974). Physical Review D 10, 2428; U. Kraemmer and A. Rebhan (2004). Reports on Progress in Physics 67, 351; R. Norton and J. Cornwall (1975). Annals of Physics 91, 106) effective action (EA) in a way appropiate to its application to nonequilibrium gauge theories. We hope this review article will stimulate new work into this field.     

Twisted Gauge Theories

Gauge theories on a space-time that is deformed by the Moyal–Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant quantities. The connection will be enveloping algebra valued in a particular representation of the Lie algebra. This gives rise to additional fields, which couple only weakly via the deformation parameter θ and reduce in the commutative limit to free fields. Consistent field equations that lead to conservation laws are derived and some properties of such theories are discussed.     

Quaternion-Octonion Analyticity for Abelian and Non-Abelian Gauge Theories of Dyons

Einstein-Schrödinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex, quaternion and octonion spaces in internal gauge groups are shown to describe the consistent field equations and generalized Dirac equation of dyons. It is also shown that quaternion and octonion representations extend the so-called unified theory of gravitation and electromagnetism to the Yang-Mill’s fields leading to two SU(2) gauge theories of internal spaces due to the presence of electric and magnetic charges on dyons.     

Gauge bosons at zero and finite temperature

Gauge theories of the Yang–Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang–Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.     

Radiative Corrections to Non-Abelian Gauge Theory in Homogeneous Self-Dual Backgrounds

We study the Euclidean version of non-Abelian gauge theories in homogeneous background fields with due regard of negative and zero modes of the gauge field kernel. For general gauge group and general background but without external currents we prove a relation between the propagators belonging to different gauge fixings. Specializing to a self-dual homogeneous background we derive nonperturbatively the propagators. Next we calculate the matter field contribution to the renormalized polarization tensor using a modified dimensional regularization scheme. We prove the validity of a modified Ward identity.     

All-order results for soft and collinear gluons

Some general features and some recent developments concerning the resummation of long-distance singularities in QCD and in more general non-Abelian gauge theories are reviewed. The field-theoretical tools of the trade are emphasized, with the focus mostly on the exponentiation of infra-red and collinear divergences in amplitudes, which underlies the resummation of large logarithms in the corresponding cross-sections. Some recent results concerning the conformal limit, notably the case of N = 4 superymmetric Yang-Mills theory are also described.      

Topological order and conformal quantum critical points

We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as quantum critical points separating these phases. All of the ground-state equal-time correlators of these theories are equal to correlation functions of a local two-dimensional classical model. The critical points therefore exhibit a time-independent form of conformal invariance. These theories characterize the universality classes of two-dimensional quantum dimer models and of quantum generalizations of the eight-vertex model, as well as and non-abelian gauge theories. The conformal quantum critical points are relatives of the Lifshitz points of three-dimensional anisotropic classical systems such as smectic liquid crystals. In particular, the ground-state wave functional of these quantum Lifshitz points is just the statistical (Gibbs) weight of the ordinary two-dimensional free boson, the two-dimensional Gaussian model. The full phase diagram for the quantum eight-vertex model exhibits quantum critical lines with continuously varying critical exponents separating phases with long-range order from a deconfined topologically ordered liquid phase. We show how similar ideas also apply to a well-known field theory with non-Abelian symmetry, the strong-coupling limit of 2+1-dimensional Yang–Mills gauge theory with a Chern–Simons term. The ground state of this theory is relevant for recent theories of topological quantum computation.     

Renormalizable N = 2 Supersymmetric Gauge Theories

Renormalizable supersymmetric models of matter multiplets coupled to a Yang Mills multiplet are studied in the conventional N = 2 superspace. It is found that a consistent formulation of the Feynman rules in superspace requires the introduction of a compensator superfield in the matter sector. If the quantization is performed within the background superfield approach, the use of the compensator is confined to the quantum corrections. The ensuing ghost structure is analyzed and the non-renormalization beyond one-loop is demonstrated. We report an N = 2 superfield calculation of the one-loop β-function via the supercurrent anomaly and thereby derive as a byproduct the finiteness criterion for N = 2 non-Abelian gauge theories.     

Gauge/string duality in confining theories

This is the content of a set of lectures given at the “XIII Jorge André Swieca Summer School on Particles and Fields”, Campos do Jordão, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non‐Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D–branes at singularities and wrapping D–branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non‐perturbative phenomena in non‐Abelian gauge theories as seen from supergravity.     

Gauge dependence of gravitational correction to running of gauge couplings

Recently an interesting idea has been put forward by Robinson and Wilczek that the incorporation of quantized gravity in the framework of Abelian and non-Abelian gauge theories results in a correction to the running of gauge coupling and, as a consequence, increase the grand unification scale and asymptotic freedom. In this Letter it is shown by explicit calculations that this correction depends on the choice of gauge.