Chiral bosonization in non-abelian gauge theories

The chiral bosonization in non-abelian gauge theories is described starting directly from the QCD functional. For a given mass scale Λ, QCD may be equivalently represented by colour chiral fields, gauge fields and high energy fermions. The effective action for colour chiral fields may admit the existence of a colour skyrmion-boson with baryon number 2/3.     

Local observables in non-abelian gauge theories

Labelling of the physical states of a non-abelian gauge theory on a lattice in terms of local observables is considered. The labelling is in terms of local color electric field observables and (separately) local color magnetic field observables. Matter fields are also included. Non-local observables required when space is multiply connected, are specified. The non-abelian version of Stokes' theorem is considered. Relevance to the continuum theory is discussed in detail.     

Electric-magnetic duality in non-abelian gauge theories

The duality transformation of the vacuum expectation value of the operator which creates magnetic vortices (the 't Hooft loop operator in the Higgs phase), is performed in the radial gauge (x_uA_u^a(x) = 0). It is found that in the weak coupling region (small g) of a pure Yang-Mills theory the dual operator creates electric vortices whose strength is $\text{1}\text{g}$. The theory is self-dual in this region, and the effective coupling of the dual Lagrangian is $\text{1}\text{g}$. (It is self-dual also in the extreme strong coupling region.) Thus the above duality transformation reduces to electric-magnetic duality where the electric field in the 't Hooft loop operators transforms into a magnetic field in the dual operator. In a spontaneously broken gauge theory these results are valid only within the region where the vortices (or the monopoles) are concentrated, or in directions of the algebra space of unbroken symmetry, as self-duality holds only for this subset of fields. Noting that the 't Hooft loop operator project into the subspace of these field configurations we find that it is an electric-magnetic duality for the spontaneously broken theory as well. In the strong coupling region a strong coupling expansion in powers $\text{1}\text{g}$ is suggested.     

Infra-red behaviour in non-abelian gauge theories

The leading infra-red divergent corrections to massive quark scattering in quantum chromodynamics are very simple to fourth order. A simple dependence on the effective coupling constant is conjectured to hold to all orders.     

Charge definition in non-abelian gauge theories

Conserved gauge-invariant electric and magnetic charges are defined for non-abelian gauge theories in terms of the asymptotic symmetries of the field configurations. They are expressed as flux integrals. Illustrations include the magnetic charge of the 't Hooft-Polyakov monopole and the electric and magnetic charges of the Julia-Zee dyon.     

The Schwinger mechanisms in non-abelian gauge theories

An alternative to the Higgs-Kibble mechanism for the formulation of spontaneously broken gauge theories has been recently proposed. It is shown how the new procedures can be generalised to the case when non-Abelian gauge groups are present.     

Forbidden ghost states in non-abelian gauge theories

A two-particle state consisting of isotriplets of scalar and zero-helicity gluons and of Faddeev—Popov ghosts is identified as being exterior to the physical subspace for a Yang—Mills theory in a manifestly covariant gauge.     

Integration over instanton parameters in non-abelian gauge theories

The measure for integrating over instanton degrees of freedom in the euclidean functional integrals for non-abelian gauge theories is discussed within the context of the construction of Atiyah, Drinfeld, Hitchin and Manin, and evaluated for the SU(2) two-instanton solution of 't Hooft.     

A path-space formula for non-abelian gauge theories

A functional integral representation is obtained for a semigroup in an indefinite metric space giving the dynamics of a cutoff Yang-Mills theory in space-time dimensions greater than two. The Fadde'av-Popov formula is shown to arise as a stochastic integral in the Feynman gauge.     

Broken conformal ward identities in non-abelian gauge theories

Integrated broken conformal Ward identities for non-abelian gauge theories are derived. There exist anomalous terms linked to the ones in the Callan-Symanzik equations. Also there is a gauge dependent term that can be predicted classically and a new term involving Faddeev-Popov ghosts. These two terms cannot be neglected asymptotically relative to the other terms for gauge variant Greens functions.     

Renormalization of non-abelian gauge theories in curved space-time

We use indirect, renormalization group arguments to calculate the gravitational counterterms needed to renormalize an interacting non-abelian gauge theory in curved space-time. This method makes it straightforward to calculate terms in the trace anomaly which first appear at high order in the coupling constant, some of which would need a 4-loop calculation to find directly. The role of gauge invariance in the theory is considered, and we discuss briefly the effect of using coordinate-dependent gauge-fixing terms. We conclude by suggesting possible applications of this work to models of the very early universe.     

Vortices and quark confinement in non-abelian gauge theories

It is shown that finite-length vortices in an SU(n) Nielsen-Olesen model require explicit introduction of monopoles, which are confined in multiples of n by the Meissner effect. The model therefore possesses a natural explanation of quark confinement.     

Operator quantization of non-abelian gauge theories in a completely fixed axial gauge

A consistent quantization of chromodynamics in a completely fixed axial gauge is carried out by using the Dirac bracket quantization procedure. The main results are: The translation of Dirac brackets into equal-time commutators is possible, without ambiguities, because of the absence of ordering problems. All equal-time commutators are compatible with constraints and gauge conditions holding as strong operator relations. All equal-time commutators are compatible with chromoelectric, chromomagnetic, and fermionic fields vanishing at spatial infinity. The colored gauge potentials A^0,a, A^1,a, and A^2,a are seen to develop a physically significant, although pure gauge, behavior at x³ = ± ∞, as required by the presence of a nontrivial topological content. Poincaré invariance is satisfied without introducing in the Hamiltonian “extra” quantum mechanical potentials. The determinant of the Faddeev-Popov matrix does not depend upon the field variables.     

Topology of the gauge condition and new confinement phases in non-abelian gauge theories

The gauge-fixing constraint in a gauge field theory is crucial for understanding both short-distance and long-distance behavior of non-abelian gauge field theories. We define what we call “non-propagating” gauge conditions such as the unitary gauge and “approximately non-propagating” or renormalizable gauge conditions, and study their topological properties. By first fixing the non-abelian part of the gauge ambiguity we find that SU(N) gauge theories can be written in the form of abelian gauge theories with N ? 1 fold multiplicity enriched with magnetic monopoles with certain magnetic charge combinations. Their electric chargesare governed by the instanton angle θ.If θ is continuously varied from 0 to 2π and a confinement mode is assumed for some θ, then at least one phase-transition must occur. We speculate on the possibility of new phases: e.g., “oblique confinement,” where $\text{θ ? π}$, and explain some peculiar features of this mode. In principle there may be infinitely many such modes, all separated by phase transition boundaries.     

Superalgebras of non-abelian gauge theories in the Manifestly-Covariant canonical formalism

Zeitschrift für Physik C Particles and Fields -     

Infrared properties of the glue propagator in non-abelian gauge theories

In a pure Yang-Mills theory, the Dyson equation for the gluon propagator is studied in the infrared regime, under the assumption that, as in QED, only those parts of the proper gluon vertex functions determined by the Ward identities are relevant. The calculations are all carried out in the axial gauge. With a number of simplifying assumptions the resulting integral equation for the gluon propagator can be solved in the IR regime. The solution displays a power singularity in the IR for the renormalized coupling constant g(q²).     

Surface integrals and monopole charges in non-abelian gauge theories

We derive a formula which gives all the magnetic charges (topological invariants) of a monopole in the adjoint representation of a non-abelian gauge theory in terms of surface integrals at infinity.Supported in part by the National Science Foundation under Grant No. PHY 79-16812Junior Fellow, Harvard University Society of Fellows