Consistent gauge-invariant chiral theories in two dimensions

We employ a gauge-invariant point-splitting procedure to solve chiral gauge theories in two dimensions. We present an explicit solution of the chiral Schwinger model. The resulting theory is gauge-invariant and unitary containing a massless physical state. The method is generalizable to higher dimensions.     

Light-cone expansion for a product of two gauge-invariant currents in QCD

A light-cone expansion for a product of two gauge-invariant currents is obtained in quantum chromodynamics. The coefficient functions in the expansion are derived from the Green functions. This has resulted in the establishment of gauge invariance and in the possibility of estimating the coefficient functions in any order of the perturbation theory. A new way of presenting the most singular part of the expansion in gauge-invariant form has been invented.     

Hamiltonian formulation of string field theory

Witten's string field theory is quantized in the hamiltonian formalism. The constraints are solved and the hamiltonian is expressed in terms of only physical degrees of freedom. Thus, no Faddeev-Popov ghosts are introduced. Instead, the action contains terms of arbitrarily high order in the string functionals. Agreement with the standard results is demonstrated by an explicit calculation of the residues of the first few poles of the four-tachyon tree amplitude.     

On the relation between the gauge-covariant formulation of string field theories

By using the language of differential forms, which illuminates the structure of the gauge symmetries of string theories in a compact notational framework, we clarify the relation between the Neveu-West-Nicolai-Schwarz formulation of the gauge-covariant string field theories and that of Banks and Peskin.     

A manifestly gauge-invariant formulation of quantum electrodynamics

A manifestly gauge-invariant formulation of quantum electrodynamics is constructed in which the basic dynamical variables are physically observable quantities. The theory is relativistically covariant, because the structure of the Poincaré group is built into it from the beginning.     

Quark confinement and vortices in massive gauge-invariant QCD

Massive gauge-invariant QCD can support vortices (analogous to Nielsen-Olesen strings) of nearly finite classical action per unit area (there is a logarithmic short-distance singularity which is of little consequence). These vortices lead, in analogy to Abelian lattice-gauge theories, to confinement of fractionally charged quarks and color screening for gluons. In this paper, we make some qualitative remarks about the (Minkowski-space) dynamics which follows from this sort of confinement, studying not only $\text{q}\text{q}$ processes but also qqq processes. For the latter, the effective long-range vortex-induced interaction is approximately described as a sum of two-body potentials each of half the strength of the $\text{q}\text{q}$ potential (just as for the asymptotically free short-distance potentials), and linearly rising non-relativistically. There is an essential two-dimensionality about the confinement process which suppresses what would be the transverse degrees of freedom of strings joining quarks. A fully relativistic dynamics is given which is amenable to a simple phenomenological joining of long- and short-distance effects, with a running coupling constant such that g²(k) ～ k^?2 for small k. Spin-dependent potentials have no linearly-rising parts, and there are no strong Van der Waals forces. Little is said about gluon dynamics, except to point out the existence of rather massive hadronic glueballs and of (classically singular) instanton-like solutions which are screened at large distances.     

On the relation between many-color QCD and the free nambu string on the lattice

A lattice gauge model is proposed, interpolating between pure Wilson lattice gauge theory and the Nambu string as an additional parameter is varied. The one-matrix analogue model is exactly solved in the many-color limit and the corresponding phase diagram is obtained. Some consequences of the phase structure and conjectures concerning the four-dimensional model are presented.     

Microscopic formulation of black holes in string theory

In this report we review the microscopic formulation of the five-dimensional black hole of type IIB string theory in terms of the D1–D5 brane system. The emphasis here is more on the brane dynamics than on supergravity solutions. We show how the low energy brane dynamics, combined with crucial inputs from AdS/CFT correspondence, leads to a derivation of black hole thermodynamics and the rate of Hawking radiation. Our approach requires a detailed exposition of the gauge theory and conformal field theory of the D1–D5 system. We also discuss some applications of the AdS/CFT correspondence in the context of black hole formation in three dimensions by thermal transition and by collision of point particles.     

Possibility of constructing a gauge-invariant quantum formulation for nongauge classical theory

A general method is proposed for the construction of a gauge-invariant canonical quantum formulation for the gauge-invariant classical theory that depends on the set of parameters. The conditions for closure of the algebra of operators, which generate quantum gauge transformations, entails constraints on the parameters of the theory. The approach described is demonstrated by the example of a closed bosonic string, interacting with a background tachyonic field. The condition of a mass shell for the tachyon is reproduced within the framework of the proposed canonical formulation. Tomsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 18–24, June, 1997.     

Duality and the phases of massive gauge-invariant QCD

I discuss the phase structure of massive gauge invariant QCD (the gauged non-linear sigma model) using an operator formalism proposed by 't Hooft. The dual variables for this system are determined and the 't Hooft loop operator is constructed from these dual field variables. Its equal time commutation relations with the Wilson loop operator is explicitly verified. The system possesses two possible phases. In the semi-classical approximation (weak coupling), magnetic confinement as indicated by an area law for the expectation value of 't Hooft loops is observed. If above a certain critical coupling a condensate of vortices is formed, then the expectation value of the 't Hooft loop in the dilute vortex approximation shows a perimeter law indicating electric confinement.     

Locally gauge-invariant formulation of parastatistics

A locally gauge-invariant formulation of parastatistics, which is equivalent to a Yang-Mills gauge theory, is given, using a complex Clifford algebra (case of SU(N)) or a real Clifford algebra (case of SO(N)). In particular, for the SU(3) case, the gauged theory of para-Fermi quarks is equivalent to quantum chromodynamics.     

A nonlinear gauge-invariant field theory of leptons

A nonlinear, singularity-free, gauge-invariant field theory of leptons is proposed which incorporates the electron, muon, and tau. Fitting the known masses leads to a lepton radius of the order 10^–16 cm, which is within the experimental range. The model considered suggests the possibility of a hierarchy of short-lived lepton states. Properties of the electron such as its energy-density distribution, Reissner-Nordström repulsion, and the fact that gravitation cannot play a significant role in its construction are discussed. All singularity-free charged particle models constructed from fields which were investigated approached the limit charge²= mass² (in geometrical units) as gravitation became a dominant force. It is suggested that this property may have great generality. The interaction-energy integrals which bind the particles are seen to increase as the energy increases, and it is suggested that a similar mechanism may also be responsible for quark confinement in hadrons.On leave from the Department of Physics and Astronomy, University of Victoria, Victoria, B.C., Canada V8W 2Y2.