Transposition-invariant equations for the unified field theory

We discuss, within the framework provided by a recently developed variational method, transposition-invariant field equations for unified field theories. Systems that are, in addition, invariant under Weyl-type gauge transformations or lambda transformations are derived. It is found that in a weak field limit two of the systems contain the equations of general relativity and the covariant Maxwell equations for a charge-free region.     

Abelian Ward identity from the background field dependence of the effective action

The dependence of the effective action for gauge theories on the background field obeys an exact identity. We show that for Abelian theories the Ward identity follows from the more general background field identity. This observation is relevant for the formulation of effective actions with an infrared cutoff since the solution of exact flow equations must obey an anomalous Ward identity.     

Fermion condensation in the field strength approach to non-abelian yang-mills theories

Within the field strength approach to Yang-Mills theories the fermionic sectors of gauge theories are bosonized for the SU(2) and SU(3) gauge group. The emerging effective meson theories are studied in the tree approximation. In this approximation the original minimal gauge coupling of the quarks to gluons is rendered into an effective local four-fermion interaction with non-trivial Lorentz and gauge structure. The Schwinger-Dyson equation is solved in the strong coupling limit and the quark condensates and constituent masses are evaluated.     

Generalized Noether theorems in canonical formalism for field theories and their applications

A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained.     

The background field method and the linearization problem for Poisson manifolds

The background field method (BFM) for the Poisson sigma model (PSM) is studied as an example of the application of the BFM technique to open gauge algebras. The relationship with Seiberg–Witten maps arising in non-commutative gauge theories is clarified. It is shown that the implementation of the BFM for the PSM in the Batalin–Vilkovisky formalism is equivalent to the solution of a generalized linearization problem (in the formal sense) for Poisson structures in the presence of gauge fields. Sufficient conditions for the existence of a solution and a constructive method to derive it are presented.     

Structure of elementary particles in a nonlinear field theory

Characteristics of nonlinear gauge-invariant singularity-free field theories of elementary particles are discussed. It is shown that the electromagnetic field, in conjunction with a scalar field which is required for gauge invariance, provides a potential mechanism for the creation of the spin and magnetic moment of the particle, in addition to its mass and charge.     

Bianchi identities and the automatic conservation of energy-momentum and angular momentum in general-relativistic field theories

Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar model. The Poincaré gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article.     

Propagators for lattice gauge theories in a background field

We prove regularity and decay properties for propagators connected with the renormalization group method in lattice gauge theories. These propagators depend on an external gauge field configuration, called a background field.Research supported in part by the National Science Foundation under Grant PHY-82-0369     

Skew-symmetric tensor gauge field theory dynamically realized in the QCD U(1) channel

It is shown that, in order for the U(1) Goldstone boson to decouple from the physical sector, a third rank skew-symmetric tensor gauge field theory has to be realized dynamically by asymptotic fields of bound states in QCD. The abelian-like gauge invariance of this tensor gauge theory is just a realization of the original QCD gauge (BRS) invariance which hence assures the decoupling of all the bound-state modes by the “quarlet mechanism”. A general procedure for fixing gauges in such types of skew-symmetric tensor gauge theories is also presented.     

Two-loop background field calculations for arbitrary background fields

The ultraviolet divergences of two-loop vacuum graphs in the presence of an arbitrary background field are determined for four-dimensional φ⁴ and gauge theories on flat space. Dimensional regularisation is employed and the heat kernel is used to analyse the short-distance singularities in the products of propagators, in the presence of the background field, that occur for two-loop graphs. The single and double poles in ? = 4 ? d are determined in a concise fashion, giving known results for the β function. A procedure for determining the remaining finite parts in terms of explicit convergent integrals in four dimensions is described.     

Point-splitting analysis of commutator anomalies in non-abelian chiral gauge theories

A gauge covariant point-splitting regularisation is employed to calculate different anomalous commutators in four dimensional chiral gauge theories. For an external gauge field the fixed time anomalous commutator of the gauge group generators is seen to violate the Jacobi identity. The cohomological prediction can be confirmed provided the electric fields do not commute. Other commutators like the current-current and current-electric field are consistent with the Bjorken-Johnson-Low (BJL) derivation.     

Instantons and monopoles in Yang-Mills gauge field theories

This is a survey article on instantons and monopoles and is intended for those who have no prior knowledge of Yang-Mills gauge field theories. With minimal amount of physical motivation and mathematical apparatus, the basic field equations and their solutions, wherever known, are presented. Particular emphasis is put on those problems which are as yet unsolved.     

Ultraviolet stability of three-dimensional lattice pure gauge field theories

We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on results of the previous papers on renormalization group method for lattice gauge theories.Work partially supported by the National Science Foundation under Grant PHY 82-03669 and DMS 84-01989On leave of absence, Postal address: Department of Physics, Harvard University, Cambridge, MA 02138, USA     

Mean fields and self consistent normal ordering of lattice spin and gauge field theories

Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived.     

Boundary conditions in quantum field theories

Several interesting and important quantum field theories must contain the coupling constant in the boundary conditions. The theories considered include quantum electrodynamics of spin-1/2 fermions and gauge field theories.     

New boundary conformal field theories indexed by the simply laced Lie algebras

We consider the field theory of N massless bosons which are free except for an interaction localized on the boundary of their (1+1)-dimensional world. The boundary action is the sum of two pieces: a periodic potential and a coupling to a uniform abelian gauge field. Such models arise in open-string theory and dissipative quantum mechanics, and possibly in edge state tunneling in the fractional quantized Hall effect. We explicitly show that conformal invariance is unbroken for certain special choices of the gauge field and the periodic potential. These special cases are naturally indexed by semi-simple, simply laced Lie algebras. For each such algebra, we have a discrete series of conformally invariant theories where the potential and gauge field are conveniently given in terms of the weight lattice of the algebra. We compute the exact boundary state for these theories, which explicitly shows the group structure. The partition function and correlation functions are easily computed using the boundary state result.     

Quantum gravity,field theory and signatures of noncommutative spacetime

A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what extent noncommutative gauge theories may be regarded as gauge theories of gravity. UV/IR mixing is explained in detail and we describe its relations to renormalization, to gravitational dynamics, and to deformed dispersion relations in models of quantum spacetime of interest in string theory and in doubly special relativity. We also discuss some potential experimental probes of spacetime noncommutativity.     

Mean field for topological excitations of Z2 spin and gauge models

A mean field approach for the disorder parameters is obtained by applying the duality transformation to a Bethe-Peierls type approximation which involves finite clusters. Applications to Z₂ models with global and local symmetries are discribed and systematical improvements are obtained by considering clusters of increasing size. For gauge theories a manifestly gauge-invariant mean field is obtained: the phenomenology of the spontaneous symmetry breaking is reproduced by considering the suitable order parameters and the standard mean field for gauge theories in four dimensions is reinterpreted.     

Propagating modes in gauge field theories of gravity

The particle content of the most general quadratic field Lagrangian for Poincaré gauge field theories is examined and restrictions on the coupling constants for absence of ghosts and tachyons are derived. Our final field Lagrangian contains three coupling constants, the usual gravitational constant in front of an Einsteinian part and two other constants governing pure torsion terms.     

Nonconservation of gauge singlet charge operators in light cone field theories

A light cone gauge theory is considered which possesses one or more conserved currents. It is shown quite generally that the usual associated charge operator is not conserved whenever the current transforms as a vector in Minkowski space. This includes the case of a conserved current which is a singlet under the operations of any group associated with a coupling to a non-abelian gauge field. As one application of this result one infers that there are no conserved flavor charge operators in the light cone formulation of quantum chromodynamics.