An explicit example of a tumbling gauge theory

We present a class of two-dimensional models with a non-abelian gauge symmetry. In one model with gauge symmetry is dynamically broken by a fermion bilinear condensate in a $\text{1}\text{n}$ expansion. We discuss the differences between a dynamical and elementary Higgs mechanism due to the presence of a non-abelian axial anomaly.     

Covariant quantization of gauge fields without Gribov ambiguity

Recently Parisi and Wu proposed a method of quantizing gauge fields whereby euclidean expectation values are obtained by relaxation to equilibrium of a stochastic process depending on an artificial fifth time parameter. In the present work the equilibrium distribution is determined directly, without reference to the artificial time, by a stationary condition which is an eigenfunction equation in the euclidean Hilbert space. The solution has a perturbative expansion which appears renormalizable by naive power counting. Because of gauge freedom, a free dimensionless gauge parameter appears in the theory although no gauge condition such as ? · A = 0 is imposed.     

Renormalization of Wilson operators in gauge theories

The operators in a Wilson expansion are not in general multiplicatively renormalized in non-Abelian gauge theories. This is because of the renormalization of the gauge transformations themselves. Renormalized fields may be defined, which have the old gauge transformations. Alternatively, a special choice of gauge may be made, in which the gauge transformations are unchanged on renormalization. In any case, one gauge invariant factor appears in the renormalization of the Wilson operators.     

Treatment of the classical relativistic string in any orthonormal gauge

It is shown that a certain set of gauge invariant functions are, for an appropriate choice of a parameter on which they depend, equal to the Fourier components of the classical relativistic string in any orthonormal gauge. These variables are natural generalizations of the classical DDF operators recently introduced by Goddard, Hanson and Ponzano. The Poisson algebra of the relativistic string in any orthonormal gauge (including the proper time gauge) is written down. Application to quantization is briefly discussed.     

Merging gauge coupling constants without grand unification

The merging of the running coupling constants of the weak, strong, and electromagnetic fields does not require the unification of these gauge fields at high energy. It can, in fact, be the property of a general fermionic system in which gauge bosons are not fundamental.     

A new gauge theory without an elementary photon

A gauge theory is formulated in two spatial dimensions different from all gauge theories previously known. Unlike quantum electrodynamics in such a space there does not exist an elementary photon in the model, even though a bound state having appropriate quantum numbers can be induced for weak coupling to a spinor field. Particularly noteworthy is the fact that despite the demonstrated covariance of the theory, there is an anomaly (i.e., noncanonical) term in the spatial transformation of the charge bearing field.     

Quantum gauge models without (classical) Higgs mechanism

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein–Glaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(–Englert–Brout–Guralnik–Hagen–Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.     

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.     

Renormalization of a gauge theory in a nonlinear gauge

We discuss renormalization of an O(3) gauge model with the gauge fixing term given by ℒ_g.f.=-1/ζ|(∂_μ-igA ₃ ^μ )W ^+μ|²-(1/2α)(∂A ³)². We utilize earlier results on the general theory of renormalization of gauge theories in quadratic gauges to prove multiplicative renormalizability of the theory together with a subtractive renormalization of gauge fixing and ghost terms. We show that this model has a double BRS invariance and that it is preserved under renormalization.     

Spontaneous symmetry breaking of Slavnov symmetry A restriction on the gauge condition

It is shown that the condition of vanishing vacuum expectation value of the gauge operator, using a gauge-fixing term quadratic in this operator, does not necessarily follow from the Slavnov identity, due to a possible spontaneous breakdown of the Slavnov symmetry. For a consistent renormalization such a condition may have to be imposed order by order in perturbation theory, depending on the choice of the gauge. This restriction on non-singular gauges is particularly relevant for the discussion of the spontaneously broken realizations of the gauge symmetry.     

On the hyperbolicity of Einstein's and other gauge field equations

It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of reduced propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable gauge source functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system.Work supported by a Heisenberg-Fellowship of the Deutsche Forschungsgemeinschaft     

Supergravity as a gauge theory of supersymmetry

In a new approach to supergravity we consider the gauge theory of the 14-dimensional supersymmetry group. The theory is constructed from 14×4 gauge fields, 4 gauge fields being associated with each of the 14 generators of supersymmetry. The gauge fields corresponding to the 10 generators of the Poincaré subgroup are those normally associated with general relativity, and the gauge fields corresponding to the 4 generators of supersymmetry transformations are identified with a Rarita-Schwinger spinor. The transformation laws of the gauge fields and the Lagrangian of lowest degree are uniquely constructed from the supersymmetry algebra. The resulting action is shown to be invariant under these gauge transformations if the translation associated field strength vanishes. It is shown that the second-order form of the action, which is the same as that previously proposed, is invariant without constraint.     

Global aspects of fixing the gauge in the Polyakov string and Einstein gravity

It is shown that there exists a possible obstruction to a continuous global gauge choice in the Polyakov string theory and in four dimensional Einstein gravity. In many circumstances this obstruction results in no global gauge existing in these two theories.Work supported by the Science and Engineering Research Council     

QCD calculations in the light-cone gauge

The non-singlet quark structure function is calculated in the leading logarithm approximation in an axial gauge with n² = 0, the light-cone gauge. The choice n² = 0 leads to a simple identity for loop integrals involving the extra n · k denominators. We compare the results graph by graph with both Feynman gauge QCD and a scalar gluon theory. The leading diagrams are the same “rainbow” diagrams as for the case of the scalar theory.The techniques are also applied to quark-quark scattering at large transverse momentum. The leading diagrams have the same dressed ladder-form factor structure.     

On gauge invariance and perturbative calculations in quantum chromodynamics

It is possible to regularize infra-red divergences of QCD by giving a mass to the gluon in such a way that the Becchi-Rouet-Stora invariance of the action is preserved. This regularization allows straightforward extension of dispersive techniques to the computation of radiative corrections to on-shell processes in QCD. Problems of gauge dependence, however, exist: care must be taken in the choice of the expansion parameter and only physically meaningful processes are gauge independent, e.g., cross sections summed over all final degenerate states.     

The double dimensional regularization and gauge theories without ghosts

A new version of dimensional regularization is introduced as calculational technique for the recently proposed gauge theory without ghosts. The method is applied to Yang-Mills theory.     

The question of gauge dependence of transition probabilities in quantum mechanics: Facts,myths and misunderstandings

We show that, in terms of physical observables, transition probabilities in quantum mechanics can be calculated in a truly gauge invariant way, i.e., independent of the choice of gauge and that recent arguments for the preference of a particular gauge are due to misconceptions.     

Obtaining gauge invariant actions via symplectic embedding formalism

The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non‐invariant ones. Both are named also as first‐ and second‐class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non‐invariant theories. Once established, this kind of mapping between first‐class (gauge invariant) and second‐class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non‐invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non‐Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non‐Abelian systems.     

Stochastic quantisation of a gauge field in the spatial axial gauge

The stochastic quantisation method of Nelson can be applied to quantise an Abelian gauge field in the spatial axial gauge.     

Static vacuum solution of direct Poincaré gauge theory in ten dimensions with four external

A torsion-free solution of the free gauge field equations of direct Poincaré gauge theory on a ten-dimensional Minkowski space is constructed. This solution exhibits nontrivial curvature two-forms, but shaves the metric structure down to that of a four-dimensional Minkowski space. Universality of this solution with respect to the choice of the free field Lagrangian is established.