Cosmological solutions in a spontaneously broken gauge theory

We consider solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically de Sitter space-time. The basic features of two classes of solutions are discussed, one of them corresponding to magnetic monopoles, the other one to sphalerons. We find that although the total mass within the cosmological horizon of these configurations is finite, their mass evaluated at timelike infinity generically diverges for most values of the cosmological constant. Also, no solutions exist in the absence of a Higgs potential.     

A spontaneously broken conformal gauge theory of gravitation

In a fusing of a few attractive ingredients, we consider a spontaneously broken conformal gauge theory of gravitation, with an underlying Riemann-Cartan-Weyl geometry. The theory contains no intrinsic dimensional parameters, is unitary, and has the Schwarzschild metric as the unique spherically symmetric solution of the vacuum field equation (thus guaranteeing agreement with observed gravitational phenomena). The particle content of the theory consists of a massless 2^. graviton, and a super-massive 1^? “conformon”.     

Weak equivalence principle from a spontaneously broken gauge theory of gravity

Further consequences of a finite topological field theory for gravity based on the SL(5,R) gauge group are reported. After symmetry breaking, it induces four-dimensional Einstein spaces with a cosmological constant related to the tiny scale of the symmetry breaking. It is shown that not only a ‘background’ metric emerges from a Higgs-like mechanism, but also consistently the geodesic equation central to Einstein?s equivalence principle. In next order of the symmetry breaking scale, the induced torsion could even provoke a tiny Lorentz violation.     

Conformal gauge fixing in Minkowski space

Conformal gauge fixing on simply connected parts of world sheets in Minkowski space is examined in detail. It is proved that conformal gauge fixing can be imposed, including the usual boundary conditions.     

Ultraviolet behaviour of spontaneously broken gauge theories

The asymptotic invariant coupling constant (ICC) in the repulsive σ⁴ interaction is shown to be finite in the second logarithmic approximation. It leads to spontaneously broken gauge theories free of ultraviolet (UV) troubles.     

The gauge fixing problem around classical solutions of the Yang-Mills theory

We show that the Gribov problem [1] does not exist for small deformations of an irreducible gauge potential, in the covariant background gauge. This justifies gauge fixing within the framework of perturbation expansion. In proving the existence of local gauge sections we investigate the global orbit structure around an irreducible gauge potential.     

Cancellation of global anomalies in spontaneously broken gauge theories

I discuss the generalization to global gauge anomalies of the familiar procedure for the cancellation of local gauge anomalies in effective theories of spontaneously broken symmetries     

Resummation of angular dependent corrections in spontaneously broken gauge theories

Recent investigations of electroweak radiative corrections have revealed the importance of higher order contributions in high energy processes, where the size of typical corrections can exceed those associated with QCD considerably. Beyond one loop, only universal (angular independent) corrections are known to all orders except for massless processes, where also angle dependent corrections exist in the literature. In this paper we present general arguments for the consistent resummation of angle dependent subleading (SL) logarithmic corrections to all orders in the regime where all invariants are still large compared to the gauge boson masses. We discuss soft isospin correlations, fermion mass and gauge boson mass gap effects, the longitudinal and Higgs boson sector as well as mixing contributions including CKM effects for massive quarks. Two loop results for the right handed Standard Model are generalized in the context of the high energy effective theory based on the standard model Lagrangian in the symmetric basis with the appropriate matching conditions to include the soft QED regime. The result is expressed in exponentiated operator form in a CKM extended isospin space in the symmetric basis. Thus, a full electroweak SL treatment based on the infrared evolution equation method is formulated for arbitrary high energy processes at future colliders. Comparisons with known results are presented. Received: 12 February 2002 / Revised version: 7 March 2002 / Published online: 8 May 2002     

Asymptotic behaviour of classical Yang-Mills fields in Minkowski space

We show how to define incoming and outgoing asymptotic fields for classical solutions of the Yang-Mills field equations without fixing the gauge. It is then seen that the Gribov ambiguities for putting the field in the Coulomb gauge reduce asymptotically to a field-independent, infinite parameter group of gauge transformations. This obscures the notion of color charge already at the classical level.     

Translation gauge field theory of gravity in Minkowski spacetime

The gravitational field h_μυ with spin-2 is introduced naturally by the requirement that the Lagrangian is locally translation invariant in Minkowski spacetime.The interactions between the h_μυ and spin-1/2,0,1 matter fields are obtained along with the Lagrangian for the gravitational field including self-interactions.The deflection angle of light when it passes through the sun is calculated with different gauge conditions as an example.Our leading-order result is the same as...     

On the concept of spontaneously broken gauge symmetry in condensed matter physics

We discuss the concept of spontaneous breaking of gauge symmetry in super-conductors and superfluids and, in particular, the circumstances under which the absolute phase of a superfluid can be physically meaningful and experimentally relevant. We argue that the study of this question pushes us toward the frontiers of what we understand about the quantum measurement process, and underline the need for a new theoretical framework that keeps pace with modern technological capabilities.     

Spinor analysis of Yang-Mills theory in the Minkowski space

Self-duality equations for Yang-Mills fields and the Dirac equation with an external (anti-) selfdual gauge field are studied in the Minkowski space by spinorial methods. For the Dirac equations, all (four) possible combinations of the fermion chirality and duality of the external fields are considered.     

Regularity of constraints in the Minkowski space Yang-Mills theory

For Yang-Mills theory in the Minkowski space it is proved that the constraint set is a smooth submanifold of the phase space consisting of square integrable Cauchy data.Partially supported by the NSERC Operating Grant No. A8091