Local and global gauge symmetries in temporal gauge

In the temporal gauge formalism, in order to make a distinction between the global limit of local gauge transformations and global ones a non-local operator, θ, is introduced. It is claimed that what kind of θ is used is equivalent to what kind of gauge-fixing schemes is chosen. Along this idea, in non-abelian theories the coulomb, axial and unitary gauges have been investigated. In the unitary gauge spontaneous breakdown of global gauge symmetry has been found to be reduced to a problem of the boundary condition for the Higgs field and the occurrence of symmetry breaking has been concluded.     

Lagrangian constraints and gauge symmetries

Within the study of degenerate Lagrangian systems, a new intrinsic expression is proposed for the conditions under which the solutions of the dynamical equation i=dE do exist and are second-order vector fields. Such conditions are expressed in terms of generalized symmetries for the Lagrangian and constitute further progress in understanding the connection between constraints and gauge invariance within the Lagrange framework.     

Space-time symmetries in gauge theories

A general definition of symmetries of gauge fields is proposed and a method developed for constructing symmetric fields for an arbitrary gauge group. Scalar fields occur naturally in the formalism and the pure gauge theory reduces to a Higgs model in lower dimensions.Laboratoire propre du C.N.R.S. associé à l'Ecole Normale Supérieure et à l'Université de Paris Sud     

Neutrino masses from gauge symmetries

A very simple extension of the Standard Model to include an Abelian family symmetry is able to describe the hierarchy of quark and lepton masses and their mixing angles together with the unification of gauge couplings. We consider the implications of this model for neutrino masses and mixing angles and show that they are determined up to a discrete ambiguity corresponding to the representation content of the Higgs sector responsible for the Majorana mass matrix.     

Hamiltonian structure and gauge symmetries of Poincaré gauge theory

This is a review of the constrained dynamical structure of Poincaré gauge theory which concentrates on the basic canonical and gauge properties of the theory, including the identification of constraints, gauge symmetries and conservation laws. As an interesting example of the general approach, we discuss the teleparallel formulation of general relativity.     

Rigid symmetries and BRST-invariance in gauge theories

The structure of the symmetry algebra of theories with simultaneous local and rigid symmetries is analyzed. BRST-invariant Faddeev-Popov gauge-fixing in such theories is discussed and it is proven that the BRST-transformations can always be made to commute with the rigid symmetries by assigning specific transformation rules to the ghosts. The problem of keeping the rigid symmetries manifest in the quantum theory is shown to reduce to the problem of finding covariant gauge conditions. Such covariant gauges exist only if the algebra of local and rigid symmetries has a semi-direct product structure.     

Internal gauge symmetries and the gravitational field

It is shown that gravitationlike gauge fields can result from compact, internal symmetry groups. In particular, when the global duality invariance of the vacuum Maxwell's equations is made into a local symmetry using the methods of Yang and Mills, the gauge field is found to have certain properties characteristic of gravity. It is conjectured that a realistic theory of gravity can be constructed as a gauge theory based on a compact, internal symmetry group.     

Dynamical symmetry breaking of extended gauge symmetries

We construct asymptotically free gauge theories exhibiting dynamical breaking of the left-right gauge group G(LR)=SU(3)(c) x SU(2)(L) x SU(2)(R) x U(1)(B-L), and its extension to the Pati-Salam gauge group G(422)=SU(4)(PS) x SU(2)(L) x SU(2)(R). The models incorporate technicolor for electroweak breaking, and extended technicolor for the breaking of G(LR) and G422 and the generation of fermion masses. They include a seesaw mechanism for neutrino masses, without a grand unified theory (GUT) scale. These models explain why G(LR) and G422 break to SU(3)(c) x SU(2)(L) x U(1)(Y), and why this takes place at a scale (approximately 10(3) TeV) large compared to the electroweak scale, but much smaller than a GUT scale.     

Stabilizing the axion by discrete gauge symmetries

The axion solution to the strong CP problem makes use of a global Peccei–Quinn U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an approximate global symmetry from discrete gauge symmetries. Simple models based on Z_N symmetries with N=11,12, etc., are presented realizing the DFSZ axion and the KSVZ axion. The discrete gauge anomalies are canceled by a discrete version of the Green–Schwarz mechanism. In the supersymmetric extension our models provide a natural link between the SUSY breaking scale, the axion scale, and the SUSY-preserving μ term.     

On the origin of gauge symmetries and fundamental constants

A statistical mechanism is proposed for symmetrization of an extra space. The conditions and rate of attainment of a symmetric configuration and, as a consequence, the appearance of gauge invariance in low-energy physics is discussed. It is shown that, under some conditions, this situation occurs only after completion of the inflationary stage. The dependences of the constants ℏ and G on the geometry of the extra space and the initial parameters of the Lagrangian of the gravitational field with higher derivatives are analyzed.     

Discrete gauge symmetries in discrete MSSM-like orientifolds

Motivated by the necessity of discrete _ZN${\mathbb{Z}}_N$ symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)$U(1)$?s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1)$U(1)$ factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)$U(1)$?s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1)$U(3)\times U(2)\times U(1)\times U(1)$ and U(3)×Sp(2)×U(1)×U(1)$U(3)\times \mathit{Sp}(2)\times U(1)\times U(1)$ configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5)$\mathit{SU}(5)$ GUT models. We find examples of models with _Z2${\mathbb{Z}}_2$ (R-parity) and _Z3${\mathbb{Z}}_3$ symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.     

Spontaneous breaking of gauge symmetries with non-linear realizations

Spontaneous breaking of gauge symmetries by non-linear realizations involving scalars is used to obtain a gauge-invariant massive-vector-meson formulation.     

Nonlinear gauge realization of spacetime symmetries including translations

We present a general scheme for the nonlinear gauge realizations of spacetime groups on coset spaces of the groups considered. In order to show the relevance of the method for the rigorous treatment of the translations in gravitational gauge theories, we apply it in particular to the affine group. This is an illustration of the family of spacetime symmetries having the form of a semidirect productH T, whereH is the stability subgroup andT are the translations. The translational component of the connection behaves like a true tensor underH when coset realizations are involved.     

Extensions of Lie superalgebras and supersymmetric abelian gauge fields

We construct an extension of Lie superalgebras which allows an algebraic descriprion of the supersymmetric Hopf fibration of the supersymmetric two-sphere. Moreover, we construct a supersymmetic generalization of electromagnetism.     

BRST-BV quantization of gauge theories with global symmetries

We consider the general gauge theory with a closed irreducible gauge algebra possessing the non-anomalous global (super)symmetry in the case when the gauge fixing procedure violates the global invariance of classical action. The theory is quantized in the framework of BRST-BV approach in the form of functional integral over all fields of the configuration space. It is shown that the global symmetry transformations are deformed in the process of quantization and the full quantum action is invariant under such deformed global transformations in the configuration space. The deformed global transformations are calculated in an explicit form in the one-loop approximation.