New Mechanism for Mass Generation of Gauge Field

A new mechanism for mass generation of gauge field is discussed in this paper.By introducing two sets of gauge fields and making the variations of these two sets of gauge fields compensated each other under local gauge transformations,the mass term of gauge fields is introduced into the Lagrangian without violating the local gauge symmetry of the Lagrangian.This model is a renormalizable quantum model.     

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.     

Non-cocyclic anomaly in the Gauss law commutator

The commutator of the Gauss law operator in chiral gauge theories with background gauge fields is calculated algebraically: the anomalous piece is not a cocycle.     

规范势可分解理论及其应用

对近几年用几何代数方法建立的规范场可分解理论进行了详细的评述 ,并给出了应用它研究欧拉示性数的新结果 .简述了一些应用领域.从目前国际研究的进展来看 ,规范势可分解理论也将为研究规范场静态解和夸克禁闭提供新的途径. The recent study of decomposition of gauge fields by means of methods of the geometric algebra was reviewed in detail. The new results in the study of the Euler characteristic by using the decomposition of gauge fields were described. On the other hand, some recent application fields of the decomposition of gauge fields and topological current theory were introduced. The new developments of the investigation in the area have also shown that the decomposition of gauge fields will provide...     

A covariant approach to gauged 2D self-dual fields

We obtain a non-Abelian version of a theory involving vector and tensor gauge fields interacting via a massive topological coupling, besides the nonminimun one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to make compatible gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case.     

Quantum gauge equivalence in QED

We discuss gauge transformations in QED coupled to a charged spinor field, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge and spinor fields, but also the forms of the operator-valued Hamiltonians are transformed. The discussion includes the covariant gauge, in which the gauge condition and Gauss's law are not primary constraints on operator-valued quantities; it also includes the Coulomb gauge, and the spatial axial gauge, in which the constraints are imposed on operator-valued fields by applying the Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb, and spatial axial gauges to what we call “common form,” in which all particle excitation modes have identical properties. We also show that, once that common form has been reached, QED in different gauges has a common time-evolution operator that defines time-translation for states that represent systems of electrons and photons. By combining gauge transformations with changes of representation from standard to common form, the entire apparatus of a gauge theory can be transformed from one gauge to another.     

Massive higher spin fields coupled to a scalar: Aspects of interaction and causality

We consider in detail the most general cubic Lagrangian which describes an interaction between two identical higher spin fields in a triplet formulation with a scalar field, all fields having the same values of the mass. After performing the gauge fixing procedure we find that for the case of massive fields the gauge invariance does not guarantee the preservation of the correct number of propagating physical degrees of freedom. In order to get the correct number of degrees of freedom for the massive higher spin field one should impose some additional conditions on parameters of the vertex. Further independent constraints are provided by the causality analysis, indicating that the requirement of causality should be imposed in addition to the requirement of gauge invariance in order to have a consistent propagation of massive higher spin fields.     

Harmonic expansions and quasi-riemannian geometry in Kaluza-Klein theories

Since Kaluza-Klein supergravity does not contain the observed particles as elementary fields, alternative approaches in Kaluza-Klein theories without external gauge fields may be considered. We take up Weinberg's suggestion of changing the tangent space group and we find that some or all of the gauge field strengths associated with isometry group vanish unless there is torsion.     

Classification of the Dirac equation with an external SU(3) gauge field admitting a first-order symmetry operator of special type

A classification is performed of massless gauge fields admitting one first-order symmetry operator of special type for the Dirac equation in Minkowski space. The gauge group is chosen to be SU(3). The factors multiplying the derivatives of the symmetry operator do not contain generators of the gauge group, which allows us to classify the fields according to symmetry operators of the free Dirac equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 22–21, June, 1989.     

球对称的SU2规范场和磁单极的规范场描述

本文讨论球对称的SU₂规范场,证明了满足最一般的球对称定义的SU₂规范场只能有三种基本类型:(1)同步球对称规范场;(2)狭义球对称规范场;(3)化约为U₁子群的球对称规范场。文中详细讨论了球对称的带同位旋向量场(Higgs场)的SU₂规范场,完全决定了它们的类型。如果把这种场看成为由电磁场和带电矢介子构成,那末就有如下的结论:如果磁单极所含的磁荷是最小单位的m倍,当|m|>1时,球对称的带Higgs场的SU₂规范场只能是纯电磁场,而不能有带电矢介子场出现。但当m=0,±1时,球对称的带电矢介子场是可以出现的。从而可见,具有非单位磁荷的磁单极隐含了某种破坏球对称的因素。     

Scalar lattice gauge theory

Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed from scalars. For suitable parameters scalar lattice gauge theories lead to confinement, with all continuum observables identical to usual lattice gauge theories. These models or their fermionic counterpart may be helpful for a realization of gauge theories by ultracold atoms. We conclude that the gauge bosons of the standard model of particle physics can arise as collective fields within models formulated for other “fundamental” degrees of freedom.     

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.     

Perturbative gauge invariance: the electroweak theory

The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is generalized to massive gauge fields. Applying it to the electroweak theory leads to a complete fixing of couplings of scalar and ghost fields and of the coupling to leptons, in agreement with the standard theory. The W/Z mass ratio is also determined, as well as the chiral character of the fermions. We start directly with massive gauge fields and leptons and, nevertheless, obtain a theory which satisfies perturbative gauge invariance.     

Hedgehog loops and finite-temperature transition in Yang-Mills theory

Physics of Atomic Nuclei - The dynamics of non-Abelian gauge theory can be described not only in terms of local gauge fields but also in terms of nonlocal gauge-invariant variables known as Wilson...     

CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge

Using Poincaré parametrization of AdS space, we study totally symmetric arbitrary spin massless fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized similarly to the ones of Stueckelberg formulation of massive fields. We demonstrate that the curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS fields can be expressed in terms of ladder operators. Realization of the global AdS symmetries in the conformal algebra basis is obtained. Modified de Donder gauge leading to simple gauge fixed Lagrangian is found. The modified de Donder gauge leads to decoupled equations of motion which can easily be solved in terms of the Bessel function. Interrelations between our approach to the massless AdS fields and the Stueckelberg approach to massive fields in flat space are discussed.     

Relativity and equivalence principles in a gauge theory of gravitation

Conclusion The principal difficulty that has obstructed the formulation of gauge gravitation for more than twenty years now is the fact that an Einstein gravitational field represents a metric or a tetradic field, while gauge fields are connections on fiber bundles.The popular approach to the resolution of this problem lies in attempts to represent tetrad fields as gauge fields of the translation subgroup within the framework of the gauge theory of the Poincaré group, but the existing set of variants of the latter theory indicate that it is a long way from completion.Our approach [2, 3] insists that in a gauge theory, apart from gauge fields, the situation of spontaneous breaking of symmetry can also admit Goldstone and Higgs fields, under which is subsumed the metric (tetrad) gravitational field by virtue of the fact that, as we have shown above, the equivalence principle is included in the gauge theory of gravitation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 79–82, June, 1981.     

NONEQUIVALENT SU(2) GAUGE POTENTIALS UNDER EQUAL FIELD STRENTHS AND SOURCES

This paper analyses some common physical characteristics of the gauge field strengths and sources with unequivalent potentials and expresses it in geometrical terms. The eigen-directions of these fields and sources form twistfree curve congrence, which has orthogonal hypersurfaces. The field is Abelianlizable (frequently, even trival) on each hypersurface, i.e. there exists Higgs field, which is invariant under translation along each hypersurface. The gauge field and sources are not altered during the variation of potentials, generated by the gauge rotation around Higgs fields with equal angles on each individual hypersurface but with unequal angles on different hypersurfaces.     

Heavy-particle-induced effective lagrangian in spontaneously broken theories (II). The abelian Higgs-Kibble model

In the context of the abelian Higgs-Kibble model with a charged fermion, we study in detail low-energy effective field theories of light particles when the heavy mass scales in the theory are generated by the Higgs-Kibble mechanism. Our analysis is based on the systematic use of factorization methods, and is valid to all orders in renormalized perturbation theory. Emphasis is given to finding the vestiges of the original (spontaneously broken) local gauge symmetry left in low-energy effective field theories, and general techniques are developed for that purpose. When only Fermi fields or / and physical Higgs fields correspond to light particles, low-energy effective field theories do not exhibit such signs. On the other hand, when physical gauge fields (together with other unphysical fields) correspond to light particles, the original local gauge symmetry restricts the resulting low-energy effective local action to a non-trivial form.     

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.