Class Of Gauge Theories Research Articles

A classical analogue of Yukawa coupling: Presymplectic formalism

A unified treatment of Yang-Mills and Higgs fields in classical gauge theory is carried out in a general relativistic context. A presymplectic formalism for a spinless test particle dwelling in this background geometry is described. The mass of this particle is found to depend specifically upon its generalized isospin and the Higgs field. This mass generating process is very much reminiscent of the so-called Yukawa coupling in the (electro-weak) standard model. The space of motions (phase space) is constructed together with a set of generalized Wong equations. Comparison with the Marsden-Weinstein symplectic reduction procedure is achieved.

Direct gauging of the Poincar� group V. Group scaling, classical gauge theory, and gravitational corrections

Homogeneous scaling of the group space of the Poincare group,P 10, is shown to induce scalings of all geometric quantities associated with the local action ofP 10. The field equations for both the translation and the Lorentz rotation compensating fields reduce toO(1) equations if the scaling parameter is set equal to the general relativistic gravitational coupling constant 8πGc −4. Standard expansions of all field variables in power series in the scaling parameter give the following results. The zeroth-order field equations are exactly the classical field equations for matter fields on Minkowski space subject to local action of an internal symmetry group (classical gauge theory). The expansion process is shown to breakP 10-gauge covariance of the theory, and hence solving the zeroth-order field equations imposes an implicit system ofP 10-gauge conditions. Explicit systems of field equations are obtained for the first- and higher-order approximations. The first-order translation field equations are driven by the momentum-energy tensor of the matter and internal compensating fields in the zeroth order (classical gauge theory), while the first-order Lorentz rotation field equations are driven by the spin currents of the same classical gauge theory. Field equations for the first-order gravitational corrections to the matter fields and the gauge fields for the internal symmetry group are obtained. Direct Poincare gauge theory is thus shown to satisfy the first two of the three-part acid test of any unified field theory. Satisfaction of the third part of the test, at least for finite neighborhoods, seems probable.

Canonical quantization of a special class of gauge theories

The class of theories (special-class theories) to which the most popular physical field theories belong is described in a general form. Various ways of quantizing special-class theories are considered, and their equivalence is demonstrated. The explicit form of the generators of the gauge transformations are obtained, and the equivalence of the definition of physical functions in the Lagrangian and the Hamiltonian formalisms is demonstrated.

The geometrical setting of Utiyama’s interaction theory

A mathematical deduction of the fiber bundle theory of interaction from Utiyama’s theory is drawn, in order to get some deeper insights into the geometry of classical gauge theories.

Higgs fields from symmetric connections—The bundle picture

The derivation (Forgács and Manton) of a classical gauge plus Higgs field theory from a purely symmetric gauge theory by dimensional reduction is translated into the pictorial language of symmetric connections on principal bundles. The bundle description provides a better understanding of symmetric gauge theories; its global nature excludes some gauge group-symmetry group combinations, and shows that the reduced gauge group is larger than the centralizer CH as previously thought. In general it is a certain factor group, NK/K, involving both the gauge and symmetry groups, and contains CH as a normal subgroup. The commonly used F2 Lagrangian of symmetric gauge theories will not prescribe the dynamics of fields associated with this larger group, unless these fields are suitably constrained. It is shown that a constrained Kaluza–Klein metric is required to construct the F2 Lagrangian, thus pointing the way to include dynamics for the NK/K group.

CP-violating effects in leptonic systems

The electric dipole moment of leptons and $T$-odd correlations in leptonic decays are calculated in a wide class of gauge theories. These theories phenomenologically realize milliweak, microweak, and superweak models of $\mathrm{CP}$ violation. The $T$-odd transverse polarization in $\ensuremath{\mu}$ (or $\ensuremath{\tau}$) leptonic decay is found to be superweak in magnitude and hence is intrinsically difficult to detect. Consideration is also devoted to the coherent admixture of opposite $\mathrm{CP}$ eigenstates in positronium. The upper limit of the mixing amplitude of the transition between states with the same $C$, but opposite $P$ and $\mathrm{CP}$, is of order ${10}^{\ensuremath{-}18}$.

Spin-isospin mixing without spontaneous symmetry breakdown

The phenomenon advertised in the title is demonstrated in an exactly symmetricSU(2) classical gauge theory with a scalar isodoublet of matter fields. Possible implications for chromodynamics are discussed briefly.

Chiral properties of supersymmetric vacua

Arguments, suggesting that chirality is (at least partly) unbroken in a class of gauge theories with exact or softly broken supersymmetry, hint at the possible relevance of such theories for constructing composite models of quarks and leptons.

Gauge-invariant local fields in a gauge theory as interpolating fields for “glueballs”

A method of constructing all gauge-invariant local fields in a classical gauge theory, based on their being generated by a finite set of “basic” invariants, is presented. A complete relativistic spin reduction of all two- and three-gluon basic invariant fields is given and their possible relevance to glueball classification indicated.

Class of very simple gauge theories which remain renormalizable even in the limit of infinite gauge coupling constant

A class of local gauge theories based on compact semisimple Lie groups is studied in the limit of infinite gauge coupling constant (g = infinity). In general, in this limit, the gauge fields become auxiliary in all gauge theories, and the system develops a richer structure of constraints. Unfortunately for most gauge theories, this limit turns out to be too singular to quantize and the theory ceases to be renormalizable. For a special class of gauge theories, however, where there are no fermions and there is only one multiplet of scalars in the adjoint representation, we prove that a consistent renormalizable quantum theory exists even in this very singular limit. We trace this exceptional behavior to a new local translationlike symmetry in the functional space that this class of gauge models possesses in the limit of infinite gauge coupling constant. By carrying out the constraint analysis, evaluating the Faddeev-Popov-Senjanovic determinant, and doing the functional integrations over the canonical momenta, the gauge fields, and most of the components of the scalar fields, we obtain an extremely simple result with no non-Abelian structure left in it. For example, for the group SU(2), the final answer reduces to the theory of a one-componentmore » self-interacting real phi/sup 4/ scalar field theory. Throughout this paper, we use functional methods and make no approximations; our results are nonperturbative and exact. We also discuss some of the possible implications of our results.« less

Gauge theories on four dimensional Riemannian manifolds

This paper develops the Riemannian geometry of classical gauge theories — Yang-Mills fields coupled with scalar and spinor fields — on compact four-dimensional manifolds. Some important properties of these fields are derived from elliptic theory: regularity, an “energy gap theorem”, the manifold structure of the configuration space, and a bound for the supremum of the field in terms of the energy. It is then shown that finite energy solutions of the coupled field equations cannot have isolated singularities (this extends a theorem of K. Uhlenbeck).

Heavy neutrinos and the evasion of cosmological bounds

We show, within a class of gauge theories, that neutrinos heavier than about 10 keV decay sufficiently fast into 3 ν e, as to avoid cosmological and astrophysical bounds which restrict stable neutrinos to have masses below 50eV.

Boundary conditions and spurious singularities in classical gauge theories

We show, at the classical level, that the so-called spurious singularities, characteristic of the axial gauges, are related to the boundary conditions one can impose on the potentials. In the spacelike case A 3 = 0 they are needed in order to avoid non-physical constraints on the external currents.

On generalized torsion tensor fields and the reduced fiber bundle

The reduction of a connection form ρ from a fiber bundle P to a subbundle Q is examined in detail; defining generalized torsion forms, we show how the usual Maurer–Cartan structural equations have to be modified. Examples and applications to classical general relativity and gauge theories are outlined.

Extended gauge theories of the electroweak interaction

We examine a class of gauge theories based on the gauge groupSU(2)⊗U(1)⊗G. The theory contains several charged as well as several neutral bosons coupled to ordinary leptons and quarks and naturally has “good” low energy behaviour. The average charged and neutral boson masses turn out to be equal to the standard modelW ± andZ 0 masses, i.e., at least one charged and at least one neutral boson must be lighter than theW ± andZ 0 of the standard model.

On the light-cone formulation of classical non-abelian gauge theory

For a classical Yang-Mills field which is periodic in the longitudinal light-cone coordinate: (a) a gauge condition is formulated, (b) the presence of field singularities in this gauge is shown, and (c) the relevance of these singularities to the topological charge is demonstrated.

The c → ∞ limit of quantum gauge theories

In a previous (~) paper classical Galilean gauge theories have been formulated, and it has been shown that they are the c -+ oo limit of the relativistic ones. The motivation was to have a simple approximation in the study of the low-energy properties of relativistic non-Abelian gauge theories, in particular of the bound-state problem. Such approximation can of course be good to the extent that it retains the characteristic features of the relativistic theory. The characteristic feature of gauge theories which is relevant here is the infra-red behaviour. This is known in the Abelian case, and i~ is determined by infra-red divergences which give rise to finite corrections (2). The same behaviour is found (1) in Galilean QED. It is therefore interesting to relate Galilean quantum gauge theories to the c -+oo limit of relativistic quantum gauge theories, in a framework which allows a control of relativistic effects. This can be obtained by an expansion in inverse powers of c. Let us start by the generating functional in the Coulomb gauge (3):

Erratum: CanSU(2)L×U(1)andSU(2)L×SU(2)R×U(1)gauge theories be distinguished at highQ2?

It is known that the low-energy weak-interaction experiments do not distinguish between the standard $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ and $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge theories. In this paper, we investigate the question of distinguishability of the two classes of gauge theories in high-${Q}^{2}$ weak-interaction experiments which are planned for the future.

Tumbling gauge theories

We consider a class of gauge theories in which chiral fermion fields are coupled to gauge fields. If the fermion content does not form a real representation of the gauge group, these theories may undergo dynamical symmetry breaking. In all but the simplest cases the breakdown appears to occur in a sequence of steps leading to a hierarchy of mass scales. This may be related to the hierarchal character of quark and lepton masses.

Suppression of Higgs flavor-changing neutral currents in a class of gauge theories

It is shown that the masses of neutral Higgs particles in the minimal $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ left-right-symmetric gauge theory which mediate flavor-changing interactions can be as large as necessary without running into conflict with experiment or with the validity of perturbation theory.