General relations among observables in a large class of neutral-current processes mediated by one,two, or threeZ bosons

Without assuming any symmetry amongμ, e andτ leptons, we consider several neutral current processes involving 73 physical parameters and deduce general relations among them implied by different classes of gauge models with one, two and three neutralZ bosons. In the single-Z boson model there are 60 general relations while the two (three)-boson model leads to 48 (36) relations. If onlyμ-e universality is imposed, the physical parameters reduce to 41 and the single (two)-Z boson model yields 31 (22) relations, while only 13 relations exist for the threeZ boson model. Imposingμ-e-τ universality decreases the number of physical parameters to 18, while the number of relations in the single- and two-Z boson models reduces to 11 and 5, respectively. In these relations are contained those obtained by Hung and Sakurai and Parida and Rajasekaran in the corresponding cases. In addition we obtain some new inequalities among the observable parameters which are to be satisfied by all gauge models.     

SU(2) × SU(2) Electroweak Theory II: Chiral and Vector Fields on the Physical Vacuum

In this letter a discussion is offered on how symmetry breaking of a theory with twisted bundle of two chiral SU(2) bundles leads to a set of gauge potentials from each group on the physical vacuum that are vector and chiral. The result is that symmetry breaking of this theory leads to massive A ³ transverse modes of the 3-photon along with electromagnetic photons plus the massive neutral and charged weakly interacting bosons. The electromagnetic sector is demonstrated to be a massless vector field and the remainder is a broken chiral field theory.     

Behaviour of gluons at high temperature

The screening of colour electric and magnetic fields and plasma oscillations in a high-temperature gluon plasma are investigated using linear response theory and self-consistent nonperturbative solutions to the Schwinger-Dyson equation. Static electric fields are screened, with

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. This result is proven to be gauge invariant in two ways: by computing π₀₀ in temporal axial, Coulomb and covariant gauges, and by computing the physical free energy of a heavy quark pair in the plasma in temporal axial gauge. To order g³ static magnetic fields are not screened.     

A unified approach to conservation laws in general relativity,gauge theories,and elementary particle physics

A unified treatment of conservation laws in general relativity, gauge theories, and elementary particle physics is formulated in the setting of principal fiber bundles. The group AUT(P) is introduced as the general gauge transformation group that covers space-time coordinate transformations. A set of master equations is exhibited for any Lagrangian density generally covariant with respect to AUT(P). The symmetry group for elementary particle theory is shown to be the structure group of the bundle only in the special case when the gauge potential is flat and the space-time is simply connected. In the general case, the symmetry group is reduced to the symmetry group of the gauge potential. This natural mechanism for a reduction of the symmetry group is speculated on as a model for spontaneous symmetry breaking.This essay received an honorable mention from the Gravity Research Foundation for the year 1981-Ed.Partially supported by a grant from the National Science Foundation.     

SU(N) supersymmetry onS 3 × R spacetime

As the whole physical community is celebrating 30 years of supersymmetry, the aim of the present paper is to analyse an 50(3,1) ×SU(N)— gauge invariant supersymmetric model on the Einstein’s universe. Thus, by exploiting the maximalS ³ symmetry, which allows the use of group theoretical techniques, we deal with a (1/2, 1, 3/2)—spin particle system on theS ³ ×R manifold. After we derive the Dirac-Rarita-Schwinger-Yang-Mills-type field equations, we focus on the additional terms that come into theory as a result of the compactness of space and spin coupling to gravity.     

<Emphasis Type="Italic">SL(2; R)</Emphasis> Duality of the Noncommutative DBI Lagrangian

We study the action of the SL(2; R) group on the noncommutative DBI Lagrangian. The symmetry conditions of this theory under the above group will be obtained. These conditions determine the extra U(1) gauge field. By introducing some consistent relations we observe that the noncommutative (or ordinary) DBI Lagrangian and its SL(2; R) dual theory are dual of each other. Therefore, we find some SL(2; R) invariant equations. In this case the noncommutativity parameter, its T -dual and its SL(2; R) dual versions are expressed in terms of each other. Furthermore, we show that on the effective variables, T -duality and SL(2; R) duality do not commute. We also study the effects of the SL(2; R) group on the noncommutative Chern–Simons action.     

Flavour-changing neutral currents in models with extra<Emphasis Type="Italic">Z′</Emphasis> boson

New neutral gauge bosonsZ′ are the features of many models addressing the physics beyond the standard model. Together with the existence of new neutral gauge bosons, models based on extended gauge groups (rank > 4) often predict new charged fermions also. A mixing of the known fermions with new states, with exotic weak-isospin assignments (left-handed singlets and right-handed doublets) will induce tree-level flavour-changing neutral interactions mediated byZ exchange, while if the mixing is only with new states with ordinary weak-isospin assignments, the flavour-changing neutral currents are mainly due to the exchange of the new neutral gauge bosonZ′. We review flavour-changing neutral currents in models with extraZ′ boson. Then we discuss some flavour-changing processes forbidden in the standard model and new contributions to standard model processes.     

Neutral currents in left-right symmetric gauge models

We analyse all the neutral-current phenomena following from the general class of gauge models based on the group SU(2) _L ⊗ SU(2) _R ⊗ U(1). It is found that the neutral-current couplings in these models bear a remarkable similarity to those in the standard Weinberg-Salam gauge model. The parameter which plays the role of sin²ϑ_w is found to lie between 0 and 1/2. Comparison with experimental data shows that even a model with the ratio of the masses of the twoZ bosons as small as 1.9 is not ruled out.     

Gauge Formulation for Two Potential Theory of Dyons

Dual electrodynamics and corresponding Maxwell’s equations (in the presence of monopole only) are revisited from the symmetry of duality and gauge invariance. Accordingly, the manifestly covariant, dual symmetric and gauge invariant two potential theory of generalized electromagnetic fields of dyons has been developed consistently from U(1)×U(1) gauge symmetry. Corresponding field equations and equation of motion are derived from Lagrangian formulation adopted for U(1)×U(1) gauge symmetry for the justification of two four potentials of dyons.     

Noncommutative theories, the axial anomaly, Fujikawa's method and the Atiyah–Singer index

Fujikawa's method is employed to compute at first order in the noncommutative parameter the U(1)_A anomaly for noncommutative SU(N). We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θ^μν, which is of “magnetic” type. Our results for SU(N) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.     

Ue(1)-covariant Rξ gauge for the two-Higgs doublet model

A U _e (1)-covariant R _ξ gauge for the two-Higgs doublet model based on BRST (Becchi-Rouet-Stora-Tyutin) symmetry is introduced. This gauge allows one to remove a significant number of nonphysical vertices appearing in conventional linear gauges, which greatly simplifies the loop calculations, since the resultant theory satisfies QED-like Ward identities. The presence of four ghost interactions in these types of gauges and their connection with the BRST symmetry are stressed. The Feynman rules for those new vertices that arise in this gauge, as well as for those couplings already present in the linear R _ξ gauge but that are modified by this gauge-fixing procedure, are presented.     

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.     

The Friedberg–Lee symmetry and minimal seesaw model

The Friedberg–Lee (FL) symmetry is generated by a transformation of a fermionic field q to q+ξz. This symmetry puts very restrictive constraints on allowed terms in a Lagrangian. Applying this symmetry to N fermionic fields, we find that the number of independent fields is reduced to N−1 if the fields have gauge interaction or the transformation is a local one. Using this property, we find that a seesaw model originally with three generations of left- and right-handed neutrinos, with the left-handed neutrinos unaffected but the right-handed neutrinos transformed under the local FL translation, is reduced to an effective theory of minimal seesaw which has only two right-handed neutrinos. The symmetry predicts that one of the light neutrino masses must be zero.     

Bäcklund transformations for harmonic maps in two independent variables

Bäcklund transformations for harmonic maps are described as the action of the structure group on harmonic one-forms or as gauge transformations of the soliton connection constructed via embedding the configuration manifold into a flat space. As an illustration, Bäcklund transformations for maps fromM ² to the Poincaré upper half-plane and for maps determining stationary vacuum gravitational fields with axial symmetry are obtained.     

The Parametrization Invariant and Gauge Invariant Effective Actions in Quantum Field Theory

The review of formulation and methods of calculation of the parametrization and gauge invariant effective actions in quantum field theory is given. As an example the Vilkovisky-De Witt Effective action (EA) is studied (this EA is a natural representative of gauge and parametrization invariant EA's). The examples where the use of the standard EA leads to the ambiguity are demonstrated. This happens as the result of dependence of the standard EA upon the choice of gauge condition. These examples are as follows: Coleman-Weinberg potential in the finite theories and symmetry breaking, EA in quantum gravity with matter and d = 5 gauged supergravity, the possibility of spontaneous supersymmetry breaking in N = 1 supergravity and the spontaneous compactification in the multidimensional R²-gravity. In all these cases the one-loop Vilkovisky-De Witt EA is found and therefore the problem of gauge dependence of EA is solved. The dependence of standard EA of composite fields upon the gauge is studied for the general gauge theories. The class of gauge and parametrization invariant EA's of the composite fields is offered.     

Hamiltonian treatment of the spherically symmetric einstein-Yang-Mills system

A canonical formalism of the dynamics of interacting spherically symmetric Yang-Mills and gravitational fields is presented. The work is based on Dirac's technique for constrained hamiltonian systems. The gauge freedom of the Yang-Mills field is treated in the same footing with the coordinate transformation freedom of the gravitational field. In particular, the fixation of coordinates and the fixation of the internal gauge are achieved by totally similar techniques. Two classes of spherically symmetric motions are considered: (i) the class for which the Yang-Mills potentials themselves are spherically symmetric (“manifest spherical symmetry”). In this case the results are valid for an arbitrary gauge group; and (ii) the class for which, in the SO(3) gauge group, a rotation in physical space is compensated by a rotation of equal magnitude but opposite direction in isospin space (“spherical symmetry up to a gauge transformation”). For manifest spherical symmetry the problem amounts to effectively dealing with an abelian gauge group and the most general solution of the field equations turns out to be the Reissner-Nordström metric with a Coulomb field. For spherical symmetry up to a gauge transformation the problem is more interesting. the formalism contains then, besides the gravitational variables, three pairs of functions of the radial coordinate that describe the degrees of freedom of the Yang-Mills field. Two pairs of these functions can be combined into a complex field ψ and its conjugate. The hamiltonian is then invariant under r-dependent rotations in the complex ψ-plane. The third degree of freedom plays the role of a compensating field associated with this invariance under localized U(l) rotations. The compensating field can always be brought to zero by a gauge transformation. After this is done the gauge is completely fixed but the problem remains invariant under position independent rotations in the ψ plane. Static solutions of the field equations in this gauge are of the form ψ(r) = (r) exp (iΘ) with Θ independent of position. The particular case Θ = 0 corresponds to the Wu-Yang ansatz. A nontrivial static solution can be found in closed form. The Yang-Mills field is of the generalized Wu-Yang type with an extra electric term, and the metric is the Reissner-Nordström one. It is pointed out that a Higgs field can be easily introduced in the formalism. The addition of the Higgs field does not destroy the invariance of the Hamiltonian under r-dependent rotations in the ψ-plane. The conserved quantity associated with the invariance under ψ → exp (i(const))ψ coincides with the electric charge as defined by 't Hooft in a more general context.     

Some consequences of neutral current systematics

Two kinds of general consequences of the ΔS=0 weak hadron neutral current independent of a gauge model are presented. Firstly are results which depend on the quark parton model. These involve bounds among neutrino inclusive cross-section and a bound onQ(Z, N) in terms of these inclusive cross-sections. Secondly are results which are independent of the quark-parton model and depend only on the SU(3) structure of the most general ΔS=0 neutral current. These tests of isopin and speciallyU-spin properties of the current are given forv+N→v+hadron+anything,v+N→v+baryon+meson ande ⁺ e ⁻→baryon+anti-baryon. In addition some conjectures are made with regard to the semi-inclusive neutrino-reactions using the quark parton model.     

Operator-valued connections,Lie connections,and Gauge field theory

Noether's first theorem tells us that the global symmetry groupG _r of an action integral is a Lie group of point transformations that acts on the Cartesian product of the space-time manifold with the space of states and their derivatives. Gauge theory constructs are thus required for symmetry groups that act indiscriminately on the independent and dependent variables where the group structure can not necessarily be realized as a subgroup of the general linear group. Noting that the Lie algebra of a general symmetry groupG _r can be realized as a Lie algebrag _r of Lie derivatives on an appropriately structured manifold,G _r -covariant derivatives are introduced through study of connection 1-forms that take their values in the Lie algebrag _r of Lie derivatives (operator-valued connections). This leads to a general theory of operator-valued curvature 2-forms and to the important special class of Lie connections. The latter are naturally associated with the minimal replacement and minimal coupling constructs of gauge theory when the symmetry groupG _r is allowed to act locally. Lie connections give rise to the gauge fields that compensate for the local action ofG _r in a natural way. All governing field equations and their integrability conditions are derived for an arbitrary finite dimensional Lie group of symmetries. The case whereG _r contains the ten-parameter Poincaré group on a flat space-timeM ₄ is considered. The Lorentz structure ofM ₄ is shown to give a pseudo-Riemannian structure of signature 2 under the minimal replacement associated with the Lie connection of the local action of the Poincaré group. Field equations for the matter fields and the gauge fields are given for any system of matter fields whose action integral is invariant under the global action of the Poincaré group.     

Colour gluons and scaling in a unified gauge model

Deep inelastic weak and electromagnetic processes are considered within the parton framework taking the partons to be integrally charged quarks and coloured gluons. Despite the participation of the spin-one gluons in these processes, scaling is shown to be maintained by treating the problem in a unified gauge model based on the groupSU (3)_colour⊗SU _L (2)⊗U(1). This is a consequence of the vector-dominance type of couplings between the gluons and the weak or electromagnetic vector bosons which are induced by the spontaneous breakdown of gauge symmetry. As a further consequence it is found that in the asymptotic region far above the gluon masses the colour octet parts of the weak and electromagnetic currents of the quarks are damped so that, in particular, the integrally charged quarks behave as fractionally charged quarks in this region.     

Supersymmetry Without Hermiticity

The PT symmetry requirement of a potential defines an inhomogeneous system of first-order differential equations for the real/imaginary and even/odd components of the relevant superpotential. By identifying the general solutions of this system we search for non-trivial supersymmetric partner potentials and analyze whether they both possess PT symmetry. As an illustrative example we present the case of the Rosen-Morse I potential.