Perturbative gauge invariance: electroweak theory II

A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction.     

Perturbative contributions to the electroweak interface tension

The main perturbative contribution to the free energy of an electroweak interface is due to the effective potential and the tree level kinetic term. The derivative corrections are investigated with one-loop perturbation theory. The action is treated in derivative, in heat kernel, and in a multi local expansion. The massive contributions turn out to be well described by the Z-factor. The massless mode, plagued by infrared problems, is numerically less important. Its perturbatively reliable part can by calculated in derivative expansion as well. A self consistent way to include the Z-factor in the formula for the interface tension is presented.     

Perturbative expansion of Chern-Simons theory with non-compact gauge group

Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly unitary format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified.Research supported in part by NSF Grant PHY86-20266     

Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: Superfield formalism

We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D spacetime variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.      

Coulomb coupling, gauge invariance and the Regge theory of photoproduction

The special nature of the Coulomb coupling of a charged particle suggests that non-analytic terms are present in the Regge theory of photoproduction. This provides a natural explanation of the sharp forward peaks observed in charged pion photoproduction off nucleons. A high energy theorem for the forward photoproduction of pseudoscalar mesons follows.     

Uniqueness of the standard electroweak gauge model

It is proved that the standard SU(2) × U(1) electroweak gauge model is unique against any extension if the effective low-energy neutral-current interaction is to be precisely of the form $\text{(4G}{}_{\mathrm{F}}\text{/}\text{2}\text{) (j}{}_{\mathrm{\mu }}{}^{\mathrm{(3)}}\text{?}\text{sin}{}^2\text{θ}{}_{\mathrm{<mtext>W</mtext>}}\text{j}{}_{\mathrm{\mu }}{}^{\mathrm{<mtext>em</mtext>}}\text{)}{}^2$naturally.     

Self-interaction and gauge invariance

A simple unified closed form derivation of the non-linearities of the Einstein, Yang-Mills and spinless (e.g. chiral) meson systems is given. For the first two, the non-linearities are required by locality and consistency; in all cases, they are determined by the conserved currents associated with the initial (linear) gauge invariance of the first kind. Use of first-order formalism leads uniformly to a simple cubic self-interaction.Supported by USAF OAR under Grant AFOSR 70-1864.     

Poincaré gauge invariance and the dynamical role of spin in gravitational theory

We classify, according to the number of independent gauge fields, Poincaré gauge invariant theoretical frameworks of describing gravity into three categories. One of them may provide the dynamical definition of the spin tensor S and that of the energy-momentum tensor T, resulting in the response equation of matter to gravity with the gravitational field strengths, D′ and F, coupled to the former tensors

$\text{T}{}_{\mathrm{\nu }}{}^{\mathrm{\mu }}\text{;}{}_{\mathrm{\mu }}\text{=D′}{}_{\mathrm{\mu \lambda \nu }}\text{T}{}^{\mathrm{\mu \lambda }}\text{+F}{}_{\mathrm{\mu \lambda \nu \rho }}\text{S}{}^{\mathrm{\rho \mu \lambda }}$

, where the right-hand side represents spin force densities. In the absence of spin the response reduces to the conventional one of general relativity, i.e., without the spin forces. For the electromagnetic field the phase-gauge invariance requires the same conclusion as for a scalar field. For a spin $\text{1}\text{2}$ particle there is torsion, which deflects its trajectory from geodesic; an explicit expression for torsion takes a simple form of the axial vector current $\text{ψ}\text{γ}{}_5\text{γ}{}_{\mathrm{k}}\text{ψ}$.     

The electroweak standard model in the axial gauge

We derive the Feynman rules of the standard model in the axial gauge. After this we prove that the fields and do not correspond to physical particles. As a consequence, these fields cannot appear as incoming or outgoing lines in Feynman graphs. We then calculate the contribution of these fields in the case of a particular decay mode of the top quark.Received: 28 January 2004, Revised: 12 February 2004, Published online: 8 April 2004     

Residual gauge invariance of Hamiltonian lattice gauge theories

The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegenbauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically.     

Test of gauge invariance reconsidered

A critical assessment is given of the conclusions drawn by Kobe and Wen from their recent investigation of a charged harmonic oscillator in an electromagnetic field as a test of gauge invariance.     

Parameters in the electroweak theory

This series of papers deals with the problem of finding relations between the parameters of the Standard Model of Glashow, Weinberg and Salam. In this first paper, the method of point splitting, suitably modified, is proposed as a useful regularization. When applied to quantum electrodynamics, this point-split regularization is indeed found to have desirable properties. More specifically, to one loop, the photon is shown to remain massless and the photon-photon scattering amplitude gauge invariant. In the following papers, this point-split regularization is applied to the electroweak theory. In the second paper, a first mass relation is obtained from the quadratic divergences. In the third paper, a second mass relation is found from the Higgs interactions. From these two relations, the masses of the Higgs boson and the top quark are determined theoretically for the Standard Model asm _H =190GeV andm _t =120GeV.Work supported in part by the Norwegian Research Council for Science and the Humanities     

Perturbative QED in terms of gauge invariant fields

A formulation of QED using only gauge invariant fields acting on a physical state space is discussed. The fields are the electromagnetic tensor F_μν and a non-local electron field ψ_f depending on a quadruple {f^μ} of auxiliary functions. The f-ambiguity is physically meaningful: the f^μ contain information on the asymptotic configuration of the electromagnetic field accompanying charged particles. Equations of motion are introduced and solved perturbatively, in the sense that expressions for the Wightman functions of the theory are derived. No information on the commutation relations between the basic fields is needed.