Natural Gauge Research Articles

The bimetric Weyl-Dirac theory and the gravitational constant

The Weyl-Dirac theory of gravitation and electromagnetism is modified by the introduction of a background metric characterized by a scale constant related to the size of the universe. One is led to a natural gauge giving\({{\dot G} \mathord{\left/ {\vphantom {{\dot G} G}} \right. \kern-\nulldelimiterspace} G} = - 5.5 \times 10^{ - 12} y^{ - 1} \). This is smaller by about a factor of ten than the value obtained on the basis of Dirac's large number hypothesis.

Neutrinoless double-βdecay in SU(2)×U(1) theories

It is shown that gauge theories give contributions to neutrinoless double-$\ensuremath{\beta}$ decay [${(\ensuremath{\beta}\ensuremath{\beta})}_{0\ensuremath{\nu}}$] which are not covered by the standard parametrizations. While probably small, their existence raises the question of whether the observation of ${(\ensuremath{\beta}\ensuremath{\beta})}_{0\ensuremath{\nu}}$ implies the existence of a Majorana mass term for the neutrino. For a natural gauge theory we argue that this is indeed the case.

First integrals for time-independent Yang-Mills equations

It is shown that a natural gauge exists for considering time-independent solutions to SU(2) Yang-Mills field equations. Integral theorems are obtained which allow one to draw general conclusions about the energy, momentum and angular momentum in the field. One conclusion is that for any source function there could exist many solutions with an energy lower than the Coulomb energy.

A four-dimensional formulation of defect dynamics and some of its consequences

A 4-dimensional formulation of the equations of defect dynamics is given through use of concepts from the exterior calculus. The formulation provides a clear separation of the three basic effects; geometric responses of bodies to loadings, evolution of dislocations, and evolution of disclinations. The theory is shown to admit a 45-fold gauge group and a system of natural gauge conditions whereby the elastic and the plastic parts of the responses may be disentangled. The gauge conditions also lead to both spatial and temporial nonlocality. Self-equilibrating dislocations and disclinations (i.e. those for which there is no plastic distortion or velocity) are shown to exist and conditions for their elimination are given. A complete analogy is established between defect dynamics and co-occupying systems of electromagnetic fields with both electric and magnetic charges and currents. Analogous magnetic charges and currents are shown to vanish only if there are no disclinations present. The gauge group structure and the electrodynamic analogy provide expectations of parallels with Yang-Mills type unified gauge theories. A constitutive theory is obtained through use of the practices of non-equilibrium thermodynamics, one example of which leads to a natural implementation of a yield criteria, an incremental law of plastic distortion, and a proof of Drucker's postulate.

On the gauge transformations admitted by the equations of defect dynamics

This paper deals with gauge invariance applied to dislocations and disclinations in the field theory formulation given by Kossecka and de Wit[1,2]. The gauge transformations of the strain, linear velocity, bend-twist, and rotational velocity that leave the dislocation and disclination densities and currents invariant are obtained explicitly, and the equations of balance of linear momentum are shown to lead to a natural gauge condition. These transformations are generated by a vector field that depends upon position and time and two vector fields that depend on time alone. The latter two fields are shown to realize superimposed rigid body motions as part of the generalized gauge transformation structure of the theory. Representation of the space and time generating vector in terms of a gradient plus the curl of another vector is shown to lead to several useful decompositions.

Source-free Yang-Mills theories

Using techniques developed in recent years in general relativity we study the general GL(R,n) and GL(C,m) gauge theories with no external sources. In particular, after casting the field equations into the spin-coefficient formalism and adapting natural (to thee formalism) gauge conditions we show how most of the equations can be integrated in the case of real asymptotically ''flat'' solutions. In the self-dual (or anti-self-dual) case the field equations are reduced to a single nonlinear wave equation for a Hertz-type potential. As a final point we show the relationship between this potential and our version of the Atiyah-Ward method of finding self-dual fields.

Ambiguities of the natural gauge in Yang-Mills theories

We study the ambiguities of the natural gauge condition for the Euclidean SU(2) Yang-Mills theory in four dimensions. Then, we show that, in the stationary-phase approximation, these ambiguities do not affect the contribution of the sector with Pontryagin index q = 1 to the correlation functions of gauge-invariant operators. They affect only the higher-order corrections to this contribution.

Remark on the Cabibbo-Ferrari two-potential approach to electric and magnetic charges

A covariant two-potential formalism is introduced after integrating the Maxwell equations with electric and magnetic charges. These two potentials essentially correspond to those of Cabibbo and Ferrari. The Cabibbo-Ferrari local expression forFμν in terms of the two potentials is derived instead of being put in as an ansatz. As a by-product of this derivation we obtain a natural covariant gauge in which the formalism is much simpler, the remaining gauge group beingU1×U1. There are no external and artificial ingredients in this formalism (as there were none in the Cabibbo-Ferrari formalism either) and the basic equations are completely equivalent to the Maxwell equations.

Gauge-symmetry hierarchies

It is shown that one cannot artifically establish a gauge hierarchy of any desired magnitude by arbitrarily adjusting the scalar-field parameters in the Lagrangian and using the tree approximation to the potential; radiative corrections will set an upper bound on such a hierarchy. If the gauge coupling constant is approximately equal to the electromagnetic coupling constant, the upper bound on the ratio of vector-meson masses is of the order of ${\ensuremath{\alpha}}^{\ensuremath{-}\frac{1}{2}}$, independent of the sclar-field masses and their self-couplings. In particular, the usual assumption that large scalar-field mass ratios in the Lagrangian can induce large vector-meson mass ratios is false. A thus far unsuccessful search for natural gauge hierarchies is briefly discussed. It is shown that if such a hierarchy occurred, it would have an upper bound of the order of ${\ensuremath{\alpha}}^{\ensuremath{-}\frac{1}{2}}$.

Quantum Electrodynamics on Null Planes and Applications to Lasers

The conventional formulation of quantum electrodynamics in which the system develops from one space-like hyperplane to the next is here replaced by one in which the development proceeds over null hyperplanes. For detailed study a quantized electromagnetic field ${A}^{\ensuremath{\mu}}$ is chosen to interact with a quantized spin-0 particle field $\ensuremath{\Phi}$ in an unquantized electromagnetic field $A_{\mathrm{ext}}^{}{}_{}{}^{\ensuremath{\mu}}$ as background. If the latter is chosen to be a laser field, the $\ensuremath{\Phi}\ensuremath{-}A_{\mathrm{ext}}^{}{}_{}{}^{\ensuremath{\mu}}$ interaction permits exact closed-form solutions (Volkov) and allows the construction of wave packets which cannot be done in the usual formulation. The perturbation solution for the $S$ matrix is therefore conveniently based on the Furry picture. The null-plane formulation has various advantages. In particular, the gauge problem which causes difficulties in the usual theory is absent in the null-plane gauge chosen here. Since there are only two dynamically independent components of ${A}^{\ensuremath{\mu}}$, the commutation relations, field equations, gauge conditions, and vacuum definition are all mutually consistent. A natural nullplane gauge is used. Similarities and differences between this and the conventional theory are pointed out. As an application the Compton scattering of a charged particle with a laser beam is shown to lead to an intensity-dependent frequency shift. The controversy on this issue is settled here without divergent phase factors, because our wave-packet description permits a clean separation of the particle beam from the laser.