Electromagnetic Gauge Transformations Research Articles

Magnetic field effects on lagrangians and neutrino self-energies in the Salam-Weinberg theory in arbitrary gauges

An analytic expression for the W-field propagator of the Salam-Weinberg theory in a constant magnetic field is obtained. To obtain the result in an arbitrary weak (ξ) gauge, gauge-fixing terms (different from those usually chosen) must be introduced which are manifestly invariant under electromagnetic gauge transformations. This W-propagator is then used to calculate an expression for the neutrino self-energy in a magnetic field. The result implies an effective neutrino “mass” analogous to that found in the MSW effect. Such a “mass” may be observable in collapsing supernovae. The effective electromagnetic lagrangian is found in an arbitrary (ξ) gauge and shown to be gauge invariant.

Covariant representations in a fibre bundle framework

Canonical and covariant representations of Lie groups of the semidirect product form G = N⊙ K with N Abelian, are analyzed in a fibre bundle framework. We exhibit first the relationship between both kinds of representations in such framework. Two complementary methods of selecting irreducible representations from the covariant ones are developed. The first one proceeds by restriction to an invariant subspace and is exemplified in the case of massive integer spin representations of the Poincaré group. The second method takes quotients and is particularly useful when we deal with reducible but indecomposable representations. A family of stepped gauge transformations is generated when the method is used to obtain the covariant massless integer helicity representations of the Poincaré group; the electromagnetic and gravitational gauge transformations are just the first two cases of such a family.

Dirac equation in Riemann space-time

We give a very simple and straightforward deduction of the Dirac equation in a Riemann world,i.e. in an Einstein gravitational field. Neither the tetrad formalism nor the spinor calculus are used. A natural generalization of the theory and a feasible association between the transformations of the general co-ordinates and the electromagnetic gauge transformations are briefly outlined.

Spatial rotations, electromagnetic gauge transformations and the fine-structure constant

Since it expresses a connection between the basic units of angular momentum /~ and electric charge e, the experimentally observed value of the fine-structure constant = eS/4~t~c may signify an underlying relationship between the associated groups for spatial rotations SOs and electromagnetic gauge transformations SOs. In the present letter, at tention is given to Haar-induced volumes of the fourand ten-dimensional envelopments #[SOs • SOs] and #[[S03] s • SOs]. I t is observed that if the lat ter volumes, denoted as V and V', are related to the radius a of SOs and the half-period b of SO s by the simple conditions in (12), then the fine-structure constant is required to have the theoretical value shown in (17). I t is customary to parametrize the SOs.group of proper rotations in physical Euclidean space in terms of r a real three-component vector defined through a sphere of radius z with antipodal surface points identified topologically: r ~-r for I~al = ~. For any SOs element the direction and magnitude (radians) of the rotation is given by the direction and magnitude of ~ . An elementary calculation yields the associated normalized Haar measure (1)

Spatial rotations, electromagnetic gauge transformations and the fine-structure constant

Spatial rotations, electromagnetic gauge transformations and the fine-structure constant

Space-time structure of weak and electromagnetic interactions

The generator of electromagnetic gauge transformations in the Dirac equation has a unique geometric interpretation and a unique extension to the generators of the gauge group SU(2) × U(1) for the Weinberg-Salam theory of weak and electromagnetic interactions. It follows that internal symmetries of the weak interactions can be interpreted as space-time symmetries of spinor fields in the Dirac algebra. The possibilities for interpreting strong interaction symmetries in a similar way are highly restricted.

Radiation gauge covariance

A manifestly covariant relation is discussed between electromagnetic gauge transformations and Lorentz transformations, while analyzing the contributions to the free field 4-potential coming exclusively from lightlike momenta. Transverse 4-potentials are thus introduced relative to each inertial frame which belong in the Lorentz gauge, behave as completely invariant objects under general guage transformations, and give rise to one and the same frame-free electromagnetic field tensor. The (proper orthochronous) Lorentz covariant transformation law of the guage-invariant transverse 4-potential is established, from the standpoint of the active transformation from one inertial observer to another.

Gauge-invariant perturbations of Reissner-Nordström black holes

We present the details of previously published results on the stability of the Reissner-Nordstr\"om family of black holes and discuss, in some detail, the reduction techniques which were used to simplify the perturbation problem. We develop the Hamiltonian formalism for the perturbations of an arbitrary static solution of the Einstein-Maxwell equations (with vanishing magnetic field) and show explicitly that the perturbed constraints are the generators of the coordinate and electromagnetic gauge transformations of the canonical perturbation variables. We show that the perturbed constraints have vanishing Poisson brackets with one another and use this result as the basis for our reduction technique. The canonical transformations which accomplish the reduction and the perturbation Hamiltonian are given explicitly for the Reissner-Nordstr\"om problem. We include a stability result for the (odd- and even-parity) $L=1$ perturbations which were not previously considered.

Asymmetry in the asymptotic identification

The compatibility of the notion of an internal symmetry group with the asymptotic identification for an electromagnetic part of the non-Abelian gauge field is investigated on the classical level. It is shown that the asymptotic identification would restrict, without the necessity of violating local gauge invariance, internal symmetry transformations to those which commute with the generator of electromagnetic gauge transformations. Local gauge transformations would be restricted in the same way in the region of definability of the gauge field’s electromagnetic part. Based upon these restrictions, a model for the structure of the gauge field’s sources and interactions is conjectured in order to illustrate how the knownSU 2 andSU 3 dynamical symmetry and internal particle labeling schemes might arise from a local gauge theory employing an asymptotic identification.