Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDual gauge concepts in electrodynamics
115
0
0.0
(
0
)
Authors
H. R. Reiss
Ask ChatGPT about the research
No Arabic abstract
Gauge invariance, a core principle in electrodynamics, has two separate meanings, only one of which is robust. The reliable concept treats the photon as the gauge field for electrodynamics. It is based on symmetries of the Lagrangian, and requires no mention of electric or magnetic fields. The other depends directly on the electric and magnetic fields, and how they can be represented by potential functions that are not unique. The first gauge concept has been fruitful, whereas the second has the defect that there exist gauge transformations from physical to unphysical states. The fields are unchanged by the gauge transformation, so that potentials are the necessary guides to correctness.
rate research
Read More
In this paper, a formulation, which is completely established on a quantum ground, is presented for basic contents of quantum electrodynamics (QED). This is done by moving away, from the fundamental level, the assumption that the spin space of bare photons should (effectively) possess the same properties as those of free photons observed experimentally. Within this formulation, bare photons with zero momentum can not be neglected when constructing the photon field; and an explicit expression for the related part of the photon field is derived. When a local gauge transformation is performed on the electron field, this expression predicts a change that turns out to be equal to what the gauge symmetry requires for the gauge field. This gives an explicit mechanism, by which the photon field may change under gauge transformations in QED.
Multiple bases are presented for the conclusion that potentials are fundamental in electrodynamics, with electric and magnetic fields as quantities auxiliary to the scalar and vector potentials -- opposite to the conventional ordering. One foundation for the concept of basic potentials and auxiliary fields consists of examples where two sets of gauge-related fields are such that one is physical and the other is erroneous, with the information for the proper choice supplied by the potentials. A major consequence is that a change of gauge is not a unitary transformation in quantum mechanics; a principle heretofore unchallenged. The primacy of potentials over fields leads to the concept of a hierarchy of physical quantities, where potentials and energies are primary, while fields and forces are secondary. Secondary quantities provide less information than do primary quantities. Some criteria by which strong laser fields are judged are based on secondary quantities, making it possible to arrive at inappropriate conclusions. This is exemplified by several field-related misconceptions as diverse as the behavior of charged particles in very low frequency propagating fields, and the fundamental problem of pair production at very high intensities. In each case, an approach based on potentials gives appropriate results, free of ambiguities. The examples encompass classical and quantum phenomena, in relativistic and nonrelativistic conditions. This is a major extension of the quantum-only Aharonov-Bohm effect, both in supporting the primacy of potentials over fields, and also in showing how field-based conceptions can lead to errors in basic applications.
Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine dynamics, and electromagnetic forces depend directly on fields. However, physical conservation principles come from symmetries such as those following from Noethers theorem, and these require potentials for their statement. Examples are given of potentials that describe fields correctly but that violate conservation principles, demonstrating that the correct statement of potentials is necessary. An important consequence is that gauge transformations are severely limited when conservation conditions must be satisfied. When transverse and longitudinal fields are present concurrently, the only practical gauge is the radiation gauge.
Source-free so-called ModMax theories of nonlinear electrodynamics in the four dimensional Minkowski spacetime vacuum are the only possible continuous deformations -- and as a function of a single real and positive parameter -- of source-free Maxwell linear electrodynamics in the same vacuum, which preserve all the same Poincare and conformal spacetime symmetries as well as the continuous duality invariance of Maxwells theory. Null field configurations of the latter however, including null electromagnetic knots, are singular for the Lagrangian formulation of any spacetime Poincare and conformal invariant theory of nonlinear electrodynamics. In particular null hopfion-Ra~nada knots are a distinguished and fascinating class on their own of topologically nontrivial solutions to Maxwells equations. This work addresses the fate of these configurations within ModMax theories. A doubled class of ModMax deformed hopfion-Ra~nada knots is thereby identified, each of which coalescing back in a continuous fashion to the original hopfion-Ra~nada knot when the nonlinear deformation parameter is turned off.
The ether concept -- abandoned for a long time but reinstated by Dirac in 1951-1953 -- has in recent years emerged into a fashionable subject in theoretical physics, now usually with the name of the Einstein-Dirac ether. It means that one special inertial frame is singled out, as the rest frame. What is emphasized in the present note, is that the idea is a natural example of the covariant theory of quantum electrodynamics in media if the refractive index is set equal to unity. A treatise on this case of quantum electrodynamics was given by the present author back in 1971, published then only within a preprint series. The present version is a brief summary of that formalism, with a link to the original paper. We think it is one of the first treatises on modern ether theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
