Gauge-invariant Electrodynamics Research Articles

Constraints on torsion from the bosonic sector of Lorentz violation and magnetogenesis data

A. Kostelecky et al. [Phys. Rev. Lett. 100 (2008) 111102], have shown that there is an exceptional sensitivity of spacetime torsion components by coupling it to fermions and constraining it to Lorentz violation. They obtain new constraints on torsion components down to the level of 10 − 31 GeV . Yet more recently, L.C. Garcia de Andrade [Phys. Lett. B 468 (2011) 28] has shown that the photon sector of Lorentz violation (LV) Lagrangian leads to linear non-standard Maxwell equations where the magnetic field decays slower giving rise to a seed for galactic dynamos. In this paper bounds are placed on torsion based on the magnetogenesis or the origin of magnetic fields in the universe. On a coherence scale of 10 kpc, galactic magnetic fields of the order of some μG yield a torsion primordial field of the order of K 0 ≈ 10 − 48 GeV . Just to give an idea of how tiny it is we mention that torsion limit in the Early universe yield K 0 ≈ 10 − 31 GeV had been obtained by V. de Sabbata and C. Sivaram. Good limits were also obtained by B.R. Heckel et al. [Phys. Rev. D 78 (2008) 092006]. In our case the advantage from astro-particle physics point of view, is that a very small seed torsion field is enough to seed galactic dynamo. C. Sivaram limit is obtained from a massive photon electrodynamics [L.C. Garcia de Andrade, C. Sivaram, Ap. Space Sci. 209 (1993) 109] where a gauge invariant electrodynamics is used. Dynamo stars data are able to raise this value of torsion up to 10 − 34 GeV at magnetar atmosphere. From these estimates one notices that they coincide with the ones obtained by A. Kostelecky et al., the difference being basically in the method. The ones here were obtained from magnetogenesis data while theirs were obtained from the Earth laboratory data from polarised electrons. Besides here one used the torsion derivatives while A. Kostelecky et al. uses the constant axial torsion tensor. Another fundamental distinction is that we use bosonic sector of the Lagrangian while they use mainly fermionic sector coupling with torsion.

Is it possible to accommodate massive photons in the framework of a gauge-invariant electrodynamics?

The construction of an alternative electromagnetic theory that preserves Lorentz and gauge symmetries, is considered. We start off by building up Maxwell electrodynamics in (3+1)D from the assumption that the associated Lagrangian is a gauge-invariant functional that depends on the electron and photon fields and their first derivatives only. In this scenario, as well-known, it is not possible to set up a Lorentz invariant gauge theory containing a massive photon. We show nevertheless that there exist two radically different electrodynamics, namely, the Chern-Simons and the Podolsky formulations, in which this problem can be overcome. The former is only valid in odd space-time dimensions, while the latter requires the presence of higher-order derivatives of the gauge field in the Lagrangian. This theory, usually known as Podolsky electrodynamics, is simultaneously gauge and Lorentz invariant; in addition, it contains a massive photon. Therefore, a massive photon, unlike the popular belief, can be adequately accommodated within the context of a gauge-invariant electrodynamics.

Principles of discrete time mechanics: I. Particle systems

We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system functions from classical Lagrangians, Cadzow's variational principle applied to the action sum, Maeda-Noether and Logan invariants of the motion, elliptic and hyperbolic harmonic oscillator behaviour, gauge invariant electrodynamics and charge conservation, and the Grassmannian oscillator. First quantised discrete time mechanics is discussed via the concept of system amplitude, which permits the construction of all quantities of interest such as commutators and scattering amplitudes. We discuss stroboscopic quantum mechanics, or the construction of discrete time quantum theory from continuous time quantum theory and show how this works in detail for the free Newtonian particle. We conclude with an application of the Schwinger action principle to the important case of the quantised discrete time inhomogeneous oscillator.

On massive and massless photons

The vanishing of the longitudinal mode of a massive photon as the photon mass goes to zero in gauge-invariant electrodynamics is investigated with the help of examples. A distinction between two forms of gauge-invariant amplitudes is made in order to clarify this limit; conditions are then obtained so that the limiting process is smooth. From these conditions results on the equality of particle charge which are usually derived by means of Ward’s identity can be obtained.

Gauge Invariance and Rest Mass

IT is well known that the main difference between Maxwell's equations and Proca's1 equations is that, whereas in the former the potentials Aµ admit the gauge transformation and describe photons of zero rest mass, in the latter there is no such transformation of the potentials which describe quanta of non-zero rest mass. This is often taken to mean that in a gauge-invariant electrodynamics the rest mass of the photon must vanish. In view of the present interest in the self-energy of the photon, it seems worth while to mention that there exist gauge-invariant wave equations which can describe quanta of non-zero rest mass. For example, the equations where f is any scalar function of the field-strengths and their derivatives of any order, are consistent with the transformation (1) of potentials and with the equation θνjν, = 0, expressing the conservation of charge. It is easy to arrange for f to be small for slowly varying or weak fields, so that, in these limiting cases, the equations reduce to Maxwell's. But the arbitrary function f must contain some parameters which have no counterpart in Maxwell's equations, and which in certain types of theory lead to the appearance of field quanta of non-zero rest mass.