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Wave propagation in axion electrodynamics

The axion contribution to the electromagnetic wave propagation is studied. We show that in order to represent the axion contribution to the wave propagation it is necessary to go beyond the geometric approximation, which is usually used in the premetric formalism. We derive a covariant dispersion relation for the axion modified electrodynamics. The wave propagation in this model is studied for an axion field with timelike, spacelike and null derivative covectors. The birefringence effect emerges in all these classes as a signal of Lorentz violation. This effect is however completely different from the ordinary birefringence appearing in classical optics. The axion field does not simple double the ordinary light cone structure, it modifies the global topological structure of light cones surfaces.

Noether procedure and dynamical geometry

The Hilbert–Noether theorem states that a current associated with diffeomorphism invariance of a Lagrangian vanishes on shell modulo a divergence of an arbitrary superpotential. Application of the Noether procedure to physical Lagrangians yields, however, meaningful (and measurable) currents. The well-known solution to this ‘paradox’ is to involve the variation of the metric tensor. Such procedure, for the field considered on a fixed (flat) background, is sophisticated logically (one needs to introduce the variation ofa fixed field) and formally. We analyze the Noether procedure for a generic diffeomorphism invariant p-form field model. We show that a consistent description of the canonical energy–momentum current is possible only if the dynamics of the geometry (gravitation) is taken into account. However, even the ordinary used ‘truncated’ consideration yields the proper expression.

Energy-momentum current for coframe gravity

The obstruction for the existence of an energy momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. It has not to be valid for alternative geometrical structures. In this talk, a general three parametric class of coframe models is considered. For a conjugate field strength $\F^a$, the field equation turns out to have a form completely similar to the Maxwell field equation $d*\F^a=\T^a$. By applying the Noether procedure, the source 3-form $\T^a$ is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source $\T^a$ of the coframe field is interpreted as the total conserved energy-momentum current. Thus even a small-parametric change of GR turns it into a well defined Lagrangian theory.

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