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Register a new userClassical Lagrange Functions for the SME
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Authors
Neil Russell
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A technique is presented for finding the classical Lagrange function corresponding to a given dispersion relation. This allows us to study the classical analogue of the Standard-Model Extension. Developments are discussed.
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Photon quantization is implemented in the standard model extension (SME) using the Gupta-Bleuler method and BRST concepts. The quantization prescription applies to both the birefringent and non-birefringent CPT-even couplings. A curious incompatibility is found between the presence of the Lorentz-violating terms and the existence of a nontrivial conjugate momentum $Pi^0$ yielding problems with covariant quantization procedure. Introduction of a mass regulator term can avoid the vanishing of $Pi^0$ and allows for the implementation of a covariant quantization procedure. Field-theoretic calculations involving the SME photons can then be performed using the mass regulator, similar to the conventional procedure used in electrodynamics for infrared-divergence regulation.
This work instigates a study of non-local field mappings within the Lorentz- and CPT-violating Standard-Model Extension (SME). An example of such a mapping is constructed explicitly, and the conditions for the existence of its inverse are investigated. It is demonstrated that the associated field redefinition can remove b-type Lorentz violation from free SME fermions in certain situations. These results are employed to obtain explicit expressions for the corresponding Lorentz-breaking momentum-space eigenspinors and their orthogonality relations.
We place limits on spherical coefficients for Lorentz violation involving operators of dimension four in the photon sector of the minimal Standard-Model Extension. The bounds are deduced from existing experimental results with optical-cavity oscillators.
A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically without splitting the space and time coordinates, i.e., space-time is treated as one identity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that particles and field reside on different manifold. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of electromagnetic fields and also a functional of particles world-lines. The other difficulty associated with the geometric setting is due to the mass-shell condition. The standard Euler-Lagrange (EL) equation for a particle is generalized into the geometric EL equation when the mass-shell condition is imposed. For the particle-field system, the geometric EL equation is further generalized into a weak geometric EL equation for particles. With the EL equation for field and the geometric weak EL equation for particles, symmetries and conservation laws can be established geometrically. A geometric expression for the energy-momentum tensor for particles is derived for the first time, which recovers the non-geometric form in the existing literature for a chosen coordinate system.
Preliminary work has been done in order to assess the perspectives of metrology and fundamental physics atomic experiments at SYRTE and LKB in the search for physics beyond the Standard Model and General Relativity. The first studies we identified are currently ongoing with the Microscope mission and with a Cs fountain clock. The latter brings significant improvement on the proton-sector coefficient $bar{c}_{TT}$ down to the $10^{-17}$ GeV level.
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