We study the finite temperature behavior of the CPT-even pure-photon sector of the Standard Model Extension, which is defined by the standard Maxwell Lagrangian plus the term (kF ) µναβ F µν F αβ . The Hamiltonian analysis is performed, from which the degrees of freedom and constraints of the theory are derived. We have explicitly calculated the partition function for an arbitrary configuration of the (kF ) µναβ coefficients, to second order, and we have used it to obtain the thermodynamic properties of the modified photon sector. We find the correction to the frequency dependence in Planck's radiation law, and we identify that the total energy density is adjusted, relative to the standard scenario, by a global proportionality constant containing the Lorentz-violating contributions. Nevertheless, the equation of state is not affected by these modifications.

The CPT-even sector of the standard model extension amounts to extending Maxwell electrodynamics by a gauge invariant term of the form − 1 4 (kF ) αβµν F αβ F µν , where the Lorentz-violating (LV) background tensor (kF ) αβµν possesses the symmetries of the Riemann tensor. The electrodynamics in ponderable media is still described by Maxwell equations in matter with modified constitutive relations which depend on the coefficients for Lorentz violation. We study the effects of this theory on the Casimir force between two semi-infinite ponderable media. The Fresnel coefficients characterizing the vacuum-medium interface are derived, and with the help of these, we compute the Casimir energy density. At leading-order in the LV coefficients, the Casimir energy density is numerically evaluated and successfully compared with the standard result. We also found a variety of intriguing effects, such as a non-trivial Kerr effect and the Casimir effect between two phases of the electromagnetic vacuum. We consider a bubble of Lorentz-symmetric (Maxwell) vacuum embedded in the infinite Lorentz-violating vacuum, and we calculate the Casimir energy at leading order, which in this case is quadratic in the LV coefficients. The Casimir force can be positive, zero, or negative, depending on the relative strengths between the LV coefficients.

The emergence of gauge particles (e.g., photons and gravitons) as Goldstone bosons arising from spontaneous symmetry breaking is an interesting hypothesis which would provide a dynamical setting for the gauge principle. We investigate this proposal in the framework of a general SO(N ) non-Abelian Nambu model (NANM), effectively providing spontaneous Lorentz symmetry breaking in terms of the corresponding Goldstone bosons. Using a nonperturbative Hamiltonian analysis, we prove that the SO(N ) Yang-Mills theory is equivalent to the corresponding NANM, after both current conservation and the Gauss laws are imposed as initial conditions for the latter. This equivalence is independent of any gauge fixing in the YM theory. A substantial conceptual and practical improvement in the analysis arises by choosing a particular parametrization that solves the nonlinear constraint defining the NANM. This choice allows us to show that the relation between the NANM canonical variables and the corresponding ones of the YM theory, A a i and E bj , is given by a canonical transformation. In terms of the latter variables, the NANM Hamiltonian has the same form as the YM Hamiltonian, except that the Gauss laws do not arise as first-class constraints. The dynamics of the NANM further guarantees that it is sufficient to impose them only as initial conditions, in order to recover the full equivalence. It is interesting to observe that this particular parametrization exhibits the NANM as a regular theory, thus providing a substantial simplification in the calculations.

In this paper we investigate, within the standard model extension framework, the influence of Lorentzand CPT-violating terms on gravitational quantum states of ultracold neutrons. Using a semiclassical wave packet, we derive the effective nonrelativistic Hamiltonian which describes the neutrons vertical motion by averaging the contributions from the perpendicular coordinates to the free falling axis. We compute the physical implications of the Lorentz-and CPT-violating terms on the spectra. The comparison of our results with those obtained in the GRANIT experiment leads to an upper bound for the symmetriesviolation c n μν coefficients. We find that ultracold neutrons are sensitive to the a n i and e n i coefficients, which thus far are unbounded by experiments in the neutron sector. We propose two additional problems involving ultracold neutrons which could be relevant for improving our current bounds; namely, gravityresonance spectroscopy and neutron whispering gallery wave.

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We present a constructive proof that, in electrodynamics, all of the gauge-invariant Lorentz scalars and pseudoscalars can be expressed as functions of the quadratic ones.

The Casimir effect is one of the most remarkable consequences of the non-zero vacuum energy predicted by quantum field theory. In this paper we use a local approach to study the Lorentz violation effects of the minimal standard model extension on the Casimir force between two parallel conducting plates in the vacuum. Using a perturbative method similar to that used for obtaining the Born series for the scattering amplitudes in quantum mechanics, we compute, at leading order in the Lorentz-violating coefficients, the relevant Green's function which satisfies given boundary conditions. The standard point-splitting technique allow us to express the vacuum expectation value of the stress-energy tensor in terms of the Green's function. We discuss its structure in the region between the plates. We compute the renormalized vacuum stress, which is obtained as the difference between the vacuum stress in the presence of the plates and that of the vacuum. The Casimir force is evaluated in an analytical fashion by two methods: by differentiating the renormalized global energy density and by computing the normal-normal component of the renormalized vacuum stress. We compute the local Casimir energy, which is found to diverge as approaching the plates, and we demonstrate that it does not contribute to the observable force.

Bumblebee models are effective field theories describing a vector field with a nonzero vacuum expectation value that spontaneously breaks Lorentz invariance. They provide an alternative way of exploring the similarities between theories with spontaneous Lorentz symmetry breaking and gauge theories. The equivalence between bumblebee models with suitable conditions and standard electrodynamics in a non-linear gauge AµA µ −b 2 = 0 is taken for granted; however, this point is very subtle and has not yet been fully addressed. The main goal of this paper is to fill in this gap. More precisely, here we study the relation between a bumblebee model, with a smooth potential of the form V (Bµ) = V (BµB µ − b 2 ), and standard electrodynamics in the non-linear gauge AµA µ − b 2 = 0, both at the classical and quantum levels. Using the Dirac's method we show that after introducing Dirac brackets with suitable initial conditions, the classical dynamics of the bumblebee model corresponds to that of standard electrodynamics in the aforementioned non-linear gauge. In the quantum case we demonstrate that perturbative calculations of Feynman amplitudes to any physical process in each model are indistinguishable. To do this, we show that the Feynman rules and propagators of standard electrodynamics in the non-linear gauge and those describing the bumblebee model are the same.