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- The boltzmann equation and equilibrium thermodynamics in Lorentz-violating theoriesPublication . Potting, Robertus
Expand In this work, we adapt the foundations of relativistic kinetic theory and the Boltzmann equation to particles with Lorentz-violating dispersion relations. The latter are taken to be those associated to two commonly considered sets of coefficients in the minimal Standard-Model Extension. We treat both the cases of classical (Maxwell-Boltzmann) and quantum (Fermi-Dirac and Bose-Einstein) statistics. It is shown that with the appropriate definition of the entropy current, Boltzmann's H-theorem continues to hold. We derive the equilibrium solutions and then identify the Lorentz-violating effects for various thermodynamic variables, as well as for Bose-Einstein condensation. Finally, a scenario with nonelastic collisions between multiple species of particles corresponding to chemical or nuclear reactions is considered.Expand - Cosmic-ray fermion decay by emission of on-shell W bosons with CPT violationPublication . Colladay, D.; Noordmans, J. P.; Potting, Robertus
Expand We study CPT and Lorentz violation in the electroweak gauge sector of the Standard Model in the context of the Standard-Model Extension. In particular, we consider the Lorentz-violating and CPT-odd Chern-Simons like parameter for the W boson, which is thus far unbounded by experiment. We demonstrate that any nonzero value of this parameter implies that, for sufficiently large energies, one of the polarization modes of the W boson propagates with spacelike four-momentum. In this scenario, an emission of W bosons by ultra-high-energy cosmic rays is possible. We calculate the induced fermion energy-loss rate, and we deduce the first limit on the pertinent Lorentz-and CPT-violating parameter that couples to the W boson. Consistency between the quantum description in various reference frames is preserved by using a recently formulated covariant quantization procedure for massive photons and applying it to the W bosons.Expand - Lorentz symmetry in ghost-free massive gravityPublication . Kostelecký, V. Alan; Potting, Robertus
Expand The role of Lorentz symmetry in ghost-free massive gravity is studied, emphasizing features emerging in approximately Minkowski spacetime. The static extrema and saddle points of the potential are determined and their Lorentz properties identified. Solutions preserving Lorentz invariance and ones breaking four of the six Lorentz generators are constructed. Locally, globally, and absolutely stable Lorentz-invariant extrema are found to exist for certain parameter ranges of the potential. Gravitational waves in the linearized theory are investigated. Deviations of the fiducial metric from the Minkowski metric are shown to lead to pentarefringence of the five wave polarizations, which can include superluminal modes and subluminal modes with negative energies in certain observer frames. The Newton limit of ghost-free massive gravity is explored. The propagator is constructed and used to obtain the gravitational potential energy between two point masses. The result extends the Fierz-Pauli limit to include corrections generically breaking both rotation and boost invariance.Expand - Standing wave solutions in Born-Infeld theoryPublication . Manojlovic, Nenad; Perlick, Volker; Potting, Robertus
Expand We study standing-wave solutions of Born-Infeld electrodynamics, with nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the electromagnetic field has only one nonzero component depending on time and on the coordinate perpendicular to the plates. the problem then reduces to solving the scalar Born-Infeld equation, a nonlinear partial differential equation in 1+1 dimensions. We apply two alternative methods to obtain standing-wave solutions to the Born-Infeld equation: an iterative method, and a "minimal surface" method. We also study standing wave solutions in a uniform constant magnetic field background. the results obtained in this work provide a theoretical background for experimental tests of Born-Infeld theory. (C) 2020 Elsevier Inc. All rights reserved.Expand - Cherenkov radiation with massive, CPT-violating photonsPublication . Colladay, Don; McDonald, Patrick; Potting, Robertus
Expand The source of CPT violation in the photon sector of the Standard Model Extension arises from a Chern-Simons-like contribution that involves a coupling to a fixed background vector field k(AF)(mu). These Lorentz- and CPT-violating photons have well-known theoretical issues that arise from missing states at low momenta when k(AF)(mu) is timelike. In order to make the theory consistent, a tiny mass for the photon can be introduced, well below current experimental bounds. The implementation of canonical quantization can then be implemented as in the CPT-preserving case by using the Stuckelberg mechanism. We explicitly construct a covariant basis of properly normalized polarization vectors at fixed three-momentum satisfying the momentum space field equations, in terms of which the vector field can be expanded. As an application of the theory, we calculate the Cherenkov radiation rate for the case of purely timelike k(AF)(mu) and find a radiation rate at high energies that has a contribution that does not depend on the mass used to regulate the photons.Expand - Degenerate behavior in nonlinear vacuum electrodynamicsPublication . Escobar, C. A.; Potting, Robertus
Expand We study nonlinear vacuum electrodynamics in the first-order formulation proposed by Plebanski. We analyze in detail the equations of motion, and identify conditions for which a singularity can occur for the time derivative of one of the field components. The resulting degenerate behavior can give rise to a shock wave with a reduction of the local number of degrees of freedom. We use an example model to illustrate the occurrence of superluminal propagation for field values approaching the singularity.Expand - CPT and Lorentz violation in the electroweak sectorPublication . Colladay, D; Noordmans, Jacob; Potting, Robertus
Expand Long ago, Carroll, Field and Jackiw introduced CPT-violation in the photon sector by adding a dimension-3 gauge-invariant term parametrized by a constant four-vector parameter k(AF) to the usual (Maxwell) Lagrangian, deriving an ultra-tight bound from astrophysical data. Here, we will discuss recent work studying the extension of this term to the full electroweak gauge sector of the Standard Model. In the context of the Standard Model Extension, CPT and Lorentz violation arises from two gauge-invariant terms parametrized by the four vectors k(1) and k(2). First we will show how upon spontaneous breaking of the electroweak gauge symmetry these two terms yield Lorentz-violating terms for the photon and the W and Z bosons. As it turns out, the resulting modified dispersion relations for the W bosons yield spacelike momentum for one of its propagating modes at sufficiently large energy. This in turn allows for the possibility of Cherenkov-like W-boson emission by high-energy fermions such as protons, provoking their decay. Analysis of ultra-high-energy cosmic ray data allows for bounding the previously unbound parameter k(2), and, by combination with the ultra-tight bound on k(AF), the parameter k(1).Expand - Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz symmetryPublication . Escobar, C. A.; Potting, Robertus
Expand We study spontaneous breaking of Lorentz symmetry in nonlinear vacuum electrodynamics. Using a first-order formulation of the latter proposed by Plebanski, we apply a Dirac constraint analysis and derive an effective Hamiltonian. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing local minima in which the field strength acquires a nonzero vacuum expectation value, thereby breaking Lorentz invariance spontaneously. These possible vacua can be classified in four classes, depending on the way Lorentz symmetry is broken. We show that the small field fluctuations around these vacua involve modes for which the dynamics can develop degeneracies, resulting in shock-wave-like and/or superluminal motion. Finally, we study the physical applicability of these models, and show how the Lorentz breaking vacua might in principle be detected by coupling the model to a suitable external current, or to gravity.Expand - Bounding CPT and Lorentz symmetry violations through ultra-high-energy cosmic raysPublication . Escobar, C A; Potting, Robertus
Expand We review recent work on CPT and Lorentz violation in the context of the Standard-Model Extension. In particular, we show that, when CPT and Lorentz violation is present in the kinetic terms of any particle in the gauge boson or the lepton sector, this will generally lead to proton decay at sufficiently high energy. Using observational data from ultra-high energy cosmic rays, this has allowed to derive new bounds on the corresponding CPT and Lorentz-violation parameters.Expand - Structural aspects of Lorentz-violating quantum field theoryPublication . Cambiaso, M; Lehnert, R; Potting, Robertus
Expand In the last couple of decades the Standard Model Extension has emerged as a fruitful framework to analyze the empirical and theoretical extent of the validity of cornerstones of modern particle physics, namely, of Special Relativity and of the discrete symmetries C, P and T (or some combinations of these). The Standard Model Extension allows to contrast high-precision experimental tests with posited alterations representing minute Lorentz and/or CPT violations. To date no violation of these symmetry principles has been observed in experiments, mostly prompted by the Standard-Model Extension. From the latter, bounds on the extent of departures from Lorentz and CPT symmetries can be obtained with ever increasing accuracy. These analyses have been mostly focused on tree-level processes. In this presentation I would like to comment on structural aspects of perturbative Lorentz violating quantum field theory. I will show that some insight coming from radiative corrections demands a careful reassessment of perturbation theory. Specifically I will argue that both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted given that the asymptotic single-particle states can receive quantum corrections from Lorentz-violating operators that are not present in the original Lagrangian.Expand