Gravitational wave propagation beyond general relativity: waveform distortions and echoes

We study the cosmological propagation of gravitational waves (GWs) beyond general relativity (GR) across homogeneous and isotropic backgrounds. We consider scenarios in which GWs interact with an additional tensor field and use a parametrized phenomenological approach that generically describes their coupled equations of motion. We analyze four distinct classes of derivative and non-derivative interactions: mass, friction, velocity, and chiral. We apply the WKB formalism to account for the cosmological evolution and obtain analytical solutions to these equations. We corroborate these results by analyzing numerically the propagation of a toy GW signal. We then proceed to use the analytical results to study the modified propagation of realistic GWs from merging compact binaries, assuming that the GW signal emitted is the same as in GR. We generically find that tensor interactions lead to copies of the originally emitted GW signal, each one with its own possibly modified dispersion relation. These copies can travel coherently and interfere with each other leading to a scrambled GW signal, or propagate decoherently and lead to echoes arriving at different times at the observer that could be misidentified as independent GW events. Depending on the type of tensor interaction, the detected GW signal may exhibit amplitude and phase distortions with respect to a GW waveform in GR, as well as birefringence effects. We discuss observational probes of these tensor interactions with both individual GW events, as well as population studies for both ground- and space-based detectors.

Dirac equation with CPRS potential and Cornell tensor interaction in the presence of spin and pseudospin symmetry

Motivated by the prominent role of tensor interactions in nuclear spectroscopy and many applications of spin and pseudospin symmetry in hadronic and nuclear physics, we solve the Dirac equation with a CPRS potential and a Cornell tensor interaction, in the spin and pseudospin symmetry limits, by using the quasi-exactly solvable method. We obtain explicitly the wave functions for the two lowest energy levels, both for spin and pseudospin symmetry. We also discuss the degeneracy of the system.

Relativistic Properties of a Lagrangian and a Hamiltonian in Quantum Theories

Relativistic properties of a Dirac Lagrangian density are compared with those of a Dirac Hamiltonian density. Differences stem from the fact that a Lagrangian density is a Lorentz scalar, whereas a Hamiltonian density is a 00-component of a second rank tensor, called the energy-momentum tensor. This distinction affects the form of an interaction term of a Dirac particle. In particular, a tensor interaction term of a Dirac Lagrangian density transforms to a difference between a vector and an axial vector of the corresponding Hamiltonian density. This outcome shows that fundamental principles can prove the V-A attribute of weak interactions. A further analysis supports these results. Inherent problems of the electroweak theory are discussed.

Comment on “Solutions of the Dirac equation with an improved expression of the Rosen–Morse potential energy model including Coulomb-like tensor interaction”

The Nikiforov–Uvarov polynomial method employed by Aguda (Can. J. Phys. 2013, 91: 689. doi: 10.1139/cjp-2013-0109 ) to solve the Dirac equation with an improved Rosen–Morse potential plus a Coulomb-like tensor potential is shown to be inappropriate because the conditions of its application are not fulfilled. We clarify the problem and construct the correct solutions in the spin and pseudospin symmetric regimes via the standard method of solving differential equations. For the bound states, we obtain the spinor wave functions in terms of the generalized hypergeometric functions 2F1(a, b, c; z) and in each regime we show that the energy levels are determined by the solutions of a transcendental equation that can be solved numerically.