Lorentz-violating scalar Hamiltonian and equivalence principle in a static metric

Abstract

In this paper, we obtain a nonrelativistic Hamiltonian from the Lorentz-violating (LV) scalar Lagrangian in the minimal SME. The Hamiltonian is obtained by two different methods. One is through the usual ansatz $\Phi (t,\vec{r})=e^{-imt}\Psi (t,\vec{r})$ applied to the LV corrected Klein-Gordon equation, and the other is the Foldy-Wouthuysen transformation. The consistency of our results is also partially supported by the comparison with the spin-independent part of the fermion Hamiltonian. In this comparison, we can also establish a relation between the set of scalar LV coefficients with their fermion counterparts. Using a pedagogical definition of the weak equivalence principle (WEP), we further point out that the LV Hamiltonian not only necessarily violates universal free fall, which is clearly demonstrated in the geodesic deviation, but also violates WEP in a semi-classical setting. As a bosonic complement, this method can be straightforwardly applicable to the spin-1 case, which shall be useful in the analysis of atomic tests of WEP, such as the case of the ${}^{87}{\text{Rb}}_1$ atom.

11 pages

References in corpus (16)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• The Confrontation between General Relativity and Experiment
• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• The MICROSCOPE mission: first results of a space test of the Equivalence Principle
• Matter-gravity couplings and Lorentz violation
• Constraints on Torsion from Lorentz Violation
• What Do We Know About Lorentz Invariance?
• Quantum Tests of the Einstein Equivalence Principle with the STE-QUEST Space Mission
• Vacuum Cerenkov Radiation in Lorentz-Violating Theories Without CPT Violation
• Observable traces of non-metricity: new constraints on metric-affine gravity
• Short-range gravity and Lorentz violation
• Classical kinematics for Lorentz violation
• Vacuum Cherenkov radiation in spacelike Maxwell-Chern-Simons theory
• Proposal for a Quantum Test of the Weak Equivalence Principle with Entangled Atomic Species
• Constraining Spacetime Nonmetricity with Neutron Spin Rotation in Liquid He-4
• CPT and Lorentz violation en the Photon and $Z$-boson sector

Cited by in corpus (7)

• Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields
• Searches for beyond-Riemann gravity
• The Quantum Field Theory Boundaries Applicability and Black Holes Thermodynamics
• Mirrors and field sources in a Lorentz-violating scalar field theory
• Observation of $\Omega (2012{)}^{-}\to \Xi (1530)\bar{K}$ and measurement of the effective couplings of $\Omega (2012{)}^{-}$ to $\Xi (1530)\bar{K}$ and $\Xi \bar{K}$
• The analogy of the Lorentz-violating fermion-gravity and fermion photon couplings
• Exact Lorentz-violating $q$-deformed O($N$) universality class