Generalized relativistic field equations have been derived for dynamics in a non-inertial reference frame interpreted as a Finsler space where events are specified by both spacetime coordinates and corresponding velocities (tangent vectors). The field equations follow in two alternative forms from exact general conservation laws derived through application of Cartan covariant differentiation within the framework of Finsler geometry. Velocity-dependent (curvature) terms in the field equations can account for the anisotropy of the gravitational field, together with the associated acceleration and expansion of the universe.

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This paper provides a scheme for generating maximally entangled qubit states in the anti-Jaynes-Cummings interaction mechanism, so called entangled anti-polariton qubit states. We demonstrate that in an initial vacuum-field, Rabi oscillations in a cavity mode in the anti-Jaynes-Cummings interaction process, occur in the reverse sense relative to the Jaynes-Cummings interaction process and that time evolution of entanglement in the anti-Jaynes-Cummings interaction process takes the same form as in the Jaynes-Cummings interaction process. With the generated anti-polariton qubit state as one of the initial qubits, we present quantum teleportation of an atomic quantum state by applying entanglement swapping protocol achieving an impressive maximal teleportation fidelity 1 F ρ = .

This article is a response to the continued assumption, cited even in reports and reviews of recent experimental breakthroughs and advances in theoretical methods, that the antiJaynes-Cummings (AJC) interaction is an intractable energy non-conserving component of the quantum Rabi model (QRM). We present three key features of QRM dynamics : (a) the AJC interaction component has a conserved excitation number operator and is exactly solvable (b) QRM dynamical space consists of a rotating frame (RF) dominated by an exactly solved Jaynes-Cummings (JC) interaction specified by a conserved JC excitation number operator which generates the U (1) symmetry of RF and a correlated counterrotating frame (CRF) dominated by an exactly solved antiJaynes-Cummings (AJC) interaction specified by a conserved AJC excitation number operator which generates the U (1) symmetry of CRF (c) for QRM dynamical evolution in RF, the initial atom-field state |e0 is an eigenstate of the effective AJC Hamiltonian HAJC, while the effective JC Hamiltonian HJC drives this initial state |e0 into a time evolving entangled state, and, in a corresponding process for QRM dynamical evolution in CRF, the initial atom-field state |g0 is an eigenstate of the effective JC Hamiltonian, while the effective AJC Hamiltonian drives this initial state |g0 into a time evolving entangled state, thus addressing one of the long-standing challenges of theoretical and experimental QRM dynamics; consistent generalizations of the initial states |e0 , |g0 to corresponding n ≥ 0 entangled eigenstates | Ψ + en , |Ψ − gn of the AJC in RF and JC in CRF, respectively, provides general dynamical evolution of QRM characterized by collapses and revivals in the time evolution of the atomic, field mode, JC and AJC excitation numbers for large initial photon numbers ; the JC and AJC excitation numbers are conserved in the respective frames RF , CRF, but each evolves with time in the alternate frame.

We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one component associated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.