Quantum interference of a de Broglie wave of a Diracparticle beyond the `hypothesis of locality´.Part II. Hermicity and non-relativistic limit - Ter-Kazarian, G.
This is the second of three articles that explore the possibility of quantum mechanical inertial properties of the Dirac particle beyond the, so-called, `hypothesis of locality´, of standard approach. This is done within the framework of the Master Space-Teleparallel Supergravity (MS gp-TSG) Ter-Kazarian (2025a) theory, which we recently proposed to account for inertial effects Ter-Kazarian (2026). Our strategy in Ter-Kazarian (2025b) (first article of three) is to compute the object of anholonomicity and connection defined with respect to the anholonomic frame. Based on this, we derived the general Dirac equation in an accelerated and rotating frame of reference beyond the`hypothesis of locality´. This equation, however, contains also residual imaginary terms, which are artifacts that due to coordinate transformations in the non-inertial frames. To eliminate these terms to all orders, in present article, at first, we apply the standard techniques used in relativistic quantum mechanics and quantum field theory, where non-Hermitian terms can be removed via suitable similarity transformations. This standard method allows us to choose a physically more suitable reference frame. We show that the expectation values of physical observables remain real. No imaginary contamination remains in physical quantities. Thus the energy, momentum, probability, etc., remain real and consistent. Secondly, we are interested in low-energy properties, avoiding solutions with negative energy. In the method employed for reducing the Dirac Hamiltonian to nonrelativistic two-component form, in order to decouple the positive and the negative energy states, we use an approximate scheme of the Foldy-Wouthuysen canonical transformation of the Dirac Hamiltonian for a free particle. This is performed by an infinite sequence of FW-transformations leading to a deformed Hamiltonian, which is an infinite series in powers of (1/m). Evaluating the operator products to the desired order of accuracy, we derive the deformed, non-relativistic Hamiltonian. We then compute the inertial effects for a massive Dirac fermion in non-relativistic approximation, which are displayed beyond the `hypothesis of locality´ as extended (deformed) versions of the standard effects. The latter are well-known important inertial effects such as the redshift effect (Colella-Overhauser-Werner experiment), the Sagnac-type effect, the spin rotation effect (Mashhoon), the kinetic energy redshift effect, the new inertial spin-orbit coupling. Expanding further the deformation coefficients, several new effects will rather appeared involving spin, angular momentum, proper linear 3-acceleration ⃗a and proper 3-angular velocity ⃗ω in various mixed combinations.
Keywords: Quantum interference