Journal or Publication Title:

Բյուրականի աստղադիտարանի հաղորդումներ: Երևանի աստղադիտարանի բյուլետեն = Сообщения Бюраканской обсерватории. Бюллетень ереванской Астрономической обсерватории = Contributions from the Burakan observatory. Bulletin of the Erevan astronomical observatory

Date of publication:

2025

Volume:

72

Number:

2

ISSN:

2579-2276

Coverage:

226-246

Abstract:

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.

Format:

pdf

Identifier:

oai:arar.sci.am:425937

General note:

Communications of the Byurakan Astrophysical Observatory (ComBAO) is a peer-reviewed scientific journal, which publishes research in observational and theoretical astronomy/astrophysics and presents recent advances in these fields. It is being published by the NAS RA V. Ambartsumian Byurakan Astrophysical Observatory (BAO) in English in electronic form. The journal publishes original papers, review papers, brief reports, book reviews, special communications, observational and theoretical results in various fields of astronomy and related sciences, and some editorial notes, including anniversaries and obituaries. Under the heading “Legacy”, the renewed magazine will republish some old articles of high value in English. The heading “Guest articles” will bring to the attention of readers the articles of researchers who are not employees of BAO. ComBAO was founded in 1946 and regularly published in 1946-1990. However, the publication was interrupted because of the economic situation after the disintegration of the Soviet Union in 1991.

Location of original object:

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