Relativistic quantum theory. Pt.1

Relativistic quantum mechanics was developed to reconcile the principles of quantum mechanics with Einstein’s theory of relativity. Despite its success in describing high-energy particles, the theory continues to face unresolved conceptual and mathematical difficulties, particularly in relation to the nature of time, causality, and relativistic consistency. In recent years, the idea of extending space-time into the complex domain has emerged as a useful and potentially meaningful approach to these problems. In this work, a theoretical synthesis is presented to examine the role of complex space-time in relativistic quantum mechanics. The study discusses how complex time arises naturally in relativistic wave equations, quantum field theory, and path integral formulations. Established methods such as Wick rotation, complex coordinate transformations, and non-Hermitian but parity–time (PT) symmetric Hamiltonians are reviewed to illustrate how complex space-time contributes to mathematical stability and clearer physical interpretation (Dirac, 1928; Wick, 1954; Bender & Boettcher, 1998). The relevance of complex space-time is further explored in the context of relativistic particle dynamics and quantum cosmology, where it helps address, issues related to vacuum structure, time evolution, and causality (Feynman & Hibbs, 1965; Hartle & Hawking, 1983). The paper suggests that complex space-time should be viewed not only as a computational technique, but as a framework that may reflect deeper features of relativistic quantum phenomena.Relativistic quantum mechanics was developed to reconcile the principles of quantum mechanics with Einstein’s theory of relativity. Despite its success in describing high-energy particles, the theory continues to face unresolved conceptual and mathematical difficulties, particularly in relation to the nature of time, causality, and relativistic consistency. In recent years, the idea of extending space-time into the complex domain has emerged as a useful and potentially meaningful approach to these problems. In this work, a theoretical synthesis is presented to examine the role of complex space-time in relativistic quantum mechanics. The study discusses how complex time arises naturally in relativistic wave equations, quantum field theory, and path integral formulations. Established methods such as Wick rotation, complex coordinate transformations, and non-Hermitian but parity–time (PT) symmetric Hamiltonians are reviewed to illustrate how complex space-time contributes to mathematical stability and clearer physical interpretation (Dirac, 1928; Wick, 1954; Bender & Boettcher, 1998). The relevance of complex space-time is further explored in the context of relativistic particle dynamics and quantum cosmology, where it helps address, issues related to vacuum structure, time evolution, and causality (Feynman & Hibbs, 1965; Hartle & Hawking, 1983). The paper suggests that complex space-time should be viewed not only as a computational technique, but as a framework that may reflect deeper features of relativistic quantum phenomena.

Recent Trends in MathematicsJan 1, 20260 citations

Relativistic Quantum Theory

James E. Dodd, Ben M. Gripaios

Cambridge University Press eBooksSep 15, 20201,058 citations

New derivation of Time-Independent Perturbation Theory

Alexander N. Kvinikhidze, Boris Blankleider

We propose a new derivation of Time-Independent Perturbation Theory (PT) that has a fundamental advantage over the usual derivations presented in textbooks on Quantum Mechanics (QM): it is simpler and much shorter. As such, it can provide an easier and quicker way for students to learn PT, than afforded by current methods. In spite of that, our approach does not require the potentials to be energy independent or the inverse free Green function $G_0^{-1}(E)$ to be a linear function of energy $E$ , as is the case in QM, and can be applied directly to various extensions of QM including Relativistic QM, the Bethe-Salpeter equation, and all kinds of quasipotential approaches in Quantum Field Theory.We propose a new derivation of Time-Independent Perturbation Theory (PT) that has a fundamental advantage over the usual derivations presented in textbooks on Quantum Mechanics (QM): it is simpler and much shorter. As such, it can provide an easier and quicker way for students to learn PT, than afforded by current methods. In spite of that, our approach does not require the potentials to be energy independent or the inverse free Green function $G_0^{-1}(E)$ to be a linear function of energy $E$, as is the case in QM, and can be applied directly to various extensions of QM including Relativistic QM, the Bethe-Salpeter equation, and all kinds of quasipotential approaches in Quantum Field Theory.

arXiv:2303.14862Mar 27, 20230 citations

Relativistic Quantum Theory

Detlef Dürr, Dustin Lazarovici

Springer eBooksJan 1, 202030 citations

THEORETICAL STUDY OF Rydberg ALKALI ATOMIC SYSTEMS in a Black-body radiation field: Relativistic APPROACH

Alina A. Kuznetsova, A. Sandler

We present the results of studying the characteristics of Rydberg alkali atomic systems in a black-body (BBR; thermal) radiation field, in particular, BBR induced Stark shift coefficient k. As theoretical approach the combined generalized relativistic energy approach and relativistic many-body perturbation theory (PT) with ab initio Dirac zeroth approximation is applied. Application of theory to computing the spectral parameters of studied atomic systems have demonstrated physically reasonable agreement between the theoretical and experimental data. carefully. It should be noted that our method takes carefully into account such important factors as the implementation of a gauge invariance principle when calculating the corresponding matrix elements, the correct degree of consideration of complex exchange-correlation effects (primarily, the effect of polarization of the core), and also generates a fairly optimal one-quasiparticle representation in within the limits of many-body relativistic PT with ab initio zeroth Dirac-Fock (Kohn-Sham) approximation. In any case, the formalism developed in this work, as it follows from the given results, can be used for precise calculations of the Stark shift coefficient k, the BBR shift parameter β, and other parameters.We present the results of studying the characteristics of Rydberg alkali atomic systems in a black-body (BBR; thermal) radiation field, in particular, BBR induced Stark shift coefficient k. As theoretical approach the combined generalized relativistic energy approach and relativistic many-body perturbation theory (PT) with ab initio Dirac zeroth approximation is applied. Application of theory to computing the spectral parameters of studied atomic systems have demonstrated physically reasonable agreement between the theoretical and experimental data. carefully. It should be noted that our method takes carefully into account such important factors as the implementation of a gauge invariance principle when calculating the corresponding matrix elements, the correct degree of consideration of complex exchange-correlation effects (primarily, the effect of polarization of the core), and also generates a fairly optimal one-quasiparticle representation in within the limits of many-body relativistic PT with ab initio zeroth Dirac-Fock (Kohn-Sham) approximation. In any case, the formalism developed in this work, as it follows from the given results, can be used for precise calculations of the Stark shift coefficient k, the BBR shift parameter β, and other parameters.

PhotoelectronicsAug 21, 20220 citations

G_0^{-1}(E)

to be a linear function of energy

E

, as is the case in QM, and can be applied directly to various extensions of QM including Relativistic QM, the Bethe-Salpeter equation, and all kinds of quasipotential approaches in Quantum Field Theory.