Manifestly Covariant Quantum Theory with Invariant Evolution Parameter in Relativistic Dynamics

Abstract

Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard Model. The anomalies include neutrino oscillations, non-locality, and gravity.The two key QFT assumptions that are altered in PRD are the following: fields depend on space and time; and interactions between fields are local. Locality and nonlocality refer to the correlation of particles with space-like separation. A local theory does not allow the existence of greater than light speed correlations, while a non-local theory does. PRD is a non-local theory that allows fields to depend on space, time and an invariant evolution parameter. A formulation of PRD is presented together with applications that can be directly compared to results from the conventional paradigm.

Comparative Analysis of Jüttner’s Calculation of the Energy of a Relativistic Ideal Gas and Implications for Accelerator Physics and Cosmology

“…Horwitz [10] (Chapter 3) discussed the construction of Fock space, quantum field theory, and creation/annihilation operators. Action-at-a-distance, nonlocality and superluminal motion are discussed by Fanchi [5,6] and Pavšič [16,19]. The relativistic ideal gas in the ultrarelativistic regime is a regime where different results by Jüttner [1] and Horwtiz et al [4] can be tested, as we discuss further in Section 4.…”

“…A more general introduction to parametrized relativistic quantum theory is provided by Fanchi [5,6], Pavšič [16], and Horwitz [10]. Parametrized relativistic quantum field theory was introduced by Fanchi [5,17], and discussed more fully by Pavšič [16] (Chapter 1), including canonical quantization and creation/annihilation operators.…”

“…Fanchi [5,6] proposed a test using the energy difference by combining an expression for the energy calculated by Horwitz et al [4] with a cosmological model that is consistent with the parametrized theory. The test showed that the calculation of the Friedmann scale factor depends on the choice of energy in the ultrarelativistic (UR) regime, but the test was not definitive because of uncertainties associated with important cosmological factors.…”

Time dispersion in quantum mechanics

“…• The relativistic dynamics program of Horwitz, Piron, Land, Collins, and others: [33,34,35,36,37,38,39,40]. This program is a natural outgrowth of Stueckelberg & Feynman's work.…”

Induced representations of tensors and spinors of any rank in the Stueckelberg-Horwitz-Piron theory

“…The unitary evolution manifests itself in an evolution equation, which generalizes that of Schrödinger for the relativistic regime: The evolution parameter, , is the generalization of the Newtonian time parameter in the Stueckelberg-Schrödinger equation [3] .…”