Generalized Catability of Relativistic Quantum States Measurement in a Unified Lie-Algebraic Foldy-Wouthuysen (FW) Framework

TL;DR

This paper develops a unified Lie-algebraic framework for analyzing relativistic quantum states, coherence, and superposition effects across arbitrary spins, incorporating a generalized Foldy-Wouthuysen transformation.

Contribution

It introduces a novel algebraic formalism for relativistic quantum systems, extending catability and coherence analysis to arbitrary spin fields within a unified Lie-algebraic approach.

Findings

Formulated a phase-sensitive catability operator for relativistic quantum dynamics.

Extended the formalism to arbitrary spin-$s$ fields, including higher-spin states.

Applied the framework to Dirac particles, analyzing relativistic fermionic catability.

Abstract

In this work, a unified Lie-algebraic formulation of catability is constructed for relativistic quantum systems with arbitrary spin within this framework. In this case, the analysis starts with constructing catability as a quantitative measure for superposed coherent states, where coherence structure and quantum interference properties are studied using algebraic representations in this framework. Also, a generalized Foldy-Wouthuysen transformation is formulated within a Lie algebraic framework, delivering a systematic procedure for block-diagonalization of relativistic Hamiltonians and separation of positive- and negative-energy components in this framework. Within this formalism, a phase-sensitive catability operator is introduced to study phase correlations and coherence effects in the relativistic quantum dynamics framework. The approach is applied to Dirac spin-$1/2$ particles, where relativistic fermionic catability is analyzed in relation to spinorial structures and symmetry generators framework. The formalism is extended through a unified geometric and Lie-algebraic treatment, establishing a consistent description of catability in a relativistic quantum mechanics framework. In this context, the generalized framework is constructed for arbitrary spin-$s$ fields, enabling investigation of higher-spin relativistic quantum states within the same algebraic structure framework. In this context, the obtained results show a generalized theoretical platform for investigating relativistic quantum coherence, superposition effects, and algebraic symmetries in the framework of fermionic and bosonic systems.