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<p>In this paper, we construct a systematic framework for relativistic quantum clocks in curved spacetimes, illustrating a detailed analysis of proper-time superposition and interference phenomena under external potentials and topological defects. The formalism explicitly quantifies interference visibility and the evolution of quantum clocks, with particular attention to cosmic string geometries and their characteristic conical structure. We generalize the approach to <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation>-dimensional curved spacetimes, examining how the dimensionality affects proper-time evolution, interference profiles, and the response to generalized external potentials. To enable a rigorous operator-based treatment, we define the proper-time interference operator in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation> dimensions, which permits direct evaluation of observables and establishes a link between quantum interference effects and the geometric and topological properties of the background spacetime. In this context, this formulation provides a unified methodology for investigating relativistic quantum dynamics, interference phenomena, and information-theoretic aspects in nontrivial curved backgrounds, showing precise tools for applications in fundamental quantum theory and relativistic quantum measurement.</p>

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Proper-Time Interference Operators and Relativistic Quantum Clocks in \(\mathcal {D}\) Dimensions

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Abdelmalek Bouzenada

摘要

In this paper, we construct a systematic framework for relativistic quantum clocks in curved spacetimes, illustrating a detailed analysis of proper-time superposition and interference phenomena under external potentials and topological defects. The formalism explicitly quantifies interference visibility and the evolution of quantum clocks, with particular attention to cosmic string geometries and their characteristic conical structure. We generalize the approach to \(\mathcal {D}\) D -dimensional curved spacetimes, examining how the dimensionality affects proper-time evolution, interference profiles, and the response to generalized external potentials. To enable a rigorous operator-based treatment, we define the proper-time interference operator in \(\mathcal {D}\) D dimensions, which permits direct evaluation of observables and establishes a link between quantum interference effects and the geometric and topological properties of the background spacetime. In this context, this formulation provides a unified methodology for investigating relativistic quantum dynamics, interference phenomena, and information-theoretic aspects in nontrivial curved backgrounds, showing precise tools for applications in fundamental quantum theory and relativistic quantum measurement.