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Local Fields Without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation

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Abstract

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. One may assume the existence of such fields only if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT-invariance. Restrictions on mass-spectrum of CPT-violating fields are found. Local fields that annihilate vacuum state and violate CPT-invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particularly needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed.

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Authors and Affiliations

  1. High Energy and Elementary Particles Physics Department, The Faculty of Physics, Saint-Petersburg State University, Saint Petersburg, Russia

    M. A. Kurkov & V. A. Franke

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  1. M. A. Kurkov
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  2. V. A. Franke
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Correspondence to V. A. Franke.

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Kurkov, M.A., Franke, V.A. Local Fields Without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation. Found Phys 41, 820–842 (2011). https://doi.org/10.1007/s10701-010-9525-0

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  • DOI: https://doi.org/10.1007/s10701-010-9525-0

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