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An Algebraic Model for Quantum Unstable States

Author

Listed:
  • Sebastian Fortin

    (CONICET, Universidad de Buenos Aires, Buenos Aires 1428, Argentina
    These authors contributed equally to this work.)

  • Manuel Gadella

    (Departamento de Física Teórica, Atómica y Optica, Universidad de Valladolid, Paseo Belén 7, 47011 Valladolid, Spain
    These authors contributed equally to this work.)

  • Federico Holik

    (Instituto de Física La Plata, UNLP, CONICET, Facultad de Ciencias Exactas, La Plata 1900, Argentina
    These authors contributed equally to this work.)

  • Juan Pablo Jorge

    (Facultad de Filosofía y Letras, Universidad de Buenos Aires, Puan 480, Buenos Aires 1428, Argentina
    Instituto de Filosofía, Universidad Austral, Mariano Acosta 1611, Argentina
    These authors contributed equally to this work.)

  • Marcelo Losada

    (Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Av. Medina Allende s/n, Córdoba 5000, Argentina
    These authors contributed equally to this work.)

Abstract

In this review, we present a rigorous construction of an algebraic method for quantum unstable states, also called Gamow states. A traditional picture associates these states to vectors states called Gamow vectors. However, this has some difficulties. In particular, there is no consistent definition of mean values of observables on Gamow vectors. In this work, we present Gamow states as functionals on algebras in a consistent way. We show that Gamow states are not pure states, in spite of their representation as Gamow vectors. We propose a possible way out to the construction of averages of observables on Gamow states. The formalism is intended to be presented with sufficient mathematical rigor.

Suggested Citation

  • Sebastian Fortin & Manuel Gadella & Federico Holik & Juan Pablo Jorge & Marcelo Losada, 2022. "An Algebraic Model for Quantum Unstable States," Mathematics, MDPI, vol. 10(23), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4562-:d:991023
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    References listed on IDEAS

    as
    1. Antoniou, I. & Suchanecki, Z. & Laura, R. & Tasaki, S., 1997. "Intrinsic irreversibility of quantum systems with diagonal singularity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 737-772.
    2. Civitarese, O. & Gadella, M., 2014. "On the entropy for unstable fermionic and bosonic states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 302-314.
    3. Castagnino, Mario, 2004. "The classical–statistical limit of quantum mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 511-517.
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