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Irreversibility and Causality Semigroups and Rigged Hilbert Spaces

Arno Böhm, H. D. Doebner, Piotr Kielanowski

Lecture notes in physicsJan 1, 199880 citations

Representations of Temporal Groups and Semigroups

Hans Primas

Springer eBooksJan 1, 20170 citations

Time asymmetric quantum theory – III. Decaying states and the causal Poincaré semigroup

Arno Böhm, Hani Kaldass, Sujeewa Wickramasekara

Abstract These Gamow kets span an irreducible representation space for Poincaré transformations which, similar to the Wigner representations for stable particles, are characterized by spin (angular momentum of the partial wave amplitude) and complex mass (position of the resonance pole). The Poincaré transformations of the Gamow kets, as well as of the Lippmann‐Schwinger plane wave scattering states, form only a semigroup of Poincaré transformations into the forward light cone. Their transformation properties are derived. From these one obtains an unambiguous definition of resonance mass and width for relativistic resonances. The physical interpretation of these transformations for the Born probabilities and the problem of causality in relativistic quantum physics is discussed.Abstract These Gamow kets span an irreducible representation space for Poincaré transformations which, similar to the Wigner representations for stable particles, are characterized by spin (angular momentum of the partial wave amplitude) and complex mass (position of the resonance pole). The Poincaré transformations of the Gamow kets, as well as of the Lippmann‐Schwinger plane wave scattering states, form only a semigroup of Poincaré transformations into the forward light cone. Their transformation properties are derived. From these one obtains an unambiguous definition of resonance mass and width for relativistic resonances. The physical interpretation of these transformations for the Born probabilities and the problem of causality in relativistic quantum physics is discussed.

arXiv:hep-th/0212282Fortschritte der PhysikMay 13, 200319 citations

Causality, symmetries and quantum mechanics

J. Anandan

arXiv:physics/0112020Foundations of Physics LettersOct 1, 200215 citations

On the Theory of the Multiplication of Causal Functions

V. Garchinskii

Soviet physics. DokladyJun 1, 19621 citation

Space−time symmetries and nonunitary representations of the Poincaré semigroup: Description of unstable particles

M. Comi, L. Lanz, Luigi A. Lugiato +1 more

In this paper we justify the use of nonunitary representations of the space−time symmetry group to describe physical systems, as, e.g., unstable particles. It is shown that such a generalization of the standard theory of symmetries is possible inside the approach to quantum mechanics recently developed by Ludwig. The Poincaré semigroup turns out to be the fundamental symmetry group and only Lorentz transformations must be unitary.

Journal of Mathematical PhysicsApr 1, 19757 citations

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