Construction of a complete set of states in relativistic scattering theory

Journal Article · Wed Jan 01 04:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531845· OSTI ID:435144

Pelc, O ^[1]; Horwitz, L P ^[2]

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1. Racah Institute of Physics, The Hebrew University, Jerusalem, 91904 (Israel)
2. School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540 (United States)

The space of physical states in relativistic scattering theory is constructed, using a rigorous version of the Dirac formalism, where the Hilbert space structure is extended to a Gel{close_quote}fand triple. This extension enables the construction of {open_quotes}a complete set of states,{close_quotes} the basic concept of the original Dirac formalism, also in the cases of unbounded operators and continuous spectra. We construct explicitly the Gel{close_quote}fand triple and a complete set of {open_quotes}plane waves{close_quotes}{emdash}momentum eigenstates{emdash}using the group of space{endash}time symmetries. This construction is used (in a separate article) to prove a generalization of the Coleman{endash}Mandula theorem to higher dimension. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 435144
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 1 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
EIGENFUNCTIONS
EIGENVALUES
GROUP THEORY
HILBERT SPACE
QUANTUM OPERATORS
RELATIVISTIC RANGE
SCATTERING
SCATTERING AMPLITUDES
SET THEORY
SPACE-TIME
SYMMETRY GROUPS