Algebraic quantisation with indefinite metric
- 1 October 1983
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 16 (14) , 3271-3290
- https://doi.org/10.1088/0305-4470/16/14/020
Abstract
A real symplectic flow may be viewed as being pseudo-unitary, provided there exists a symplectic complex structure J which commutes with it. The author determines the class of dynamical systems for which J exists. Such systems may be quantised algebraically but the state space may have indefinite metric. This procedure admits a larger class of classical systems than does Segal's algebraic quantisation but there are problems in interpreting the indefinite metric and these are listed and discussed.Keywords
This publication has 25 references indexed in Scilit:
- Existence theorems for Segal quantization via spectral theory in Krein spaceThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1983
- On a pathology in indefinite metric inner product spaceCommunications in Mathematical Physics, 1982
- Fermi-Dirac quantization of linear systemsAnnals of Physics, 1981
- Canonical forms for quadratic HamiltoniansPhysica A: Statistical Mechanics and its Applications, 1981
- Existence of a complex structure for quadratic Hamiltonians?Annals of Physics, 1981
- Normal forms for classical and boson systemsPhysica A: Statistical Mechanics and its Applications, 1979
- Electromagnetic interaction of higher-spin fieldsPhysical Review D, 1978
- A note on the Fermi quantisation of Landau gaugeLetters in Mathematical Physics, 1978
- Lorentz Invariance, Local Field Theory, and Faster-than-Light ParticlesPhysical Review B, 1968
- On quantum theories with indefinite metricNuclear Physics, 1958