Relativistic harmonic oscillator revisited
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-2535 (United States)
The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example, as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory), while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approach that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost-free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover, all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.
- OSTI ID:
- 21260024
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 79, Issue 4; Other Information: DOI: 10.1103/PhysRevD.79.045009; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ANNIHILATION OPERATORS
CASIMIR EFFECT
EIGENVALUES
GAUGE INVARIANCE
HARMONIC OSCILLATORS
LORENTZ GROUPS
MANY-DIMENSIONAL CALCULATIONS
OSCILLATORS
QUANTUM FIELD THEORY
QUANTUM NUMBERS
RELATIVISTIC RANGE
SO GROUPS
SPACE-TIME
SPECTRA
STRING MODELS
SU GROUPS
SYMMETRY