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Quantum noncompact σ models (1987)

van Holten, J. W.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 28 (1987), S. 1420-1429

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: Two possible quantization procedures for field theories with noncompact symmetry are discussed: one in a positive-definite Hilbert space with negative-energy states and one in a Hilbert space with indefinite metric and positive-definite energy. The physical interpretation of these alternative procedures is explained in terms of the realization of the noncompact symmetry, which is broken in one case and not in the other. It is shown that in exactly solvable quantum σ models the noncompact symmetry is broken in the vacuum. Some arguments supporting the general validity of this result are given. It is concluded that in contrast to theories like quantum electrodynamics, the noncompact σ models are to be quantized in the positive-definite Hilbert space with negative-energy modes.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.527496

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