Abstract
Performing the equal-time limit under the integral of the spectral representation for the vacuum expectation value of the current commutator it is shown (as already suggested by models) that the vacuum expectation value of the equal-time commutator of a hermitean charge and the divergence of the corresponding (hermitean) vector or axial vector current (“σ-term”) vanishes only if the current is conserved. This then implies that a nonconserved hermitean charge cannot annihilate the vacuum, in agreement with Coleman's theorem.
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Meinem verehrten Lehrer, Herrn Professor F. Bopp, zum 60. Geburtstag gewidmet.
Supported by the Deutsche Forschungsgemeinschaft.
The author would like to thank Prof. R. Haag for hospitality at the II. Institute. He would like to thank Prof. S. Gasiorowicz for a critical reading of the manuscript and for useful suggestions. Thanks are also due Prof. R. Haag, Dr. J. Katz, and Dr. J. Langerholc, who has checked the argument, for discussions. The author would like to thank the Deutsche Forschungsgemeinschaft for a financial grant.
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Genz, H. On the vacuum expectation value of the σ-term. Z. Physik 229, 206–208 (1969). https://doi.org/10.1007/BF01396246
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DOI: https://doi.org/10.1007/BF01396246