The origin of three-cocycles in quantum field theory |
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| Institution: | 1. Medical Genetics, University of Siena, Siena, Italy;2. Mitochondrial Biology Unit, Medical Research Council Cambridge, Cambridge, UK;3. Department of Translational Research and New Technologies in Medicine and Surgery, University of Pisa, Pisa, Italy;4. Department of Biochemical Sciences, Sapienza University, Rome, Italy;5. Department of Medical Biotechnologies, University of Siena, Siena, Italy;6. Unit of Diagnostic and Therapeutic Neuroradiology, Department of Neurosciences, Azienda Ospedaliera Universitaria Senese, Siena, Italy;7. Clinica Pediatrica, University of Siena, Siena, Italy;8. Genetica Medica, Azienda Ospedaliera Universitaria Senese, Siena, Italy |
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| Abstract: | When quantising a classical field theory it is not automatic that a group of symmetries of the classical system is preserved as a symmetry of the quantum system. Apart from the phenomenon of symmetry breaking it can also happen (as in Faddeev's Gauss law anomaly) that only an extension of the classical group acts as a symmetry group of the quantum system. We show here that rather than signalling a failure of the associative law as has been suggested in the literature, the occurrence of a non-trivial three-cocycle on the local gauge group is an “anomaly” or obstruction to the existence of an extension of the local gauge group acting as a symmetry group of the quantum system. |
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