Summary
The proof of unitarity for gauge theories involving a Faddeev-Popov ghost is revisited. We assume the existence of a generatorF of the Slavnov transformations. The subspace of the unphysical one-particle states is that spanned byF. Under the assumption thatF is conserved and obeys the conditionF 2=0, we prove that the unphysical states do not contribute to the unitarity equation restricted to the physical subspace.
Riassunto
Si riesamina la prova dell’unitarietà per teorie di gauge che contengono un fantasma di Faddeev e Popov. Si assume l’esistenza di un generatore delle trasformazioni di Slavnov. Il sottospazio degli stati a una particella non fisica rappresenta in modo non banaleF. Nell’ipotesi cheF sia conservato e che obbedisca alla condizioneF 2=0, si dimostra che gli stati non fisici non contribuiscono all’equazione di unitarietà ristretta al sottospazio dei vettori fisici.
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References
C. Becchi, A. Rouet andR. Stora:Gauge field models, inLectures Given at the Erice Summer School (1975). This paper gives the references of the previous works.
G. Curci andR. Ferrari:Phys. Lett.,63 B, 91 (1976).
N. N. Bogoliubov andD. V. Shirkov:Introduction to the Theory of Quantized Fields, Chap. III (New York, N. Y., 1959).
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Work supported in part by the Alexander von Humboldt Stiftung.
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Curci, G., Ferrari, R. An alternative approach to the proof of unitarity for gauge theories. Nuov Cim A 35, 273–279 (1976). https://doi.org/10.1007/BF02730284
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DOI: https://doi.org/10.1007/BF02730284