Global conformal invariance in quantum field theory

Journal Article · Tue Apr 01 04:00:00 EDT 1975 · Commun. Math. Phys., v. 41, no. 3, pp. 203-234

DOI:https://doi.org/10.1007/BF01608988· OSTI ID:4136239

Luescher, M; Mack, G

Suppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal group G approximately = SO(5.1). We show that its Hilbert space of physical states carries then a unitary representation of the universal (infinitely-sheeted) covering group G* of the Minkowskian conformal group SO(4.2)Z$sub 2$. The Wightman functions can be analytically continued to a domain of holomorphy which has as a real boundary an infinitely-sheeted covering M tilde of Minkowski-space M$sup 4$. It is known that G* can act on this space M tilde and that M tilde admits a globally G*-invariant causal ordering; M is thus the natural space on which a globally G*-invariant local QFT could live. We discuss some of the properties of such a theory, in particular the spectrum of the conformal Hamiltonian H = 1/2(P$sup 0$ + K$sup 0$). (orig./BJ)

• Research Organization: Bern Univ. (Switzerland). Inst. fuer Theoretische Physik
• NSA Number: NSA-33-011135
• OSTI ID: 4136239
• Journal Information: Commun. Math. Phys., v. 41, no. 3, pp. 203-234, Journal Name: Commun. Math. Phys., v. 41, no. 3, pp. 203-234; ISSN CMPHA
• Country of Publication: Germany
• Language: English

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WIGHTMAN FIELD THEORY