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Conformal quantum field theory in \(D\)-dimensions. (English) Zbl 0896.70001

Mathematics and its Applications (Dordrecht). 376. Dordrecht: Kluwer Academic Publishers. xii, 461 p. (1996).
Since the discovery of conformal invariance of Maxwell’s equations, going back to Cunningham and Bateman in 1909, the idea of conformal and scale invariance underlying physical phenomena has played a constant and fruitful source of inspiration. But it is only in the early seventies that particle physics has provided strong support to such geometric dream: in the ultraviolet or infrared region, a universal scale invariant behaviour is exhibited regardless to dimensional parameters and to the initial Hamiltonian.
The strategy pursued in this work is to derive constraints to the effective interactions from purely model-independent quantum field theoretic general principles and examining the consequences of assuming local conserved fields (energy-momentum tensor and local currents related to internal symmetries – QFT-Noether’s theorem). This leads to the study of all possible conformally invariant Ward identities which govern, in turn, the possible types of field interactions.
This book addresses itself primarily to the case \(D>2\), and speculates about the possible existence of a Virasoro-like symmetry even in this more general case, which would ease the actual construction of explicit models. The book is well written, and a clear and comprehensive introduction brings full motivation and historical perspective to the subject.
Reviewer: F.Cardin (Padova)

MSC:

70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
81T05 Axiomatic quantum field theory; operator algebras
81T20 Quantum field theory on curved space or space-time backgrounds
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