To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Superstring theoryをめぐって(放談室)

This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov Parasiuk Hepp-Zimmermann renormalization scheme is used throughout, including the renormalized action principle proved by Lowenstein and Lam. The whole study is based on the fulfillment to all orders of perturbation theory of the Slavnov identities which express the invariance of the Lagrangian under a supergauge type family of non-linear transformations involving the Faddeev-Popov ghosts. Direct combinatorial proofs are given of the gauge independence and unitarity of the physicalS operator. Their simplicity relies both on a systematic use of the Slavnov identities as well as suitable normalization conditions which allow to perform all mass renormalizations, including those pertaining to the ghosts, so that the theory can be given a setting within a fixed Fock space. Some simple gauge independent local operators are constructed.

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Renormalization of the Abelian Higgs-Kibble Model

Renormalizable asymptotically free quantum theory of gravity

Antibracket, antifields and gauge-theory quantization

One loop finiteness of quantum gravity off mass shell

A generalized version is proposed for the field–antifield formalism. The antibracket operation is defined in arbitrary field–antifield coordinates. The antisymmetric definitions are given for first- and second-class constraints. In the case of second-class constraints the Dirac's antibracket operation is defined. The quantum master equation as well as the hypergauge fixing procedure are formulated in a coordinate–invariant way. The general hypergauge functions are shown to be antisymmetric first–class constraints whose Jacobian matrix determinant is constant on the constraint surface. The BRST-type generalized transformations are defined and the functional integral is shown to be independent of the hypergauge variations admitted. In the case of reduced phase space the Dirac's antibrackets are used instead of the ordinary ones.

On Possible Generalizations of Field-Antifield Formalism

Reparametrization invariance treated as a gaugesymmetry shows some specific peculiarities. We studythese peculiarities both from a general point of viewand by concrete examples. We consider the canonical treatment of reparametrization-invariantsystems in which one fixes the gauge on the classicallevel by means of time-dependent gauge conditions. Insuch an approach one can interpret different gauges as different reference frames. We discuss therelation between different gauges and the problem ofgauge invariance in this case. Finally, we establish ageneral structure of reparametrizations and itsconnection with the zero-Hamiltonian phenomenon.

Reparametrization invariance as gauge symmetry

The multilevel geometrically covariant generalization of the field-antifield BV formalism is suggested. The structure of quantum generating equations and hypergauge conditions is studied in details. The multilevel formalism is established to be physically equivalent to the standard BV version.

On the multilevel generalization of the field-antifield formalism

The new quantization scheme is proposed for theories with second class constraints. The formalism possesses the properties intermediate between those of the conversion method and quantum deformation of the Dirac bracket: on the one hand, all the phase variable operators have nonsingular commutators while the physical states are determined by weak equations; on the other hand, no extra degrees of freedom are introduced.

Igor Viktorovich Tyutin

Papers

One loop finiteness of quantum gravity off mass shell

On Possible Generalizations of Field-Antifield Formalism

Reparametrization invariance as gauge symmetry

On the multilevel generalization of the field-antifield formalism

Split involution and second class constraints