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

We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d+1)-dimensional Minkowski space.

/pdf/spinning-conformal-correlators-40nzqig95u.pdf

Spinning conformal correlators

In this article, an introduction to the nonlinear equations for completely symmetric bosonic higher spin gauge fields in anti de Sitter space of any dimension is provided. To make the presentation self-contained we explain in detail some related issues such as the MacDowell-Mansouri-Stelle-West formulation of gravity, unfolded formulation of dynamical systems in terms of free differential algebras and Young tableaux symmetry properties in terms of Howe dual algebras.

Nonlinear higher spin theories in various dimensions

Local BRST cohomology in gauge theories

Motivated by the computation of scattering amplitudes at strong coupling, we consider minimal area surfaces in AdS
 5 which end on a null polygonal contour at the boundary. We map the classical problem of finding the surface into an SU(4) Hitchin system. The polygon with six edges is the first non-trivial example. For this case, we write an integral equation which determines the area as a function of the shape of the polygon. The equations are identical to those of the Thermodynamics Bethe Ansatz. Moreover, the area is given by the free energy of this TBA system. The high temperature limit of the TBA system can be exactly solved. It leads to an explicit expression for a special class of hexagonal contours.

https://www.strings.ph.qmul.ac.uk/~theory/Amplitudes2010/Talks/LFA2010.pdf

Thermodynamic bubble ansatz

Higher-order singletons, partially massless fields, and their boundary values in the ambient approach

For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space–time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.

Parent Field Theory and Unfolding in BRST First-Quantized Terms

Unified BRST description of AdS gauge fields

Massless Poincare modules and gauge invariant equations

For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space--time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.

Maxim Grigoriev

Papers

Higher-order singletons, partially massless fields, and their boundary values in the ambient approach

Parent Field Theory and Unfolding in BRST First-Quantized Terms

Unified BRST description of AdS gauge fields

Massless Poincare modules and gauge invariant equations

Parent field theory and unfolding in BRST first-quantized terms