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

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection we present an overview of the achievements and the status of this subject as of the year 2010.

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Review of AdS/CFT Integrability: An Overview

One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.

Quantum Inverse Scattering Method and Correlation Functions

We discuss possible phase factors for the S-matrix of planar gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMN scaling, Kotikov?Lipatov transcendentality in the universal scaling function for large-spin twist operators may be preserved. One particularly natural choice, unique up to one constant, modifies the overall contribution of all terms containing odd-zeta functions in the earlier proposed scaling function based on a trivial phase. Excitingly, we present evidence that this choice is non-perturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS5 ? S5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve the long-standing AdS/CFT discrepancies between gauge and string theory.

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Transcendentality and crossing

We consider two generalizations of the = 6 superconformal Chern-Simons-matter theories with gauge group U(N) × U(N). The first generalization is to = 6 superconformal U(M) × U(N) theories, and the second to = 5 superconformal O(2M) × USp(2N) and O(2M+1) × USp(2N) theories. These theories are conjectured to describe M2-branes probing C4/Zk in the unitary case, and C4/k in the orthogonal/symplectic case, together with a discrete flux, which can be interpreted as |M−N| fractional M2-branes localized at the orbifold singularity. The classical theories with these gauge groups have been constructed before; in this paper we focus on some quantum aspects of these theories, and on a detailed description of their M theory and type IIA string theory duals.

https://iopscience.iop.org/article/10.1088/1126-6708/2008/11/043/pdf

Fractional M2-branes

Understanding the finite-size corrections to the fundamental excitations of a theory is the first step towards completely solving for the spectrum in finite volume. We compute the leading exponential correction to the quantum energy of the fundamental excitation of the light-cone gauged string in AdS5×S^5, which is the giant magnon solution. We present two independent ways to obtain this correction: the first approach makes use of the algebraic curve description of the giant magnon. The second relies on the purely field-theoretical Luscher formulas, which depend on the world-sheet S-matrix. We demonstrate the agreement to all orders in (Delta/sqrt( lambda ))^-1 of these approaches, which, in particular, presents a further test of the S-matrix. We comment on generalizations of this method of computation to other string configurations.

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Quantum wrapped giant magnon

We derive the two loop expressions for polygonal Wilson loops by starting from the one loop expressions and applying an operator product expansion. We do this for polygonal Wilson loops in R
 1,1 and find a result in agreement with previous computations. We also discuss the spectrum of excitations around flux tube that connects two null Wilson lines.

Bootstrapping null polygon Wilson loops

We consider light-like Wilson loops with hexagonal geometry in the planar limit of N=4 Super-Yang-Mills theory. Within the Operator-Product-Expansion framework these loops receive contributions from all states that can propagate on top of the colour flux tube sourced by any two opposite edges of the loops. Of particular interest are the two-particle contributions. They comprise virtual effects like the propagation of a pair of scalars, fermions, and gluons, on top of the flux tube. Each one of them is thoroughly discussed in this paper. Our main result is the prediction of all the twist-2 corrections to the expansion of the dual 6-gluons MHV amplitude in the near-collinear limit at finite coupling. At weak coupling, our result was recently used by Dixon, Drummond, Duhr and Pennington to predict the full amplitude at four loops. At strong coupling, it allows us to make contact with the classical string description and to recover the (previously elusive) AdS(3) mode from the continuum of two-fermion states. More generally, the two-particle contributions serve as an exemplar for all the multi-particle corrections.

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Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions

We extend the Operator Product Expansion (OPE) for scattering amplitudes in planarN = 4 SYM to account for all possible helicities of the external states. This is done by constructing a simple map between helicity congurations and so-called charged pentagon transitions. These OPE building blocks are generalizations of the bosonic pen- tagons entering MHV amplitudes and they can be bootstrapped atnite coupling from the integrable dynamics of the color ux tube. A byproduct of our map is a simple realization of parity in the super Wilson loop picture.

http://www.crm.umontreal.ca/2015/Symmetries15/pdf/gomez_cordova.pdf

Pedro Vieira

Papers

Quantum wrapped giant magnon

Bootstrapping null polygon Wilson loops

Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions

OPE for all helicity amplitudes

Gluing hexagons at three loops