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Large N Field Theories, String Theory and Gravity

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 article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.

Noncommutative field theory

Superstring theoryをめぐって(放談室)

The quantum mechanics of the relativistic material point is discussed in the light of some recent ideas, developed for the study of the interacting string model. In accordance with these ideas the interaction among the particles is introduced in a geometrical way, but we also show how to interpret such an interaction as due to an external field. The same considerations are briefly applied to the string model.

The relativistic point revisited in the light of the string model

The action for a Galilean superstring is found from a non-relativistic limit of the closed Green-Schwarz (GS) superstring; it has zero tension and provides an example of a massless super-Galilean system. A Wess-Zumino term leads to a topological central charge in the Galilean supersymmetry algebra, such that unitarity requires a upper bound on the total momentum. This Galilean-invariant bound, which is also implied by the classical phase-space constraints, is saturated by solutions of the superstring equations of motion that half-preserve supersymmetry. We discuss briefly the extension to the Galilean supermembrane.

/pdf/the-galilean-superstring-4nz13rjs95.pdf

The Galilean superstring

The Hamiltonian (gauge) symmetry generators of non-local (gauge) theories are presented. The construction is based on the d+1 dimensional space-time formulation of d dimensional non-local theories. The procedure is applied to U(1) space-time non-commutative gauge theory. In the Hamiltonian formalism the Hamiltonian and the gauge generator are constructed. The nilpotent BRST charge is also obtained. The Seiberg-Witten map between non-commutative and commutative theories is described by a canonical transformation in the superphase space and in the eldantield space. The solutions of classical master equations for non-commutative and commutative theories are related by a canonical transformation in the antibracket sense.

/pdf/gauge-and-brst-generators-for-space-time-non-commutative-u-1-3ojpuz3ics.pdf

Gauge and BRST generators for space-time non-commutative U(1) theory

We study a non-commutative non-relativistic scalar field theory in 211 dimensions. The theory shows the UV-IR mixing typical of QFT on non-commutative spaces. The one-loop correction to the two-point function turns out to be given by a d function in momentum space. The one-loop correction to the four-point function is of logarithmic type. We also evaluate the thermodynamic potential at two-loop order. To avoid an IR singularity we have to introduce a chemical potential. The suppression of the non-planar contribution with respect to the planar one turns out to depend crucially on the value of the chemical potential.

/pdf/nonrelativistic-noncommutative-field-theory-and-uv-ir-mixing-4uby0ngh1d.pdf

Nonrelativistic noncommutative field theory and UV-IR mixing

We consider two distinct limits of General Relativity that in contrast to the standard non-relativistic limit can be taken at the level of the Einstein-Hilbert action instead of the equations of motion. One is a non-relativistic limit and leads to a so-called Galilei gravity theory, the other is an ultra-relativistic limit yielding a so-called Carroll gravity theory. We present both gravity theories in a first-order formalism and show that in both cases the equations of motion (i) lead to constraints on the geometry and (ii) are not sufficient to solve for all of the components of the connection fields in terms of the other fields. Using a second-order formalism we show that these independent components serve as Lagrange multipliers for the geometric constraints we found earlier. We point out a few noteworthy differences between Carroll and Galilei gravity and give some examples of matter couplings.

/pdf/carroll-versus-galilei-gravity-4v3ap4g7b2.pdf

Joaquim Gomis

Papers

The relativistic point revisited in the light of the string model

The Galilean superstring

Gauge and BRST generators for space-time non-commutative U(1) theory

Nonrelativistic noncommutative field theory and UV-IR mixing

Carroll versus Galilei Gravity