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

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical viewpoint; it is in a sense a generally covariant quantum field theory, albeit one in which general covariance is unbroken, there are no gravitons, and the only excitations are topological.

/pdf/topological-quantum-field-theory-4kaklz82as.pdf

Topological quantum field theory

We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant background three-form tensor field. The paper includes an introduction for mathematicians to the IKKT formulation of Matrix theory and its relation to the BFSS Matrix theory.

https://iopscience.iop.org/article/10.1088/1126-6708/1998/02/003/pdf

Noncommutative Geometry and Matrix Theory: Compactification on Tori

In recent years an increasing amount of attention has been devoted to quantum materials with topological characteristics that are robust against disorder and other perturbations. In this context it was discovered that topological materials can be classified with respect to their dimension and symmetry properties. This review provides an overview of the classification schemes of both fully gapped and gapless topological materials and gives a pedagogical introduction into the field of topological band theory.

Classification of topological quantum matter with symmetries

Superstring theoryをめぐって(放談室)

We analyze global anomalies for elementary Type II strings in the presence of D-branes. Global anomaly cancellation gives a restriction on the D-brane topology. This restriction makes possible the interpretation of D-brane charge as an element of K-theory.

https://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/1999/0003/0004/AJM-1999-0003-0004-a006.pdf

Anomalies in string theory with D-branes

This volume has been designed to explore the confluence of techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds It aims to be beneficial to those graduate students or mathematical researchers who wish to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology

Instantons and Four-Manifolds

In this paper we specialize the results obtained in [BF1] to the case of a family of Dirac operators. We first calculate the curvature of the unitary connection on the determinant bundle which we introduced in [BF1].

/pdf/the-analysis-of-elliptic-families-ii-dirac-operators-eta-190aszrxtc.pdf

The analysis of elliptic families. II. Dirac operators, eta invariants, and the holonomy theorem

Anomalies in String Theory with D-Branes

In this paper, we construct the Quillen metric on the determinant bundle associated with a family of elliptic first order differential operators. We also introduce a unitary connection on λ and calculate its curvature. Our results will be applied to the case of Dirac operators in a forthcoming paper.

/pdf/the-analysis-of-elliptic-families-i-metrics-and-connections-26yodpt8qa.pdf

Daniel S. Freed

Papers

Anomalies in string theory with D-branes

Instantons and Four-Manifolds

The analysis of elliptic families. II. Dirac operators, eta invariants, and the holonomy theorem

Anomalies in String Theory with D-Branes

The analysis of elliptic families. I. Metrics and connections on determinant bundles