相关论文: K-Theory in Quantum Field Theory

In this paper we will analyse some interesting structures that occur in scalar quantum field theory. We will quantize this theory using path integrals. We will analyse the Bogomolny Bound for scalar quantum field theory in two dimensions.…

The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.

After a brief historical review of the emergence of QCD as the quantum field theory of strong interactions, the basic notions of colour and gauge invariance are introduced leading to the QCD Lagrangian. The second lecture is devoted to…

Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…

We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global…

This talk deals with the old problem of formulatingn a covariant quantum theory of superstrings, ``covariant'' here meaning having manifest Lorentz symmetry and supersymmetry. The advantages and disadvantages of several quantization methods…

The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…

Quantum K-theory of a smooth projective variety at genus zero is a collection of integers that can be assembled into a generating series $J(Q,q,t)$ that satisfies a system of linear differential equations with respect to $t$ and…

A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…

We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…

We give a modern geometric viewpoint on anomalies in quantum field theory and illustrate it in a 1-dimensional theory: supersymmetric quantum mechanics. This is background for the resolution of worldsheet anomalies in orientifold…

These lectures give an introduction to duality in Quantum Field Theory. We discuss the phases of gauge theories and the implications of the electric-magnetic duality transformation to describe the mechanism of confinement. We review the…

The present paper is the continuation of the paper "Nonlinear field theory I". In the paper it is shown that a fully correspondence between the quantum and the nonlinear electromagnetic forms of the Dirac electron theory exists, so that…

In the example of complex grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of…

The simple quantum gravity model, based on a new conjecture within the canonically quantized 3+1 general relativity, is presented. The conjecture states that matter fields are functionals of an embedding volume form only, and reduces the…

A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…

Description of two three-dimensional topological quantum field theories of Witten type as twisted supersymmetric theories is presented. Low-energy effective action and a corresponding topological invariant of three-dimensional manifolds are…

We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and…

Anomalies are a very powerful tool in constraining theories beyond the standard model. We give a pedagogical overview of some topics illustrating the important role played by spacetime anomalies in string theory. After discussing the…