N = 8 supersingleton quantum field theory

1 8 N ov 1 99 8 The Density Matrix Renormalization Group , Quantum Groups and Conformal Field Theory

We present an overview of the Density Matrix Renormalization Group and its connections to Quantum Groups, Matrix Products and Conformal Field Theory. We emphasize some common formal structures in all these theories. We also propose two-dimensional extensions of the variational matrix product ansatzs.

N = 1 Superconformal Symmetry in Four Dimensional Quantum Field Theory

The implications of N = 1 superconformal symmetry for four dimensional quantum field theories are studied. Superconformal covariant expressions for two and three point functions of quasi-primary superfields of arbitrary spin are found and connected with the operator product expansion. The general formulae are specialised to cases involving a scalar superfield L, which contains global symmetry c...

Enumeration of N -rooted maps using quantum field theory

A one-to-one correspondence is proved between the N -rooted ribbon graphs, or maps, with e edges and the (e−N + 1)-loop Feynman diagrams of a certain quantum field theory. This result is used to obtain explicit expressions and relations for the generating functions of N -rooted maps and for the numbers of N -rooted maps with a given number of edges using the path integral approach applied to th...

Quantum Field Theory Course

Part I. Classical Mechanics 9 0. Intro 9 0.1. Mechanical systems 9 0.2. Lagrangian and Hamiltonian formulation 9 1. Lagrangian approach 10 1.1. Manifolds 10 1.2. Differentiation 11 1.3. Calculus of Variations on an interval 11 1.4. Lagrangian reformulation of Newton‘s equation 13 2. Hamiltonian approach 14 2.1. Metrics: linear algebra 14 2.2. The passage to the cotangent vector bundle via the k...

Relativistic Quantum Field Theory