Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of CFT appear in a more straightforward manner; and because it has important applications: in string theory in the physics of open strings and D-branes, and in ...

1 Basic formalism for interacting theories 4 1.1 Perturbative approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Correlation functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Diagrammatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Asymptotic states and S-matrix . . . . . . . . . . . . . . . . . . . . . . . . . 6...

closed curve C ). This implies F = −∇V for some potential function V . (Think of V as potential energy.) The total energy is E = T + V with T the kinetic energy T = 1 2 ∑ mi |vi| . The total energy is conserved because of the second law, because dE dt = mv · dv dt +∇V · dx dt = (ma− F ) · v = 0. In Hamiltonian mechanics, momentum p = mv is used instead of v as a primary object. The Hamiltonian ...

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 vie...

Following P. A. M. Dirac's critique in " Lectures on Quantum Field Theory " of the usual formalism, I will discuss the role of the time parameter to solve R. Haag's no-go theorem on the non-equivalence of the conventional Schrödinger picture and the Heisenberg picture. This is possible by first defining in a correct way the concept of the vacuum state at a given time in relativity. I will also ...

We give a review of the application of perturbative techniques to topologi-cal quantum eld theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.

We discuss the field theory of 3-brane probes in F-theory compactifications in two configurations, generalizing the work of Sen and of Banks, Douglas and Seiberg. One configuration involves several parallel 3-brane probes in F-theory compactified onT/Z2, while the other involves a compactification of F-theory on T/Z2×Z2 (which includes intersecting D4 singularities). In both cases string theory...