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...

The author discusses the general principles underlying quantum field theory and attempts to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality. A few of quantum field theory’s most striking successes, both achieved and prospective are mentioned, and possible limitations of the theory are ...

We show that the space of chains of smooth maps from spheres into a fixed compact oriented manifold has a natural structure of a transversal d-algebra. We construct a structure of transversal 1-category on the space of chains of maps from a suspension space S(Y ), with certain boundary restrictions, into a fixed compact oriented manifold. We define homological quantum field theories HLQFT and c...

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 operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is...

Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates of the observer. It is then useful to consider the tangent bundle of spacetime with spacetime in the base manifold and four-velocity space in the fiber. A ph...