K-theory in quantum field theory

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...

Quantum field theory

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 ...

Homological Quantum Field Theory

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∗

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...

Quantum Field Theory