Axiomatic Quantum Field Theory in Terms of Operator Product Expansions: General Framework, and Perturbation Theory via Hochschild Cohomology

Axiomatic Topological Quantum Field Theory

This dissertation provides an introduction to the ideas employed in topological quantum field theory. We illustrate how the field began by considering knot invariants of three-manifolds and demonstrating the consequences of defining such a theory axiomatically. The ideas of category theory are introduced and we show that what we are actually concerned with are symmetric monoidal functors from t...

Current Trends in Axiomatic Quantum Field Theory

In this article a non–technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras of observables, their relation to the underlying fields and the significance of their relative positions. Moreover, the physical interpretation of the theory i...

Axiomatic, Parameterized, Off-Shell Quantum Field Theory

Axiomatic QFT attempts to provide a rigorous mathematical foundation for QFT, and it is the basis for proving some important general results, such as the well-known spin-statistics theorem. Free-field QFT meets the axioms of axiomatic QFT, showing they are consistent. Nevertheless, even after more than 50 years, there is still no known non-trivial theory of quantum fields with interactions in f...

Tate Cohomology in Axiomatic Stable Homotopy Theory

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods[1]. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H , into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behav...