Quantum field theory on quantized Bergman domain

Quantized Kronecker flows and almost periodic quantum field theory

We define and study the properties of the infinite dimensional quantized Kronecker flow. This C-dynamical system arises as a quantization of the corresponding flow on an infinite dimensional torus. We prove an ergodic theorem for a class of quantized Kronecker flows. We also study the closely related almost periodic quantum field theory of bosonic, fermionic and supersymmetric particles. We pro...

Combinatorial algebra for second-quantized Quantum Theory

We describe an algebra G of diagrams that faithfully gives a diagrammatic representation of the structures of both the Heisenberg–Weyl algebra H – the associative algebra of the creation and annihilation operators of quantum mechanics – and U(LH), the enveloping algebra of the Heisenberg Lie algebra LH. We show explicitly how G may be endowed with the structure of a Hopf algebra, which is also ...

Lectures on quantum field theory

Notes on Quantum Field Theory

UCSB Notes for the first quarter of a QFT course, based mostly on ϕ 3 theory in six dimensions. Please send any comments or corrections to

Conformal Field Theory on R× S from Quantized Gravity

Conformal algebra on R × S derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess-Zumino action managing non-perturbative dynamics of the conformal factor in the metric field. It is shown that the residual diff...