This book is addressed to one problem and to three audiences. The problem is the mathematical structure of modem physics: statistical physics, quantum mechanics, and quantum fields. The unity of… Expand

Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified… Expand

Since the early part of the twentieth century, it has been understood that the description of nature at the subatomic scale requires quantum mechanics. In quantum mechanics, the position and velocity… Expand

Abstract:In earlier work, we derived an expression for a partition function ?(λ), and gave a set of analytic hypotheses under which ?(λ) does not depend on a parameter λ. The proof that ?(λ) is… Expand

Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the… Expand

We construct a cocycle on an infinite dimensional generalization of ap-summable Fredholm module. Our framework is related to Connes' cyclic cohomology and is motivated by our work on index theory on… Expand

We study the effective actionsS(k) obtained byk iterations of a renormalization transformation of the U(1) Higgs model ind=2 or 3 spacetime dimensions. We identify a quadratic approximationSQ(k)… Expand