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 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

SummaryIt is shown that a positive definite local energy density is incompatible with the usual postulates of local field theory. The question whether it can be bounded below is briefly discussed but… Expand

Quantum fields, from a mathematical point of view, are highly singular. These fields are believed to describe the interactions of elementary particles. For the interaction of electrons with light… Expand