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Quantum Physics: A Functional Integral Point of View
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 ofExpand
Recent Developments in Gauge Theories
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 unifiedExpand
Quantum Yang-Mills theory
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 velocityExpand
Quantum Invariants
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) isExpand
“Theoretical mathematics”: toward a cultural synthesis of mathematics and theoretical physics
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is theExpand
Quantum $K$-theory. I. The Chern character
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 onExpand
Renormalization of the Higgs model: Minimizers, propagators and the stability of mean field theory
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