Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including… Expand

It is shown that if G is a compact ergodic group of *-automorphisms on a unital C*-algebra A then the unique G-invariant state is a trace. Hence if A is a von Neumann algebra then it is finite and… Expand

We construct for a boson field in two-dimensional space-time with polynomial or exponential interactions and without cut-offs, the positive temperature state or the Gibbs state at temperature 1/β. We… Expand

We study by methods of nonstandard analysis second order differential operators with zero order coefficients which are too singular to be defined by standard functions. In particular we study… Expand