Functional Integration And Quantum Physics

Great book, thanks.

This is an uneven book and although it has much to say it is hard to learn from it. Some things are explained in detail, while some things are explained so sketchily that it would only serve as a memory aid for someone who already knows the material. I found it hard to learn anything from this book because Simon doesn't help the reader become familiar with the objects but instead gives a compressed definition and then starts working with them, like Wick ordering, which is a strange idea that a reader could use help swallowing. I certainly would have been frustrated and failed to learn Brownian motion and Gaussian processes from this book; for a meticulous and understandable presentation of these, the best books I've found are Bauer,  Probability Theory (Philosophie Und Wissenschaft) , and Parthasarathy,  Probability Measures on Metric Spaces (Ams Chelsea Publishing) , the latter of which has the best proof I've seen of Donsker's theorem, which is also proved in Simon.This book does have the only satisfying proof I've found in the literature of the Trotter product formula for unbounded operators. And although the Trotter product formula is the only result for which I recommend this book, I do recommend paging through this book to build a feeling for the connections between functional analysis and stochastic processes.