Born-Jordan Quantization

This book presents a comprehensive mathematical study of the operators behind the BornJordan quantization scheme. The Schrdinger and Heisenberg pictures of quantum mechanics are equivalent only if the BornJordan scheme is used. Thus, BornJordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop BornJordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.