Born-Jordan Quantization | Maurice de Gosson

This book presents a comprehensive mathematical study of§the operators behind the Born-Jordan quantization scheme. The Schrödinger and§Heisenberg pictures of quantum mechanics are equivalent only if the Born-Jordan§scheme is used. Thus, Born-Jordan quantization provides the only physically§consistent quantization scheme, as opposed to the Weyl quantization commonly§used by physicists. In this book we develop Born-Jordan 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. §