Born Jordan Quantization : Theory and Applications Born Jordan Quantization: Physical Motivation: On the Quantization Problem Quantization of Monomials Basic Hamiltonian Mechanics Wave Mechanics and the Schrödinger Equation Mathematical Aspects of Born Jordan Quantization: The Weyl Correspondence The Cohen Class Born Jordan Quantization Shubins Pseudo Differential Calculus Born Jordan Pseudo Differential Operators Weak Values and the Reconstruction Problem Some Advanced Topics: Metaplectic Operators Symplectic Covariance Properties Symbol Classes and Function Spaces. 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.