Beyond Conventional Quantization

This text describes novel treatments of quantum problems using enhanced quantization procedures, generally involving extended correspondence rules for the association of a classical and a quantum theory. Beginning with a review of classical mechanics, the book goes on to detail Hilbert space, quantum mechanics, and scalar quantum field theory. Later chapters further develop analytical skills, study a special class of models, and present a discussion of continuous and discontinuous perturbations. The final chapter offers a brief summary, concluding with a conjecture regarding interacting covariant scalar quantum field theories. Throughout, symmetry is used as a tool to help develop solutions for simple and complex problems alike. Challenging exercises and detailed references are included.

This text describes novel treatments of quantum problems using enhanced quantization procedures. Beginning with a review of classical mechanics, Hilbert space, quantum mechanics, and scalar quantum field theory, symmetry is repeatedly used as a tool to help develop solutions for simple and complex problems alike. Challenging exercises and detailed references are included. Requiring only a modest prior knowledge of quantum mechanics and quantum field theory, this book discusses topics outside the scope of a traditional textbook of interest to graduate students and researchers in theoretical physics, mathematical physics, and mathematics.