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.

1. Introduction and overview; 2. Classical mechanics; 3. Hilbert space: the arena of quantum physics; 4. Quantum mechanics; 5. Scalar quantum field theory; 6. Expanding the data base; 7. Rotationally symmetric models; 8. Continuous and discontinuous perturbations; 9. Independent-value models; 10. Ultralocal models; 11. Summary and outlook.