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International Journal of Theoretical Physics Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators.
Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time.
Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory.
Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrodinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems.
Throughout, symmetry is used as a tool to help develop solutions for simple and complex problems alike. Challenging exercises and detailed references are included. Pages: Product dimensions: 5. Introduction and overview; 2.
Classical mechanics; 3. Hilbert space: the arena of quantum physics; 4.
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Quantum mechanics; 5. Scalar quantum field theory; 6.
Expanding the data base; 7. Rotationally symmetric models; 8. Continuous and discontinuous perturbations; 9.
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