Mathematical quantization Mathematical quantization In physics, canonical quantization is one of many procedures for quantizing a classical theory. Historically, this was the earliest method to be used to build quantum mechanics. When applied to a classical field theory it was initially called second quantization. This name has now fallen out of fashion. The word canonical refers actually to a certain structure of the classical theory (called the symplectic structure) which is preserved in the quantum theory. This was first emphasized by Paul Dirac, in his attempt to build quantum field theory. ...more on Wikipedia about "Canonical quantization"
In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest. For example, the similarity between the Heisenberg equation in the Heisenberg picture of quantum mechanics and the Hamilton equation in classical physics should be built in. ...more on Wikipedia about "Geometric quantization"
In mathematics, the Heisenberg group, named after Werner Heisenberg, is a group of 3×3 upper triangular matrices of the form ...more on Wikipedia about "Heisenberg group"
In mathematics, a Lagrangian foliation or polarization is a foliation of a symplectic manifold. It is one of the steps involved in the geometric quantization of a square-integrable functions on a symplectic manifold. ...more on Wikipedia about "Lagrangian foliation"
In mathematics, the Moyal product generalizes the idea of the Poisson bracket, with the goal of defining a product of functions on a symplectic manifold that resembles in certain ways the operator product of observables in quantum mechanics. ...more on Wikipedia about "Moyal product"
In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the procedure for building quantum mechanics from classical mechanics. One also speaks of field quantization, as in the "quantization of the electromagnetic field", where one refers to photons as field "quanta" (for instance as light quanta). This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics. ...more on Wikipedia about "Quantization (physics)"
In mathematics and in theoretical physics, the Stone–von Neumann theorem is any one of a number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators. The name is for Marshall Stone and John von Neumann. ...more on Wikipedia about "Stone–von Neumann theorem"
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