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Lecture 36, 4/4/08
Lecture 36, 4/4/08

dilation theorems for completely positive maps and map
dilation theorems for completely positive maps and map

... Q(∆)x = EM (e(∆)Φ(x)) for some ∗-representation Φ of M in N and a conditional expectation EM of N onto M. 4. Dilations in conditional expectations scheme. In this section we compare our results of Sections 2 and 3 with theorems concerning measures with values being positive operators in L1 . It turn ...
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Introduction to Quantum Field Theory
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Snimka 1 - BEO Centre of Excellence
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Hydrogen atom - Indiana University Bloomington
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Canonical quantization

In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible.Historically, this was not quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac introduced it in his 1926 doctoral thesis, the ""method of classical analogy"" for quantization, and detailed it in his classic text. The word canonical arises from the Hamiltonian approach to classical mechanics, in which a system's dynamics is generated via canonical Poisson brackets, a structure which is only partially preserved in canonical quantization.This method was further used in the context of quantum field theory by Paul Dirac, in his construction of quantum electrodynamics. In the field theory context, it is also called second quantization, in contrast to the semi-classical first quantization for single particles.
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