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The pure state space of quantum mechanics as Hermitian symmetric space

✍ Scribed by R. Cirelli; M. Gatti; A. Manià

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
131 KB
Volume
45
Category
Article
ISSN
0393-0440

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✦ Synopsis

The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kähler manifold. The classical principles of quantum mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability Principle) and Spectral Theory of observables are discussed in this non-linear geometrical context.

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If | 1 , | 2 are two pure gauge-invariant states of the Cuntz algebra O d , we show that there is an automorphism : of O d such that | 1 =| 2 b :. If | is a general pure state on O d and . 0 is a given Cuntz state, we show that there exists an endomorphism : of O d such that . 0 =| b :.