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Non-commutative solitons in finite quantum mechanics

✍ Scribed by E.G. Floratos; S. Nicolis

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
220 KB
Volume
119
Category
Article
ISSN
0920-5632

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✦ Synopsis

We construct the unitary evolution operators that realize the quantization of linear maps of SL(2, W) over phase spaces of arbitrary integer discretization N and show the non-trivial dependence on the arithmetic nature of N. We discuss the corresponding uncertainty principle and construct the corresponding coherent states, that may be interpreted as non-commutative solitons.

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We establish the exact renormalization group equation for the potential of a one quantum particle system at finite and zero temperature. As an example we use it to compute the ground state energy of the anharmonic oscillator. We comment on an improvement of the Feynman-Kleinert's variational method