Meeting Descartes and Klein Somewhere in a Noncommutative Space

Details Meeting Descartes and Klein Somewhere in a Noncommutative Space Meeting Descartes and Klein Somewhere in a Noncommutative Space

2001-12-30

arxiv.org/abs/math-ph/0112059v1

Highlights of Mathematical Physics (A.~Fokas et al, eds.), AMS, 2002, pp. 165--189.

Physics

Mathematical Physics

LaTeX 25p, amsproc style, 5 PS pics

Scientific paper

We combine the coordinate method and Erlangen program in the framework of noncommutative geometry through an investigation of symmetries of noncommutative coordinate algebras. As the model we use the coherent states construction and the wavelet transform in functional spaces. New examples are a three dimensional spectrum of a non-normal matrix and a quantisation procedure from symplectomorphisms. Keywords: Heisenberg group, special linear group, symplectic group, Hardy space, Segal-Bargmann space, Clifford algebra, Cauchy-Riemann-Dirac operator, M\"obius transformations, functional calculus, Weyl calculus (quantization), quantum mechanics, Schr\"odinger representation, metaplectic representation.

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