Star-product formulas on finite groups
Abstract
Given a finite group G, associative and noncommutative products * will be constructed on the function space L²(G), where these star-products are parametrized by the unitary dual Ĝ of G. If Rf:L²(G)→ L²(G) is the convolution operator Rf(f1)=f*f1, then the projections of Rf on the irreducible spaces of the elements of Ĝ is equivalent to Rf*, Rf*(f1)=f*f1. It is thus natural to consider Harmonic Analysis/Quantum Mechanics on L²(G) using the star-product. In this work, we establish star-product formulas on finite groups, both in the position and momentum representation.
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From laboratory to society: Physics in nation building
29 May-1 June 2019, Tagbilaran City
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