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Finite Canonical Commutation Relations

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Author:Bill Hammel
Description: A working paper on finite canonical commutation relations (FCCR) nxn matrices as local kinematical replacement for CCR, and construction of REPS of CCR by pxp matrices over Galois fields. Contents include truncated creation and annihilation operators, QM and limits of unbounded n, higher commutators, algebra of observables, P(n) and Q(n) as algebra generators (irreducibility, solvability v. unitarity), discrete n-Fourier transforms, FCCR structural theorems and matrix element calculations, eigenvalue problems, diagonalizing transformations, invariance group of G(n) (right and left G(n)-Hermiticity, adjoint and coadjoint actions - orbits, and analogy to the Lorentz group), homogeneous complex spaces (complex Lorentzian hypercones), uncertainty relations, and IRREPS of SU(2), SU(1,1) SL(2,C) (quantized noncommutative geometry).

Levels: College, Research
Languages: English
Resource Types: Preprints
Math Topics: Modern Algebra

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