Finite Canonical Commutation Relations

   You can never solve a problem on the level on which it was created.

	-- Albert Einstein (1879-1955)

   "Silence will save me from being wrong (and foolish), but it will also
   deprive me of the possibility of being right.

	-- Igor Stravinsky, composer (1882-1971)

A working paper on FCCR nxn matricies as local kinematical replacement for CCR, and construction of REPS of CCR by pxp matricies over Galois fields.

Some remaining text of the chapters is still being translated to hypertext. An abstract and a brief summary of the essentials are available. The central object of interest here is a chain of algebras given in terms of nxn complex matricies that connect the quantum mechanical Canonical Commutation Relations (CCR) for n unbounded with the Canonical Anticommutation Relations (CAR) for n=2, which seem to provide a local, finite, discrete quantum theory. Finite dimensional representations of CCR by matricies over Galois fields are constructed in appendix J.

The detail of mathematics, physics and philosophy presented here is far more than what would be usual in an any professional journal. I believe it to be sufficient that any mathematician/physicist should be able to reproduce and confirm (or correct!) every detail in the exposition.

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Created: 1996
Last Updated: May 28, 2000
Last Updated: November 28, 2002
Last Updated: February 24, 2004