Minnowbrook Symposium
David Finkelstein
Spin, Statistics and Space-time Structure

Below the quark scale space-time, matter, measurement and the dynamical law can no longer be separated operationally but fuse into one variable, which we call the dynamic D of the system. D can be considered as an atomized and unified generalization of the s matrix. D acts on a composite of space-time-dynamic elements --chronons for short -- whose statistics is crucial. Each of the classical groups generates a unique natural quantum statistics. A groups generate Fermi-dirac statistics; C Bose-Einstein; and B and D, the newer Schur-Wilczek statistics, where the individual is described in a quadratic space and the composite in its spinor space. Of these on S-W is 2-valued and gives rise to spinors, so we infer that chronons have S-W statistics. This implies a large Clifford algebra Cliff(N+, N-)  of possible dynamics with one Clifford unit for each chronon, representing permutations. Now swaps are basic, not creation and annihilation or spin. The dynamic is maximally described by one element from which both space-time and the usual fields are to be constructed in the limit  . This theory links the period 8 of the chessboard of Clifford algebras to the dimension 4 of space-time, and accounts for the apparent Maxwell-Boltzman statistics of classical space-time points. Earlier we suggested that spin and statistics are correlated because  rotation is homotopic to a swap. Now they are correlated because rotations are swaps.


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