arXiv subjects
Publications and source records attributed to David Ritz Finkelstein.
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum measurement performs a computation that dynamical computation cannot accomplish as efficiently.
We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using such representations for their permutations obey Clifford statistics. The vectors supporting the Clifford algebras of permutations and rotations are plexors and spinors respectively. Physical spinors may actually be plexors describing quantum ensembles, not simple individuals. We use Clifford statistics to define quantum fields on a quantum space-time, and to formulate a quantum dynamics-field-space-time unity that evades the compactification problem. The quantum bits of history regarded as a quantum computation seem to obey a Clifford statistics.
Let a quantum network be a Fermi-Dirac assembly of Fermi-Dirac assemblies of ...of quantum points, interpreted topologically. The simplest quantum-network vacuum modes with exact conservation of relativistic energy-momentum and angular momentum also support the local non-Abelian groups of the standard model, torsion and gravity. The spacetime points of these models naturally obey parastatistics. We construct a left-handed vacuum network among others.
Seeking a relativistic quantum infrastructure for gauge physics, we analyze spacetime into three levels of quantum aggregation analogous to atoms, bonds and crystals. Quantum spacetime points with no extension make up more complex link units with microscopic extension, which make up networks with macroscopic extension. Such a multilevel quantum theory implies parastatistics for the lowest level entities without additional physical assumptions. Any hypercubical vacuum mode with off-diagonal long-range order that is covariant under $\POINCARE$ also has bonus internal symmetries somewhat like those of the standard model. A vacuum made with the dipole link proposed earlier has too much symmetry. A quadrupole link solves this problem.