ar X iv : q ua nt - p h / 96 08 02 3 v 1 1 5 A ug 1 99 6 Beneath Gauge

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 POINCARÉ 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. 1 Quantum gauge theory Andrzej Trautman is a well known pioneer in fiber bundle physics, the invariant formulation of gauge theory. We therefore focus here on the quantum infrastructure of classical gauge theories. We dedicate these projections to him in friendship and respect. The fundamental problem of physics today is to harmonize our spacetime and quantum concepts and precepts. Their discoverers, Einstein and Heisenberg, violated each other’s main principles and their theories suffered for it. Einstein believed that the Bohr-Heisenberg complementarity of descriptions was less fundamental than the alleged completeness of classical description. His tangent vectors offend against the Heisenberg uncertainty relation. Heisenberg believed that spacetime points were not fundamental and referred all quantities to one reference time. His operator-algebra concept infringes Einstein’s locality School of Physics, Georgia Institute of Technology, Atlanta Georgia 30332. E-mail: [email protected] Heisenberg Institute of Theoretical Physics, Munich, Germany D-80805. E-mail: [email protected] School of Physics, Georgia Institute of Technology, Atlanta Georgia 30332. E-mail: [email protected]. Supported by the M. & H. Ferst Foundation.