Gauge Symmetry in Phase Space Consequences for Physics and SpaceTime
Abstract
Position and momentum enter at the same level of importance in the formulation of classical or quantum mechanics. This is reflected in the invariance of Poisson brackets or quantum commutators under canonical transformations, which I regard as a global symmetry. A gauge symmetry can be defined in phase space (X^{M}, P_{M}) that imposes equivalence of momentum and position for every motion at every instant of the worldline. One of the consequences of this gauge symmetry is a new formulation of physics in spacetime. Instead of one time there must be two, while phenomena described by onetime physics in 3+1 dimensions appear as various "shadows" of the same phenomena that occur in 4+2 dimensions with one extra space and one extra time dimensions (more generally, d+2). The 2Tphysics formulation leads to a unification of 1Tphysics systems not suspected before and there are new correct predictions from 2Tphysics that 1Tphysics is unable to make on its own systematically. Additional data related to the predictions, that provides information about the properties of the extra 1space and extra 1time dimensions, can be gathered by observers stuck in 3+1 dimensions. This is the probe for investigating indirectly the extra 1+1 dimensions which are neither small nor hidden. This 2T formalism that originated in 1998 has been extended in recent years from the worldline to field theory in d+2 dimensions. This includes 2T field theories that yield 1T field theories for the Standard Model and General Relativity as shadows of their counterparts in 4+2 dimensions. Problems of ghosts and causality in a 2T spacetime are resolved automatically by the gauge symmetry, while a higher unification of 1T field theories is obtained. In this paper the approach will be described at an elementary worldline level, and the current status of 2Tphysics will be summarized.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2010
 DOI:
 10.1142/S0217751X10051128
 arXiv:
 arXiv:1004.0688
 Bibcode:
 2010IJMPA..25.5235B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 22 pages, LaTeX, 3 figures