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A very simple field theory in noncommutative phase space X^{M},P^{M} in d+2dimensions, with a gauge symmetry based on noncommutative u*(1,1), furnishesthe foundation for the field theoretic formulation of Two-Time Physics. Thisleads to a remarkable unification of several gauge principles in d dimensions,including Maxwell, Einstein and high spin gauge principles, packaged togetherinto one of the simplest fundamental gauge symmetries in noncommutative quantumphase space in d+2 dimensions. A gauge invariant action is constructed and itsnonlinear equations of motion are analyzed. Besides elegantly reproducing thefirst quantized worldline theory with all background fields, the field theoryprescribes unique interactions among the gauge fields. A matrix version of thetheory, with a large N limit, is also outlinedComment: 24 pages, LaTe

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">u</mml:mi></mml:mrow><mml:mrow><mml:mi>⋆</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mn /><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>noncommutative gauge theory as the foundation of two-time physics in field theory

u⋆(1,1)noncommutative gauge theory as the foundation of two-time physics in field theory