We show that a class of matrix theories can be understood as an extension of quantum \ufb01eld theory which has non-local interactions. This reformulation is based on the Wigner-Weyl transformation, and the interactions take the form of Moyal (cid:63) -product on a doubled geometry. We recover local dynamics on the spacetime as a low-energy limit. This framework opens up the possibility for studying novel high-energy phenomena, including the uni\ufb01cation of gauge and geometric symmetries in a gauge theory.<\/p>\n","protected":false},"excerpt":{"rendered":"
We show that a class of matrix theories can be understood as an extension of quantum \ufb01eld theory which has non-local interactions. This reformulation is based on the Wigner-Weyl transformation, and the interactions take the form of Moyal (cid:63) -product on a doubled geometry. We recover local dynamics on the spacetime as a low-energy limit. 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