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We propose a naive unification of electromagnetism and general relativity based on enlarging the gauge group of Ashtekar's new variables. We construct the connection and loop representations and analyze the space of states. In the loop representation, the wave functions depend on two loops, each of them carrying information about both gravitation and electromagnetism. We find that the Chern-Simons form and the Jones polynomial play a role in the model. © 1993 The American Physical Society.

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Physical Review D