Loop quantum gravity and discrete space-time

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McCabe, Gordon
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preprint description
Loop quantum gravity purports to be a viable candidate for a physical theory which quantizes general relativity, and captures the discrete nature of space-time at a fundamental level. This paper subjects that joint claim to critical scrutiny. The paper begins by reviewing the canonical formulation, proceeds to an exposition of Ashtekar's 'new variables', and then details the development of loop quantum gravity, focusing on the definition of spin-network states and area operators. The paper concludes with a critical analysis of loop quantum gravity's credentials as a physical theory. A number of the widely-held beliefs, particularly those related to the discrete nature of space, are rejected as misconceptions.