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First Steps to a Theory of Quantum Gravity

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Abstract

As discussed in the previous section, we wish to attempt to canonically quantise GR, which means turning the Hamiltonian, diffeomorphism and Gauss constraints into operators and replacing Poisson brackets with commutation relations.

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Notes

  1. 1.

    It is important to mention one aspect of background independence that is not implemented, a priori in the LQG framework. This is the question of the topological degrees of freedom of geometry. On general grounds, one would expect any four dimensional theory of quantum gravity to contain non-trivial topological excitations at the quantum level. Classically, these excitations would correspond to defects which would lead to deviations from smoothness of any coarse-grained geometry.

  2. 2.

    For the detailed derivation of these constraints starting with the self-dual Lagrangian see for e.g. [2, Sect. 6.2]

  3. 3.

    The transformation to new variables, as implemented by most authors, including Barbero and Immirzi, does not involve changing the triad. In this case the Poisson brackets between the new variables picks up a factor of \( \gamma \). However if we transform the triad also, as is done here following [1], the factor of \( \gamma \) cancels out when taking the Poisson brackets.

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Authors and Affiliations

  1. Department of Physics, National Institute of Technology, Surathkal, Karnataka, India

    Deepak Vaid

  2. School of Chemistry and Physics, University of Adelaide, Adelaide, SA, Australia

    Sundance Bilson-Thompson

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  1. Deepak Vaid
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  2. Sundance Bilson-Thompson
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Correspondence to Deepak Vaid .

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Vaid, D., Bilson-Thompson, S. (2017). First Steps to a Theory of Quantum Gravity. In: LQG for the Bewildered. Springer, Cham. https://doi.org/10.1007/978-3-319-43184-0_5

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