2011

A new look at Lorentz-Covariant Loop Quantum Gravity

Geiller, Marc, Lachieze-Rey, Marc, Noui, Karim

Understand

In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity.

This connection has been found after solving the second-class constraints inherited from the canonical analysis of the Holst action without the time-gauge.
We show that it has the property of lying in the conjugacy class of a pure $\su(2)$ connection, a result which enables one to construct the kinematical Hilbert space of the Lorentz-covariant theory in terms of the usual $\SU(2)$ spin-network states.
Furthermore, we show that there is a unique Lorentz-covariant electric field, up to trivial and natural equivalence relations.

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