Jack Gegenberg, Viqar Husain
We study a type of geometric theory with a non-dynamical one-form field. For a manifold that is $\mathbb{R}^4$, this is equivalent to a theory formulated on a symplectic manifold. Its dynamical variables are an $su(2)$ gauge field and a triad of $su(2)$ valued one-forms. Hamiltonian decomposition reveals that the theory has a true Hamiltonian, together with spatial diffeomorphism and Gauss law constraints, which generate the only local symmetries. Although perturbatively non-renormalizable, the model provides a test bed for the non-perturbative quantization techniques of loop quantum gravity.
View original:
http://arxiv.org/abs/1210.7222
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