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arXiv · 1107.4921

Loop quantum $f(R)$ theories

Xiangdong Zhang·Yongge Ma
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Abstract

As modified gravity theories, the 4-dimensional metric $f(R)$ theories are cast into connection dynamical formalism with real $su(2)$-connections as configuration variables. This formalism enables us to extend the non-perturbative loop quantization scheme of general relativity to any metric $f(R)$ theories. The quantum kinematical framework of $f(R)$ gravity is rigorously constructed, where the quantum dynamics can be launched. Both Hamiltonian constraint operator and master constraint operator for $f(R)$ theories are well defined. Our results show that the non-perturbative quantization procedure of loop quantum gravity are valid not only for general relativity but also for a rather general class of 4-dimensional metric theories of gravity.

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Xiangdong Zhang, Yongge Ma. 2011-07-25. Loop quantum $f(R)$ theories. https://doi.org/10.1103/physrevd.84.064040

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