1112.2085 (Yongge Ma)
Yongge Ma
The successful background-independent quantization of Loop Quantum Gravity
relies on the key observation that classical General Relativity can be cast
into the connection-dynamical formalism with the structure group of SU(2). Due
to this particular formalism, Loop Quantum Gravity was generally considered as
a quantization scheme that applies only to General Relativity. However, we will
show that the nonperturbative quantization procedure of Loop Quantum Gravity
can be extended to a rather general class of metric theories of gravity, which
have received increased attention recently due to motivations coming form
cosmology and astrophysics. In particular, we will first introduce how to
reformulate the 4-dimensional metric $f(R)$ theories of gravity, as well as
Brans-Dicke theory, into connection-dynamical formalism with real SU(2)
connections as configuration variables. Through these formalisms, we then
outline the nonpertubative canonical quantization of the $f(R)$ theories and
Brans-Dicke theory by extending the loop quantization scheme of General
Relativity.
View original:
http://arxiv.org/abs/1112.2085
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