Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path Integral and Effective Hamiltonian in Loop Quantum Cosmology   We study the path integral formulation of Friedmann universe filled with a
massless scalar field in loop quantum cosmology. All the isotropic models of
$k=0,+1,-1$ are considered. To construct the path integrals in the timeless
framework, a multiple group-averaging approach is proposed. Meanwhile, since
the transition amplitude in the deparameterized framework can be expressed in
terms of group-averaging, the path integrals can be formulated for both
deparameterized and timeless frameworks. Their relation is clarified. It turns
out that the effective Hamiltonian derived from the path integral in
deparameterized framework is equivalent to the effective Hamiltonian constraint
derived from the path integral in timeless framework, since they lead to same
equations of motion. Moreover, the effective Hamiltonian constraints of above
models derived in canonical theory are confirmed by the path integral
formulation.

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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
2
The categories of this paper are: math