Path Integral and Effective Hamiltonian in Loop Quantum Cosmology

Understand

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.