Will geometric phases break the symmetry of time in quantum cosmology?

Abstract

We investigate the Wheeler-DeWitt equation for a quantum minisuperspace cosmological model with minimal scalar fields. The adiabatic basis and the nonadiabatic basis of the scalar field Hamiltonian induce mode-dependent gauge potentials to the matrix effective graviational Hamiltonian equation in the projected minisuperspace. In particular, in the nonadiabatic basis the matrix effective gravitational Hamiltonian equation decouples except for a quadratic term of the gauge potential at the classical level. For a closed loop in the projected minisuperspace of the expanding and subsequently recollapsing universe, the mode-dependent geometric phases may break the symmetry of the cosmological time defined along classical trajectories of mode-dependent wave functions. © 1994 The American Physical Society.