Quantum Gravity and the Berry Phase
The equations describing quantum gravity in the presence of matter are decomposed into coupled equations by writing the total wave function as the product of a gravitational and a matter-gravity part. Although the total wave function is gauge-invariant (“neutral”) the gravitation and matter parts acquire opposite and, in general, non-integrable phases which are the anholonomy associated with the parallel transport of the state vector with respect to a connection. Further in the coupled equations describing the system one also has a scalar potential which is associated with a metric tensor on a manifold of quantum states and is related to fluctuations. The (Berry) phases, like the fluctuations, can lead to observable effects in suitably constructed matter-gravity systems.
KeywordsWave Function Couple Equation Parallel Transport Matter Field Adiabatic Approximation
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