# Quantum Gravity and the Berry Phase

## Abstract

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.

## Keywords

Wave Function Couple Equation Parallel Transport Matter Field Adiabatic Approximation## Preview

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## References

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