The Quantum Gauge Principle

Details The Quantum Gauge Principle The Quantum Gauge Principle

1996-04-29

arxiv.org/abs/hep-th/9604180v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages (Latex); AMS fonts, dina4p.sty and citesort.sty are needed

Scientific paper

We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an infinite-dimensional vector bundle over the space-time manifold. The time evolution equation and the dynamical equations for the matter fields are invariant under an arbitrary local change of frames along the restriction of the bundle to the worldline of an observer, thus implementing a ``quantum gauge principle''. We derive dynamical equations for the connection and a complex scalar quantum field based on a gauge field action. In the limit of vanishing curvature of the vector bundle, we recover the standard equation of motion of a scalar field in a curved background space-time.

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