Derivation of Local Gauge Freedom from a Measurement Principle

Details Derivation of Local Gauge Freedom from a Measurement Principle Derivation of Local Gauge Freedom from a Measurement Principle

1997-01-06

arxiv.org/abs/funct-an/9701002v4

"Photon and Poincare Group," V. Dvoeglazov (ed.), Nova Science Publishers (1999) 315-325

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX (printed version)

Scientific paper

We define operator manifolds as manifolds on which a spectral measure on a Hilbert space is given as additional structure. The spectral measure mathematically describes space as a quantum mechanical observable. We show that the vectors of the Hilbert space can be represented as functions on the manifold. The arbitrariness of this representation is interpreted as local gauge freedom. In this way, the physical gauge principle is linked with quantum mechanical measurements of the position variable. We derive the restriction for the local gauge group to be U(m), where m is the number of components of the wave functions.

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