Quantum Space-time Geometry

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Quantum Space-time Geometry: Superspace Cavity QED: The topological aspects of quantum field theory and geometrical formalism makes the situation more broad in this monograph. In fact, the relationship with chiral anomaly links the Pontryagin term to the Berry phase, which may be thought of as a more extended Bohm-Ahranov effect. In this sense the insertion of a direction vector or vortex line associated to a space-time point effectively attaches a background magnetic field and the charge corresponding to the gauge field effectively represents magnetic charge. Therefore, the geometry of a charged particle traveling through a magnetic monopoles field may be related to that of a vortex line. The fact that in 3+1 dimension the gauge orbit space U/G has the topology of a ring indicates that there is a hole in it. So the magnetic flux through the hole in the gauge orbit space is nonzero. In view of this the vacuum may be taken to arise from the Bohm-Ahranov type of effect in ordinary space. In 2+1 dimension the topology of the gauge orbit space corresponding that of a sphere representing a magnetic monopole may thus be taken to arise from the same geometrical feature.