Long-range interaction of electromagnetic field induced by Chern–Simons field

Abstract

The canonical quantization to a Ginzburg–Landau-like theory is shown by considering the potentials of the electromagnetic field and the Chern–Simons field independently. The operator of matter fields which carries fractional spin and obeys the fractional statistics is constructed. The transportation of flux between those of the corresponding gauge field and Chern–Simons field is found. This leads to a striking conclusion that the electromagnetic field induced a topological term, which gives photon mass and leads to a Meissner effect different than happens in ordinary Ginzburg–Landau theory. The induction of a Chern–Simons term for the electromagnetic field is considered the origin of fractional statistics in general, through the transportation of flux is equivalent to the transportation of the long-distance interaction in the text. That the Chern–Simons field is hidden in the constructed matter field gives rise to a theoretical interpretation of the off-diagonal long-range order in the theory.