Sagnac interferometry as a probe to the commutation relation of a macroscopic quantum mirror

Single photon Sagnac interferometry as a probe to macroscopic quantum mechanics is considered at the theoretical level. For a freely moving macroscopic quantum mirror susceptible to radiation pressure force inside a Sagnac interferometer, a careful analysis of the input-output relation reveals that the particle spectrum readout at the bright and dark ports encode information concerning the noncommutativity of position and momentum of the macroscopic mirror. A feasible experimental scheme to probe the commutation relation of a macroscopic quantum mirror is outlined to explore the possible frontier between classical and quantum regimes. In the Appendix, the case of Michelson interferometry as a feasible probe is also sketched.

BRST invariant theory of a generalized 1+1 Dimensional nonlinear sigma model with topological term

We give a generalized Lagrangian density of 1 + 1 Dimensional O( 3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint. N = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter beta originating from the freedom degree of BRST transformation in a general O( 3) nonlinear sigma model, and we gain the general commutation relations of ghost field.