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Path integral in the representation of coherent state for the simplest semisimple Lie group SU(2) and its classical consequences are investigated. Using the completeness relation of the coherent state, we derive a path integral expression for the transition amplitude which connects a pair of SU(2) coherent states. In the classical limit we arrive at a canonical equation of motion in a ’’curved phase space’’ (two-dimensional sphere) which reproduces the ordinary Euler’s equation of a rigid body when applied to a rotator.

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By starting with the Maxwell theory of electromagnetism, we study the change of polarization state of light transmitting through optically anisotropic media. The basic idea is to reduce the Maxwell equation to the Schrödinger like equation for two levels (or states) representing polarization. By using the quantum mechanical technique, the density matrix, and path integral, the evolution of the Stokes parameters results in the equation of motion for a pseudospin representing a point on the Poincaré sphere. Two typical examples relevant to actual experiments are considered; the one gives the generalized Faraday effect, and the other realizes an optical analog of magnetic resonance.

A dynamical model is presented for chiral change in DNA molecules. The model is an extension of the conventional elastic model, which incorporates the structure of base pairs and uses a spinor representation for the DNA configuration together with a gauge principle. Motivated by a recent experiment reporting chiral transitions between right-handed B-DNA and left-handed Z-DNA [Lee et al., Proc. Natl. Acad. Sci. (USA) 107, 4985 (2010)], we analyze the free energy for the particular case of linear DNA with an externally applied torque. The model shows that there exists, at low temperature, a rapid structural change depending on the torque exerted on the DNA, which causes switching in B and Z domain sizes. This can explain the frequent switches of DNA extension observed in experiments.