Semiclassical quantization for the motion of the guiding center using the coherent state path integral

A new form of Bohr-Sommerfeld quantization is given for the motion of the guiding center in a strong magnetic field. This is obtained from the effective action for the degree of the guiding center which is deduced from the coherent state path integral for the two types of motion under mutual interaction: cyclotron motion and the motion of the guiding center.