FINITE EUCLIDEAN MAGNETIC GROUP AND THETA FUNCTIONS

The Euclidean magnetic group of translations and rotations in a constant magnetic field is discussed in detail. The eigenfunctions of finite magnetic translations are shown to be related to the quasi periodic Jacobi theta functions, whose group theoretical properties under modular transformations are simply discussed. Invariance under finite rotations is very important; it leads to the two fundamental lattices of 60° and 90° already appearing in the theory of the phase transitions of Type II superconductors.