Boson pair production in an alternating external field

Group-theoretical aspects of the problem of boson pair production in a homogeneous alternating external field are discussed. It is shown that the dynamical symmetry group of this problem is $SU(N,N) (N=2S+1$, where $S$ is the particle spin) and that the state of the system that arises during the process of evolution from the vacuum state is a generalized coherent state. The pair production probability is given by the square of the modulus of the matrix element of the representation of this group.