Abstract:
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.
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