Abstract:
Group-theoretical aspects of the problem of fermion pair creation in a homogeneous alternating external field are considered. It is shown that the dynamical symmetry group of this problem is $SU(2N)$ ($N=2s+1$, where $s$ is the particle spin) and that the state of the system that arises during evolution is a generalized coherent state associated with this group. The probability of pair creation is given by the square of the modulus of the matrix element of a definite representation of $SU(2N)$. For particles of spin 1/2 in certain cases the symmetry
group reduces to $SU(2)\times SU(2)$.
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