Single-particle states of an arbitrarily coupled scalar field

It is shown that the method, proposed in [1, 2], for determining single-particle states and the vacuum of a conformally coupled ( = 1/6) scalar field by diagonalizing the metric Hamiltonian is not applicable if 1/6, since it leads to a physically meaningless result: an infinite number of particles is created in the model where particles should not be created at all. For this reason, it is proposed that in the method of diagonalization the metric Hamiltonian be replaced by a canonical Hamiltonian, the freedom of choosing which makes it possible to impose some necessary conditions. Implementing this program permits determining the single-particle states of an arbitrarily coupled scalar field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 49–53, October, 1990.