Abstract
A theory is considered for a free scalar field with a conformal connection in a curved space-time with a Bianchi type-I metric. A representation is obtained for the Green's functionG∼in<0¦Tϕ(x)ϕ(x′)¦0> in in the form of an integral of a Schwinger-DeWitt kernel along a contour in a plane of complex-valued proper time. It is shown how a transition may be accomplished from Green's functions in space with the Euclidean signature to Green's functions in space with Minkowski signature and vice versa.
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Translated from Izvestiya Vyssnikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 20–27, June, 1988.
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Bukhbinder, I.L., Kirillova, E.N. Green's functions in Bianchi type-I spaces. Relation between Minkowski and Euclidean approaches. Soviet Physics Journal 31, 440–446 (1988). https://doi.org/10.1007/BF00897604
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DOI: https://doi.org/10.1007/BF00897604