The up-to-second-order contributions to the two-point (Wightman) function 〈 ϕ I ( x ) ϕ I ( y ) 〉 Ω of the interacting field with potential λ 4 ϕ ( x ) 4 + μ ( x ) 2 ϕ ( x ) 2 . We omit the labels of the external vertices after the first line using the convention that the left external vertex is always the x-vertex.

The up-to-second-order contributions to the two-point (Wightman) function 〈 ϕ I ( x ) ϕ I ( y ) 〉 Ω of the interacting field with potential λ 4 ϕ ( x ) 4 + μ ( x ) 2 ϕ ( x ) 2 . We omit the labels of the external vertices after the first line using the convention that the left external vertex is always the x-vertex.

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We develop a renormalisation scheme for time--ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This scheme is directly applicable to spacetimes with Lorentzian signature, manifestly generally covariant, invari...

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