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Srednicki in his QFT book introduces the the Hamiltonian operator of the quantum field theory (equation 1.32). Here what are $U \bf(x)$ and $V\bf(x-y)$?

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He explains what they are just above Eq. (1.30). He is describing a set of particles, each of which is subject to some potential $U(x)$ and interacting through $V(x-y)$. You probably have seen these objects in a normal quantum mechanics class. – Vibert Feb 27 at 20:03

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