Scalar Field Theory on a Causal Set in Histories Form
نویسنده
چکیده
We recast into histories-based form a quantum field theory defined earlier in operator language for a free scalar field on a background causal set. The resulting decoherence functional resembles that of the continuum theory but the counterpart of the d’Alembertian operator is nonlocal and a generalized inverse of the discrete retarded Green function. We comment on the significance of this and we also suggest how to include interactions.
منابع مشابه
Sum-over-histories representation for the causal Green function of free scalar field theory.
A set of Green functions Gα(x − y), α ∈ [0, 2π[, for free scalar field theory is introduced, varying between the Hadamard Green function ∆1(x − y) ≡ 〈0 | {φ(x), φ(y)} | 0〉 and the causal Green function Gπ(x − y) = i∆(x − y) ≡ [φ(x), φ(y)]. For every α ∈ [0, 2π[ a path-integral representation for Gα is obtained both in the configuration space and in the phase space of the classical relativistic ...
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