An analytic representation of quantum field theory
Tóm tắt
The connection between a space of quadratically integrable functions of real variablesq and a Hilbert space of analytic functions of complex variablesz established byBargmann is used to introduce quantised field operators for which the δ-functions of the commutation relations inq-space are replaced by analytic kernel functions inz-space, and a reference to distributions can be avoided.Bargmann's representation is first somewhat modified, so that the derivative terms in the field equations retain their form in the new representation. Local interaction terms inq-space obtain a non-local appearance inz-space. The transition to a 4-dimensional formulation inz-space has to resort to a Euclidean metric. The equations can be derived directly by starting from an action integral inz-space, and applying a variational calculus in which variations are restricted to analytic functions. Explicit analytic expressions are given for free field propagators.
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