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A Note on Commutation Relation in Conformal Field Theory

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arxiv 2101.04090 v2 pith:SQVA6OCB submitted 2021-01-11 hep-th

Lento Nagano , Seiji Terashima This is my paper · ORCID
classification hep-th
keywords conformalfieldtheoryscalarspacecommutatorcommutatorscylinder
verification ladder T0 review T1 audit T2 compute T3 formal

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In this note, we explicitly compute the vacuum expectation value of the commutator of scalar fields in a d-dimensional conformal field theory on the cylinder. We find from explicit calculations that we need smearing not only in space but also in time to have finite commutators except for those of free scalar operators. Thus the equal time commutators of the scalar fields are not well-defined for a non-free conformal field theory, even if which is defined from the Lagrangian. We also have the commutator for a conformal field theory on Minkowski space, instead of the cylinder, by taking the small distance limit. For the conformal field theory on Minkowski space, the above statements are also applied.

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Cited by 3 Pith papers

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