https://doi.org/10.1140/epjp/s13360-022-03228-y
Tutorial
On the equivalence of two definitions of conformal primary fields in d > 2 dimensions
Bethe Center for Theoretical Physics, Physikalisches Institut der
Universität Bonn, Nussallee 12, 53115, Bonn, Germany
a
ruben.camposdelgado@gmail.com
Received:
27
April
2022
Accepted:
22
August
2022
Published online:
11
September
2022
Conformal primary fields are of central importance in a conformal field theory with d > 2 spacetime dimensions. They can be defined in two ways. A first definition involves commutators between the field and the generators of the conformal group; a second definition characterizes a primary field according to its behaviour under a finite conformal transformation. In the existing literature, the proof of the equivalence of the definitions is either omitted or carried out with little details. In this paper we present a clear and concise review of the two definitions and provide a simple and detailed proof for their equivalence, using some minimal results from quantum field theory and basic properties of conformal transformations. The paper is intended as a tutorial for an introductory lecture course in conformal field theory.
© The Author(s) 2022
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