Operator-Product Expansions and Anomalous Dimensions in the Thirring Model

An example of an operator-product expansion is worked out for the Thirring model. The Thirring model involves a two-dimensional zero-mass Dirac field interacting via the Fermi interaction. The model is scale invariant but the dimensions of local fields in the model vary with the coupling constant. It is shown that has dimension 12+ ({^2}4{^2}) (1-{{^2}4{^2}) }^-1, while the composite fields and ₅, appropriately defined, have the dimension (1-2) (1+{2) }^-1.