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 ψ interacting via the Fermi interaction. The model is scale invariant but the dimensions of local fields in the model vary with the coupling constant λ. It is shown that ψ has dimension 1/2+(λ²4π²)(1-λ²4π²)^-1, while the composite fields ψψ and ψγ₅ψ, appropriately defined, have the dimension (1-λ2π)(1+λ2π)^-1.