Axial anomaly and Schwinger terms in two-dimensional general quantum field theory

H. G. Embacher and G. Grübl
Institut für Theoretische Physik der Universität Innsbruck, A-6020 Innsbruck, Austria

(Received: 1 February 1988)

Abstract. We compute the vacuum expectation value tex2html_wrap_inline28 for a realistic, Hermitian, not necessarily local vector field in two-dimensional space-time when tex2html_wrap_inline30 holds in tex2html_wrap_inline32 , the space of tempered distributions. As the space-time symmetry group of the model we take the inhomogeneous proper orthochronous Lorentz group tex2html_wrap_inline34 . tex2html_wrap_inline36 is verified to have anomalous (axial-)vector Ward identities due to nonvanishing equal-time current-current commutators. Additional conditions on tex2html_wrap_inline38 are specified which imply that tex2html_wrap_inline38 is a free zero-mass Wightman field with tex2html_wrap_inline42 .

AMS subject classification (1991). 42B10, 46F12, 81T40.

Phys. Rev. D 38, 597 - 600 (1988).

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