Equations from Non-Linear Chiral Transformations

Details Equations from Non-Linear Chiral Transformations Equations from Non-Linear Chiral Transformations

1994-10-27

arxiv.org/abs/hep-th/9410211v1

Z. Phys. C66 (1995) 309-314

Physics

High Energy Physics

High Energy Physics - Theory

17 pages in tex, to appear in Z. Phys. C

Scientific paper

10.1007/BF01496605

In comparison with the $WT$ chiral identity which is indispensable for renormalization theory, relations deduced from the non-linear chiral transformation have a totally different physical significance. We wish to show that non-linear chiral transformations are powerful tools to deduce useful integral equations for propagators. In contrast to the case of linear chiral transformations, identities derived from non-linear ones contain more involved radiative effects and are rich in physical content. To demonstrate this fact we apply the simplest non-linear chiral transformation to the Nambu-Jona-Lasinio model, and show how our identity is related to the Dyson-Schwinger equation and Bethe-Salpeter amplitudes of the Higgs and $\pi$. Unlike equations obtained from the effective potential, our resultant equation is exact and can be used for events beyond the LEP energy.

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