Abstract
In comparison with theWT 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 π. 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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References
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Jacquot, J.L., Richert, J. & Umezawa, M. Equations from non-linear chiral transformations. Z. Phys. C - Particles and Fields 66, 309–314 (1995). https://doi.org/10.1007/BF01496605
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DOI: https://doi.org/10.1007/BF01496605