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Are there any references on the Weyl invariance of the Dirac Lagragian in general spacetime?

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I presume you mean massless Dirac Lagrangian. – Ron Maimon Sep 21 '11 at 15:59
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The (massless) Dirac Lagrangian is Weyl invariant on-shell. Please see the following review article by Forger and Romer. In this article, a theorem (5.1) was formulated stating that actions have stress energy tensors of vanishing trace iff they are locally Weyl invariant on shell.

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How could the Dirac Lagrangian be Weyl invariant with a mass term? I assume you mean massless, but then, please say so. – Ron Maimon Sep 22 '11 at 6:30

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