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This is my first post on this website so please excuse any poor formatting.

In the lecture series on quantum integrable models, much attention is focused towards the Thirring model, $$\mathscr{L} = \psi_i \partial_{\bar{w}} \psi^i + \bar{\psi}_i \partial_w \bar{\psi}^i - \psi_i \psi^j \bar{\psi}^i\bar{\psi}_j,$$ where the $\psi_i, \psi^i$ are called chiral fermions and $\bar{\psi}_i, \bar{\psi}^i$ are called antichiral fermions.

First, I am unsure as to the exact meaning of calling a fermion chiral. From my brief exposure to chirality, I am used to saying that a particle has left or right chirality, but not that it itself is 'chiral'. My best guess of calling the fermions, themselves, chiral is saying that the physics depends on the chirality of the particles (akin to when we call a theory chiral).

Second, I am unsure as to the meaning of antichiral. I have found some papers using this word, but the context is different so I assume that they are using the word with a different meaning. My best guess is that the antichiral fermions, $\bar{\psi}$, are just the anti particles to the fermions, $\psi$. Is that correct? If incorrect, what does antichiral mean?

Thank you!

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    $\begingroup$ Hyperlinks, italics, LaTeX. Nothing to excuse, a good first post. Welcome to the site. $\endgroup$
    – JamalS
    Apr 21, 2020 at 18:07

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