Free fermion

수학노트
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introduction

  • \(c=1/2\) (for \(\psi\) real)
  • \(c=1\) (for \psi complex)


action

\(S= \int\!d^2x\, \psi^\dagger \gamma^0 \gamma^\mu \partial_\mu \psi= \int\!d^2z\, \psi^\dagger_R \bar\partial \psi_R + \psi_L^\dagger \bar\partial \psi_L\,\)


OPE of fermionic fields

  • \(\psi(z)\psi(w) \sim \frac{1}{(z-w)}\)
  • \(\partial \psi(z) \psi(w) \sim -\frac{1}{(z-w)^2}\)
  • \(\partial \psi(z) \partial \psi(w) \sim -\frac{2}{(z-w)^3}\)


energy-momentum tensor

  • \(T(z)=-\frac{1}{2}:\psi(z)\partial \psi(z):=-\frac{1}{2}\left(\lim_{w\to z}\psi(z)\partial \psi(z)+\frac{1}{(z-w)^2}\right)\)
  • \(T(z)\psi(w) \sim \frac{\psi(w)}{2(z-w)^2}+\frac{\partial \psi(w)}{(z-w)}\)
  • \(T(z)\partial \psi(w) \sim \frac{\psi(w)}{2(z-w)^3}+\frac{3\partial \psi(w)}{2(z-w)^2}+\frac{\partial^2 \psi(w)}{(z-w)}\)
  • \(T(z)T(w) \sim \frac{1}{4(z-w)^4}+\frac{2T(w)}{(z-w)^2}+\frac{\partial T(w)}{(z-w)}\)


related items


computational resource


expositions

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LEMMA': 'zitterbewegung'}]
  • [{'LOWER': 'trembling'}, {'LEMMA': 'motion'}]