Bosonization

In theoretical condensed matter physics and quantum field theory, bosonization is a mathematical procedure by which a system of interacting fermions in (1+1) dimensions can be transformed to a system of massless, non-interacting bosons. The method of bosonization was conceived independently by particle physicists Sidney Coleman and Stanley Mandelstam; and condensed matter physicists Daniel C. Mattis and Alan Luther in 1975. In particle physics, however, the boson is interacting (cf. the Sine-Gordon model), and notably through topological interactions (cf. the Wess–Zumino–Witten model). The basic physical idea behind bosonization is that particle-hole excitations are bosonic in character. However, it was shown by Tomonaga in 1950 that this principle is only valid in one-dimensional systems. Bosonization is an effective field theory that focuses on low-energy excitations.

In theoretical condensed matter physics and quantum field theory, bosonization is a mathematical procedure by which a system of interacting fermions in (1+1) dimensions can be transformed to a system of massless, non-interacting bosons. The method of bosonization was conceived independently by particle physicists Sidney Coleman and Stanley Mandelstam; and condensed matter physicists Daniel C. Mattis and Alan Luther in 1975. In particle physics, however, the boson is interacting (cf. the Sine-Gordon model), and notably through topological interactions (cf. the Wess–Zumino–Witten model). The basic physical idea behind bosonization is that particle-hole excitations are bosonic in character. However, it was shown by Tomonaga in 1950 that this principle is only valid in one-dimensional systems. Bosonization is an effective field theory that focuses on low-energy excitations. \psi_+ = :\exp\left(+i\int^z_\infty\partial_{++}\phi\right):,\qquad \bar\psi_+ = :\exp\left(-i\int^z_{\infty}\partial_{++}\phi\right): where the currents of these two models are related by \partial_{++}\phi=:\bar\psi_+\psi_+: where composite operators must be defined by a regularization and a subsequent renormalization.

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