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.

[1] 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.

[1] In particle physics, however, the boson is interacting, cf, the Sine-Gordon model, and notably through topological interactions,[2] cf.

However, it was shown by Tomonaga in 1950 that this principle is only valid in one-dimensional systems.

[3] Bosonization is an effective field theory that focuses on low-energy excitations.

, one being the conjugate variable of the other, can be described in terms of a chiral boson

where composite operators must be defined by a regularization and a subsequent renormalization.

The standard example in particle physics, for a Dirac field in (1+1) dimensions, is the equivalence between the massive Thirring model (MTM) and the quantum Sine-Gordon model.

[5] The Luttinger liquid model, proposed by Tomonaga and reformulated by J.M.

Luttinger, describes electrons in one-dimensional electrical conductors under second-order interactions.

Daniel C. Mattis and Elliott H. Lieb proved in 1965[6] that electrons could be modeled as bosonic interactions.

The response of the electron density to an external perturbation can be treated as plasmonic waves.

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