Partial Bosonisation of Fermions

Bosonisation is a technique for studying one-dimensional fermion systems by the means of transforming them to a boson system. S. Coleman showed that the correlation functions for the Sine Gordon field, a massless boson with a cosine interaction term, coincide with those of the massive Thirring model, which is a Dirac fermion with self-interactions. An explicit map can be found between these two systems, and it can in fact be generalised to an entire class of fermions in which the boson-fermion correspondence is a well-defined operator equality in Fock space. More generally, it is a widely used technique to transform a model into another whose nature simplifies the solution or allows for obtaining more information that appears more clearly in the new representation. Another example is the Jordan Wigner transformation, which associates quantum spin chains to one-dimensional fermions. Some aspects about the statistical properties of the chain can be inferred from the fermionic representation, and more properties can be studied by applying bosonisation and examine the system in this new representation.Bosonisation is a technique for studying one-dimensional fermion systems by the means of transforming them to a boson system. S. Coleman showed that the correlation functions for the Sine Gordon field, a massless boson with a cosine interaction term, coincide with those of the massive Thirring model, which is a Dirac fermion with self-interactions. An explicit map can be found between these two systems, and it can in fact be generalised to an entire class of fermions in which the boson-fermion correspondence is a well-defined operator equality in Fock space. More generally, it is a widely used technique to transform a model into another whose nature simplifies the solution or allows for obtaining more information that appears more clearly in the new representation. Another example is the Jordan Wigner transformation, which associates quantum spin chains to one-dimensional fermions. Some aspects about the statistical properties of the chain can be inferred from the fermionic representation, and more properties can be studied by applying bosonisation and examine the system in this new representation.

Jul 7, 20260 citations

Bosonization of fermion interaction

Seiju Ami

Sep 13, 19960 citations

One-Dimensional Fermions and Bosonization

Yoshio Kuramoto

Lecture notes in physicsJan 1, 20201 citation

Bosonisation in any dimension

H. S. Sharatchandra

The mechanism underlying any bosonisation or fermionisation is exposed.It is shown that any local theory of fermions on a lattice in any spatial dimension greater than one is equivalent to a local theory of Ising spins coupled to a $Z_{2}$ gauge field.There is a close relation to the description of anyons using a Chern-Simons term.The mechanism underlying any bosonisation or fermionisation is exposed.It is shown that any local theory of fermions on a lattice in any spatial dimension greater than one is equivalent to a local theory of Ising spins coupled to a $Z_{2}$ gauge field.There is a close relation to the description of anyons using a Chern-Simons term.

arXiv:hep-th/9301130Jan 31, 19931 citation

Z_{2}

gauge field.There is a close relation to the description of anyons using a Chern-Simons term.