# Is two dimension equal to three for bosonization?

I have been reading about bosonization lately and really appreciated Luttinger liquid bosonization in 1 dimension. Also, I got interested in higher dimensional bosonization but I only find Haldane's (whose paper I cannot unfortunately find) method applied to 2-dimensional Fermi liquids. May I deduce that the dimension 3 procedure is similar then? (it seems reasonable but I new in the topic and I might oversee some difficulties)

• Consider for clarity to specify whether you count spatial dimensions or spacetime dimensions. Mar 20, 2020 at 12:22
• Yes, sorry. I meant 3 spatial dimensions Mar 21, 2020 at 10:40

I believe the Haldane article you refer to is available as https://arxiv.org/abs/cond-mat/0505529:

Luttinger's Theorem and Bosonization of the Fermi Surface, F. D. M. Haldane (Submitted on 21 May 2005)

A course of four lectures given at the International School of Physics "Enrico Fermi", Varenna, Italy, July 1992, in which the underlying algebraic structure needed for bosonization of the Fermi surface in two- or three-dimensions was first described. This is an unchanged 1993 preprint version of a published but hard-to-find (and often mis-cited) 1994 article in the Varenna Summer School proceedings. The d > 1 dimensional generalization of the Kac-Moody algebra on the Fermi surface is presented, and the Gaussian reduction of the Fermi liquid to harmonic oscilator modes is derived. One-dimensional bosonization and the symmetries of spin-charge separation are also reviewed.

Comments: 17 pages, 0 figures; A 1993 preprint form of a published but hard-to-find article based on lectures presented at the International School of Physics "Enrico Fermi", Varenna, Italy, July 1992

• This is a good summary of the lectures. But it does not answer the question which has been asked. Mar 21, 2020 at 20:48