# Questions tagged [bosonization]

Bosonization is a mathematical procedure mapping a system of interacting fermions in 1+1 dimensions to a system of massless, bosons (excitations).

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### Is bosonization possible in any number of dimensions?

Is bosonization applicable to an arbitrary number of spacetime dimensions?
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### 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 (...
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### Computing correlation function $\langle e^{i\beta \phi(x)}e^{-i\beta\phi(0)}\rangle$ for massless scalar field $\phi$

I am currently reading Shankar's "Bosonization: How to make it work for you in condensed matter" (http://inspirehep.net/record/408901/). In page 9, I am stuck with computing the correlation function ...
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### Bosonization and gauge symmetry

The bosonization map relates the fermionic current $\bar{\psi}\gamma\psi$ to the bosonic current $\partial\phi$, and also the components of $\psi$ to $e^{i\sqrt{\pi}\left(\phi\pm\bar\phi\right)}$. ...
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### Two inconsistent expression of density operator $\rho(x)$ in Giamarchi's book

I am currently reading Giamarchi's "Quantum Physics in One Dimension". From (2.28) one easily obtain $$\rho(x)=\rho_R(x)+\rho_L(x)=-\frac{1}{\pi}\nabla\phi(x).$$ (Actually (2.55) exactly states this ...
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### Density fluctuation and derivative of the field operator $\partial_x \phi(x)$

In a literature about bosonization, one argues that $\partial_x \phi(x)$ represents the density fluctuation. Why can we think that the derivative is about the density fluctuation? My guess: For small ...
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### Fermion creation operator in boson basis

I've been reading Giamarchi, Quantum Physics in One Dimension, Chapter 2 on 1d bosonization, and in appendix B.1, he derives equation B.2, which represents the fermion creation operator $\psi_r (x)$ ...
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### Is there an explicit mapping between N free bosonic fields and the $SU(N)_1$ WZW model + free boson?

Witten's nonabelian bosonization tells us that $N$ free Dirac fields can by written in terms of an $SU(N)_1$ WZW model and one free boson. But bosonization also tells us that we could just as well ...
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### Explicit form of Klein factors in Giamarchi

In Giamarchi, Quantum Physics in One Dimension, Appendix B, I don't understand how he did his last step in equation B.8, as shown below. If anyone has gone over the derivation, I would really ...
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### Can the terms in the microscopic model with nonzero conformal spin generate some new term(s) under RG (renormalization group) flow?

As in the book Bosonization and Strongly Correlated Systems at page 66, it says that "We see that the original perturbation with nonzero conformal spin generates the perturbation with zero conformal ...
In 1+1 dim bosonization, one introduce the Klein factors, which are Hermitian and satisfies Clifford algebra. (1) In the case of 1 dim space is a 1D ring ($S^1$ circle), then one have left-right ...