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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).

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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$\phi^4$ theory kinks as fermions?

In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \partial^\mu \phi + \frac{\alpha}{\beta^2}\cos \beta…
octonion
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Compact or non-compact boson from bosonization?

In some discussions of bosonization, it is stressed that the duality between free bosons and free fermions requires the use of a compact boson. For example, in a review article by Senechal, the following statement is made: In order for bosonization…
Zack
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Jordan-Wigner transformation v.s. Bosonization

Jordan-Wigner transformation is a powerful tool, mapping between models with spin-1/2 degrees of freedom and spinless fermions. The key idea is that there is a simple mapping between the Hilbert space of a system with a spin-1/2 degree of freedom…
wonderich
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Mathematical content of Thirring/Sine-Gordon duality

I'm a mathematician who is intrigued by the duality between the Thirring and Sine-Gordon models as established by Sidney Coleman. Can someone explain the mathematical content of this duality to me? (Or is this somehow just a duality in an…
Brian Klatt
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Jordan-Wigner transformation on a circle and spin structures?

Is there an analog of the Jordan-Wigner transformation between fermion algebra on a circle and a Pauli algebra? For example, the continuum analog of bosonization of "compact boson $\leftrightarrow$ Dirac fermion" there's an analog of the…
Joe
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"$\theta$-$\phi$ duality" and $T$-duality -- is the free fermion theory self-dual?

When bosonizing an interacting spinless Luttinger liquid, the action can be written as \begin{equation} S=\frac{K}{2\pi}\int dx d\tau\ (\partial_\mu\phi)^2 = \frac{1}{2\pi K}\int dx d\tau\ (\partial_\mu\theta)^2, \end{equation} where…
pathintegral
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Bosonization and supersymmetry

In 2D (time + space) there is no notion of statistic. So particles can be described in terms of bosonic and fermionic fields. Well-known example is Thirring/Sine-Gordon duality. There are also some examples: $\phi^4$ theory kinks as fermions? Are…
Nikita
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Is bosonization possible in any number of dimensions?

Is bosonization applicable to an arbitrary number of spacetime dimensions?
TheQuantumMan
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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 $e^{i\sqrt{\pi}\left(\phi\pm\bar\phi\right)}$. Here I'm using $\bar{\phi}$ to denote the dual field…
octonion
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Question on functional bosonization

Let me be sort of specific. We consider a Weyl particles on $S^{1}$, with the following Hamiltonian $$\mathcal{H}=v\int_{0}^{2\pi}\psi^{\dagger}(x)(-i\partial_{x})\psi(x)dx$$ Such particles have the property that…
Kiryl Pesotski
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Bosonization and Commutation Relation

I'm playing a bit with bosonization $ψ→:e^{-φ}:$ and $ψ^*→:e^{φ}:$ in the sense that $$ \Bigg\langle 0_\mathrm{F} \Bigg|∏_{i=1}^nψ(z_i)ψ^*(w_i)\Bigg|0_\mathrm{F}\Bigg\rangle = \Bigg\langle…
MaPo
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Book recommendation for CFT in condensed matter theory

I've been looking for sources about conformal field theory (CFT) applications in condensed matter theory (CMT) like bosonization, critical phenomena, and QFT anomalies. I have studied CFT from Blumenhagen and several other review papers, and I have…
Abdülcanbaz
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Point splitting in bosonization

I was following two lecture notes on bosonization: https://arxiv.org/abs/cond-mat/9805275 and https://stanford.idm.oclc.org/login?url=https://www.worldscientific.com/doi/10.1142/9789814447027_0006 I have a question about the point splitting…
Kyung-Su
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Bosonisation of two non-interacting Fermions

Assume we have 2 sets of non-interacting fermions which I show by $\psi^{\pm}$ and $\chi^{\pm}$ where we have $\left< \psi^{+}(z) \psi^{-}(0) \right>=\frac{1}{z}$ and similar for $\chi$. Now we bosonise the fermions by setting $\psi^{\pm}=e^{\pm i…
mathvc_
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The correct definition of Klein Factor

Klein factors are the operators which make sure that the anticommutation between the different species is correct during the bosonization procedure. According to this famous review by Jan Von Delft, they are the operators responsible for raising or…
Boa_Constrictor
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