# 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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### Non-local commutator $[\phi(x), \phi(y)] = i\pi \textrm{sgn}(x-y)$ of 1D chiral boson: why?

It is well-known from bosonization that 1D chiral boson has the commutation relation $$[\phi(x), \phi(y)] = i\pi \mathrm{sgn}(x-y). \tag{1}$$ This gives the correct anticommutation relation for the ...
1 vote
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### Why does normal-ordering ensure finiteness?

I will be using Jan von Delft's rigorous construction of bosonization/refermionization as an example, but I will try to explain my question in more general terms. Consider an (countably) infinite-dim (...
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### SUSY vs bosonization and fermionization

(New to the concepts.) From what was known SUSY described a theory consisted of both a boson and a fermion pair as a symmetric counter part. Bosonization and Fermionization on the other hand described ...
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### Connection of Sugawara construction to the regular energy-momentum tensor

Update: As pointed out by @ConnorBehan this problem is related to the rearrangement lemma in the 'Yellow Book'. In fact this problem is already mentioned page 649 in the book in the discussion about ...
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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 ...
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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 ...
1 vote
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### Derivation of anomalous commutators of currents in Fradkin's book

I am trying to understand the derivation of the anomalous commutators of the left- (and right)-moving currents in Fradkin's book (see e.g. here). I am not sure I understand how (6.71) leads to (6.72). ...
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### Anomalous commutators in bosonization

I am trying to learn about abelian bosonization, and I'm finding there to be very many subtle issues. One of these issues lies in the anomalous commutator, on which the constructive approach to ...
1 vote
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### Interacting electrons in 1D

In Senechal’s review on Bosonization https://arxiv.org/pdf/cond-mat/9908262.pdf he starts with a microscopic Hamiltonian $$H_{\mathrm{F}}=\sum_{k} \varepsilon(k) c^{\dagger}(k) c(k)$$ before stating ...
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