Bosonization: Fermionic Operator Scaling & Correlation Functions

[gonadas91]

Hi! I am sttrugled with a question concerning the bosonization technique. When you express the fermionic operator as a vertex operator depending on the bose field, for interacting systems, the scaling of the operator is different of 1/2. That is, for non-interacting electrons, d=1/2. When interactions are switched on this changes and, can we still consider the operator to be a "fermionic" one, or is it, instead an "anyon"?

Finally, in terms of calculation of correlation functions, can we compute the single particle Green's function from this picture? (In principle, Wick's theorem doesn't hold)

Thank you!

 

[eljose79]

Hi there,

Thank you for your question regarding the bosonization technique and its application to interacting systems. The short answer is that the operator can still be considered fermionic, but with a different scaling factor, and yes, the single particle Green's function can still be computed using this technique.

To provide a bit more explanation, bosonization is a powerful technique used in condensed matter physics to study interacting systems of fermions. It involves expressing the fermionic operators in terms of bosonic fields, which allows for the use of bosonic techniques and simplification of calculations.

In non-interacting systems, the scaling factor for the fermionic operator is indeed 1/2. However, when interactions are present, the scaling factor changes due to the effects of interactions on the fermions. This does not mean that the operator is no longer fermionic, but rather that it behaves differently due to the interactions.

In terms of calculating correlation functions, it is still possible to use the bosonization technique to compute the single particle Green's function. While Wick's theorem may not hold in this picture, there are other techniques that can be used to calculate correlation functions in interacting systems.

I hope this helps to clarify your question. If you have any further inquiries, please don't hesitate to ask.