Bosonization of non-relativistic fermions on a circle: Tomonaga's problem revisited

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dc.creatorDhar, Avinash
dc.creatorMandal, Gautam
dc.date2006-03-20
dc.date.accessioned2026-07-07T10:46:14Z
dc.date.available2026-07-07T10:46:14Z
dc.descriptionWe use the recently developed tools for an exact bosonization of a finite number $N$ of non-relativistic fermions to discuss the classic Tomonaga problem. In the case of noninteracting fermions, the bosonized hamiltonian naturally splits into an O$(N)$ piece and an O$(1)$ piece. We show that in the large-N and low-energy limit, the O$(N)$ piece in the hamiltonian describes a massless relativistic boson, while the O$(1)$ piece gives rise to cubic self-interactions of the boson. At finite $N$ and high energies, the low-energy effective description breaks down and the exact bosonized hamiltonian must be used. We also comment on the connection between the Tomonaga problem and pure Yang-Mills theory on a cylinder. In the dual context of baby universes and multiple black holes in string theory, we point out that the O$(N)$ piece in our bosonized hamiltonian provides a simple understanding of the origin of two different kinds of nonperturbative O$(e^{-N})$ corrections to the black hole partition function.
dc.descriptionlatex, 28 pages, 5 epsf figures
dc.identifierhttps://arxiv.org/abs/hep-th/0603154
dc.identifierhttp://arxiv.org/abs/hep-th/0603154
dc.identifierPhys.Rev.D74:105006,2006
dc.identifierdoi:10.1103/PhysRevD.74.105006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183166
dc.subjectHigh Energy Physics - Theory
dc.subjectStatistical Mechanics
dc.titleBosonization of non-relativistic fermions on a circle: Tomonaga's problem revisited
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