Bosonization of nonrelativistic fermions on a circle: Tomonaga’s problem revisited

Dhar, Avinash ; Mandal, Gautam (2006) Bosonization of nonrelativistic fermions on a circle: Tomonaga’s problem revisited Physical Review D - Particles, Fields, Gravitation and Cosmology, 74 (10). Article ID 105006. ISSN 1550-7998

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Official URL: https://journals.aps.org/prd/abstract/10.1103/Phys...

Related URL: http://dx.doi.org/10.1103/PhysRevD.74.105006

Abstract

We use the recently developed tools for an exact bosonization of a finite number N of nonrelativistic 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.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:103582
Deposited On:26 Dec 2017 11:14
Last Modified:26 Dec 2017 11:14

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