Non-Abelian bosonization and topological aspects of BCS systems

Anupam Garg; V. P. Nair; Michael Stone

doi:10.1016/0003-4916(87)90096-0

Non-Abelian bosonization and topological aspects of BCS systems

Anupam Garg^*, V. P. Nair, Michael Stone

^*Corresponding author for this work

Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

It is shown that many features of the low energy behaviour of weak coupling BCS systems are topological in character. This is done by writing the BCS action as a Fermi surface sum of (1 + 1)-dimentional non-Abelian actions, each one of which can be bosonized à la Witten. This process leads to the correct current generating parts (as found by Cross) in the effective action for the gap function, and in addition a Wess-Zumino term. The mass and spin currents are calculated for the three-dimensional theory, and it is shown that upon averaging over all directions on the Fermi surface, the contribution from the Wess-Zumino term vanishes for a pure spin singlet or pure spin triplet gap, but not otherwise.

Original language	English (US)
Pages (from-to)	149-162
Number of pages	14
Journal	Annals of Physics
Volume	173
Issue number	1
DOIs	https://doi.org/10.1016/0003-4916(87)90096-0
State	Published - Jan 1987

Funding

This research was supported by the National Science Foundation under Grant PHY82-17853, supplemented by funds from the National Aeronautics and Space Administration. at the University of California, Santa Barbara, and by the National Science Foundation under Grants DMR83-16981 and DMR84-15063 at the University of Illinois at Urbana-Champaign.

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/0003-4916(87)90096-0

Cite this

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title = "Non-Abelian bosonization and topological aspects of BCS systems",

abstract = "It is shown that many features of the low energy behaviour of weak coupling BCS systems are topological in character. This is done by writing the BCS action as a Fermi surface sum of (1 + 1)-dimentional non-Abelian actions, each one of which can be bosonized {\`a} la Witten. This process leads to the correct current generating parts (as found by Cross) in the effective action for the gap function, and in addition a Wess-Zumino term. The mass and spin currents are calculated for the three-dimensional theory, and it is shown that upon averaging over all directions on the Fermi surface, the contribution from the Wess-Zumino term vanishes for a pure spin singlet or pure spin triplet gap, but not otherwise.",

author = "Anupam Garg and Nair, {V. P.} and Michael Stone",

note = "Funding Information: This research was supported by the National Science Foundation under Grant PHY82-17853, supplemented by funds from the National Aeronautics and Space Administration. at the University of California, Santa Barbara, and by the National Science Foundation under Grants DMR83-16981 and DMR84-15063 at the University of Illinois at Urbana-Champaign.",

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T1 - Non-Abelian bosonization and topological aspects of BCS systems

AU - Garg, Anupam

AU - Nair, V. P.

AU - Stone, Michael

N1 - Funding Information: This research was supported by the National Science Foundation under Grant PHY82-17853, supplemented by funds from the National Aeronautics and Space Administration. at the University of California, Santa Barbara, and by the National Science Foundation under Grants DMR83-16981 and DMR84-15063 at the University of Illinois at Urbana-Champaign.

PY - 1987/1

Y1 - 1987/1

N2 - It is shown that many features of the low energy behaviour of weak coupling BCS systems are topological in character. This is done by writing the BCS action as a Fermi surface sum of (1 + 1)-dimentional non-Abelian actions, each one of which can be bosonized à la Witten. This process leads to the correct current generating parts (as found by Cross) in the effective action for the gap function, and in addition a Wess-Zumino term. The mass and spin currents are calculated for the three-dimensional theory, and it is shown that upon averaging over all directions on the Fermi surface, the contribution from the Wess-Zumino term vanishes for a pure spin singlet or pure spin triplet gap, but not otherwise.

AB - It is shown that many features of the low energy behaviour of weak coupling BCS systems are topological in character. This is done by writing the BCS action as a Fermi surface sum of (1 + 1)-dimentional non-Abelian actions, each one of which can be bosonized à la Witten. This process leads to the correct current generating parts (as found by Cross) in the effective action for the gap function, and in addition a Wess-Zumino term. The mass and spin currents are calculated for the three-dimensional theory, and it is shown that upon averaging over all directions on the Fermi surface, the contribution from the Wess-Zumino term vanishes for a pure spin singlet or pure spin triplet gap, but not otherwise.

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Non-Abelian bosonization and topological aspects of BCS systems

Abstract

Funding

ASJC Scopus subject areas

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