Bose-Einstein Condensation and Spontaneous Symmetry Breaking1

Elliott H. Lieb; Robert Seiringer; Jakob Yngvason

doi:10.1016/S0034-4877(07)80074-7

Bose-Einstein Condensation and Spontaneous Symmetry Breaking1

Elliott H. Lieb, Robert Seiringer, Jakob Yngvason

Mathematics

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

17 Scopus citations

Abstract

After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long-range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented. The proof is based on a rigorous validation of Bogoliubov's c-number substitution for the k = 0 mode operator α₀.

Original language	English (US)
Pages (from-to)	389-399
Number of pages	11
Journal	Reports on Mathematical Physics
Volume	59
Issue number	3
DOIs	https://doi.org/10.1016/S0034-4877(07)80074-7
State	Published - Jun 2007

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Bose-Einstein condensation
c-number substituions
gauge symmetry

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10.1016/S0034-4877(07)80074-7

Cite this

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title = "Bose-Einstein Condensation and Spontaneous Symmetry Breaking1",

abstract = "After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long-range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented. The proof is based on a rigorous validation of Bogoliubov's c-number substitution for the k = 0 mode operator α0.",

keywords = "Bose-Einstein condensation, c-number substituions, gauge symmetry",

author = "Lieb, {Elliott H.} and Robert Seiringer and Jakob Yngvason",

note = "Funding Information: *Work partially supported by U.S. National Science Foundation grant PHY 01 3998. tWork partially supported by U.S. National Science Foundation grant PHY 03 53181, and by an A.P. Sloan Fellowship. ~Work partially supported by FWF grant P17176-N02 and EU grant HPRN-CT-2002-00277. 1Contribution to the Proceedings of the 21st Max Born Symposium, Wroctaw, Poland, June 26-28, 2006. Talk given by J. Yngvason.",

year = "2007",

month = jun,

doi = "10.1016/S0034-4877(07)80074-7",

language = "English (US)",

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journal = "Reports on Mathematical Physics",

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T1 - Bose-Einstein Condensation and Spontaneous Symmetry Breaking1

AU - Lieb, Elliott H.

AU - Seiringer, Robert

AU - Yngvason, Jakob

N1 - Funding Information: *Work partially supported by U.S. National Science Foundation grant PHY 01 3998. tWork partially supported by U.S. National Science Foundation grant PHY 03 53181, and by an A.P. Sloan Fellowship. ~Work partially supported by FWF grant P17176-N02 and EU grant HPRN-CT-2002-00277. 1Contribution to the Proceedings of the 21st Max Born Symposium, Wroctaw, Poland, June 26-28, 2006. Talk given by J. Yngvason.

PY - 2007/6

Y1 - 2007/6

N2 - After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long-range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented. The proof is based on a rigorous validation of Bogoliubov's c-number substitution for the k = 0 mode operator α0.

AB - After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long-range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented. The proof is based on a rigorous validation of Bogoliubov's c-number substitution for the k = 0 mode operator α0.

KW - Bose-Einstein condensation

KW - c-number substituions

KW - gauge symmetry

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DO - 10.1016/S0034-4877(07)80074-7

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VL - 59

SP - 389

EP - 399

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

IS - 3

ER -

Bose-Einstein Condensation and Spontaneous Symmetry Breaking1

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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