Elitzur's theorem (original) (raw)
In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing expectation values are ones that are invariant under local gauge transformations. An important implication is that gauge symmetry cannot be spontaneously broken. The theorem was proved in 1975 by Shmuel Elitzur in lattice field theory, although the same result is expected to hold in the continuum. The theorem shows that the naive interpretation of the Higgs mechanism as the spontaneous symmetry breaking of a gauge symmetry is incorrect, although the phenomenon can be reformulated entirely in terms of gauge invariant quantities in what is known as the Fröhlich–Morchio–Strocchi mechanism.
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| dbo:abstract | In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing expectation values are ones that are invariant under local gauge transformations. An important implication is that gauge symmetry cannot be spontaneously broken. The theorem was proved in 1975 by Shmuel Elitzur in lattice field theory, although the same result is expected to hold in the continuum. The theorem shows that the naive interpretation of the Higgs mechanism as the spontaneous symmetry breaking of a gauge symmetry is incorrect, although the phenomenon can be reformulated entirely in terms of gauge invariant quantities in what is known as the Fröhlich–Morchio–Strocchi mechanism. (en) Теоре́ма Елітцу́ра — є теоремою квантової та статистичної теорії поля, яка стверджує, що локальні калібрувальні симетрії неможливо спонтанно порушити. Теорема була запропонована в 1975 році Шмуелем Еліцуром, який довів її для абелевих калібрувальних полів на гратці. Тим не менш, можливо спонтанно порушити глобальну симетрію в рамках теорії, яка має локальну калібрувальну симетрію, як у механізмі Хіггса. (uk) |
| dbo:wikiPageExternalLink | http://www.itp3.uni-stuttgart.de/lehre/Archiv/Courses_upto_ss13/Lattice_gauge_theory_SS_2009/Chapter3.pdf |
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| rdfs:comment | In quantum field theory and statistical field theory, Elitzur's theorem states that in gauge theories, the only operators that can have non-vanishing expectation values are ones that are invariant under local gauge transformations. An important implication is that gauge symmetry cannot be spontaneously broken. The theorem was proved in 1975 by Shmuel Elitzur in lattice field theory, although the same result is expected to hold in the continuum. The theorem shows that the naive interpretation of the Higgs mechanism as the spontaneous symmetry breaking of a gauge symmetry is incorrect, although the phenomenon can be reformulated entirely in terms of gauge invariant quantities in what is known as the Fröhlich–Morchio–Strocchi mechanism. (en) Теоре́ма Елітцу́ра — є теоремою квантової та статистичної теорії поля, яка стверджує, що локальні калібрувальні симетрії неможливо спонтанно порушити. Теорема була запропонована в 1975 році Шмуелем Еліцуром, який довів її для абелевих калібрувальних полів на гратці. Тим не менш, можливо спонтанно порушити глобальну симетрію в рамках теорії, яка має локальну калібрувальну симетрію, як у механізмі Хіггса. (uk) |
| rdfs:label | Elitzur's theorem (en) Теорема Елітцура (uk) |
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