Supersymmetry algebra (original) (raw)
초대칭 대수(超對稱代數, 영어: supersymmetry algebra)는 푸앵카레 대칭과 초대칭을 나타내는 리 초대수다.
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| dbo:abstract | In theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains not only the Poincaré algebra and a compact subalgebra of internal symmetries, but also contains some fermionic supercharges, transforming as a sum of N real spinor representations of the Poincaré group. Such symmetries are allowed by the Haag–Łopuszański–Sohnius theorem. When N>1 the algebra is said to have extended supersymmetry. The supersymmetry algebra is a semidirect sum of a central extension of the super-Poincaré algebra by a compact Lie algebra B of internal symmetries. Bosonic fields commute while fermionic fields anticommute. In order to have a transformation that relates the two kinds of fields, the introduction of a Z2-grading under which the even elements are bosonic and the odd elements are fermionic is required. Such an algebra is called a Lie superalgebra. Just as one can have representations of a Lie algebra, one can also have representations of a Lie superalgebra, called supermultiplets. For each Lie algebra, there exists an associated Lie group which is connected and simply connected, unique up to isomorphism, and the representations of the algebra can be extended to create group representations. In the same way, representations of a Lie superalgebra can sometimes be extended into representations of a Lie supergroup. (en) In fisica teorica, un'algebra di supersimmetria (o un'algebra SUSY) è un'algebra di Lie che incorpora la supersimmetria, ovvero una relazione tra bosoni e fermioni. In un mondo supersimmetrico, ogni bosone ha un fermione partner di pari massa a riposo e ogni fermione ha un bosone partner di pari massa a riposo. I campi bosonici commutano, mentre i campi fermionici anticommutano; al fine di mettere in relazione i due tipi di campi in un'unica algebra, si fa uso dell'introduzione di un'algebra graduata ("algebra Graded") in base alla quale si richiede che gli elementi pari siano bosoni e gli elementi dispari siano fermioni. Un tale algebra è chiamata superalgebra di Lie. D'altra parte, il teorema spin-statistica dimostra che i bosoni hanno spin intero, mentre i fermioni hanno spin semi-intero. Di conseguenza, gli elementi dispari in un'algebra di supersimmetria è necessario che abbiano spin semi-intero che è in contrasto con le più tradizionali simmetrie in fisica classica. Nelle simmetrie fisiche che sono associate ad un'algebra di Lie si possono costruire le loro rappresentazioni, così si può avere anche delle rappresentazioni di una superalgebra Lie. Ogni algebra di Lie è legata ad un gruppo di Lie così allo stesso modo ogni superalgebra di Lie è legata ad un supergruppo di Lie. (it) 초대칭 대수(超對稱代數, 영어: supersymmetry algebra)는 푸앵카레 대칭과 초대칭을 나타내는 리 초대수다. (ko) |
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| rdfs:comment | 초대칭 대수(超對稱代數, 영어: supersymmetry algebra)는 푸앵카레 대칭과 초대칭을 나타내는 리 초대수다. (ko) In theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains not only the Poincaré algebra and a compact subalgebra of internal symmetries, but also contains some fermionic supercharges, transforming as a sum of N real spinor representations of the Poincaré group. Such symmetries are allowed by the Haag–Łopuszański–Sohnius theorem. When N>1 the algebra is said to have extended supersymmetry. The supersymmetry algebra is a semidirect sum of a central extension of the super-Poincaré algebra by a compact Lie algebra B of internal symmetries. (en) In fisica teorica, un'algebra di supersimmetria (o un'algebra SUSY) è un'algebra di Lie che incorpora la supersimmetria, ovvero una relazione tra bosoni e fermioni. In un mondo supersimmetrico, ogni bosone ha un fermione partner di pari massa a riposo e ogni fermione ha un bosone partner di pari massa a riposo. (it) |
| rdfs:label | Algebra supersimmetrica (it) 초대칭 대수 (ko) Supersymmetry algebra (en) |
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