The Holstein–Primakoff transformation in quantum mechanics is a mapping to the spin operators from boson creation and annihilation operators, effectively truncating their infinite-dimensional Fock space to finite-dimensional subspaces. The transformation was developed in 1940 by Theodore Holstein, a graduate student at the time, and Henry Primakoff. This method has found widespread applicability and has been extended in many different directions.
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| - Holstein-Primakoff-Boson (de)
- Holstein–Primakoff transformation (en)
- ホルシュタイン–プリマコフ変換 (ja)
- Преобразование Гольштейна — Примакова (ru)
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| - ホルシュタイン–プリマコフ変換（ホルシュタイン–プリマコフへんかん、英: Holstein–Primakoff transformation）とは、次のようなスピン演算子からボゾンの生成消滅演算子への変換のことをいう。 (ja)
- Преобразование Гольштейна — Примакова — переход от операторов спина к операторам рождения и уничтожения магнонов (являющихся бозонами). Было предложено (1915—1985, иногда фамилию пишут «Хольштейн») и Генри Примаковым (1914—1983) в оригинальной работе 1940 года. (ru)
- Holstein-Primakoff-Bosonen bzw. die Holstein-Primakoff-Transformation sind eine Methode, um Spins zu beschreiben. Die Methode stammt von Henry Primakoff und Theodore Holstein. Hierbei werden die Spinoperatoren folgendermaßen durch bosonische Erzeugungs- und Vernichtungsoperatoren ersetzt: Wie man leicht zeigt, genügen die so definierten Operatoren der Drehimpulsalgebra . Die Holstein-Primakoff-Darstellung wird unter anderem in der Theorie der Spinwellen verwendet, hier betrachtet man oft den Grenzfall kleiner Bosonenzahl, , in dem die Wurzeln entwickelt werden können. (de)
- The Holstein–Primakoff transformation in quantum mechanics is a mapping to the spin operators from boson creation and annihilation operators, effectively truncating their infinite-dimensional Fock space to finite-dimensional subspaces. The transformation was developed in 1940 by Theodore Holstein, a graduate student at the time, and Henry Primakoff. This method has found widespread applicability and has been extended in many different directions. (en)
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| - Holstein-Primakoff-Bosonen bzw. die Holstein-Primakoff-Transformation sind eine Methode, um Spins zu beschreiben. Die Methode stammt von Henry Primakoff und Theodore Holstein. Hierbei werden die Spinoperatoren folgendermaßen durch bosonische Erzeugungs- und Vernichtungsoperatoren ersetzt: Wie man leicht zeigt, genügen die so definierten Operatoren der Drehimpulsalgebra . Die Holstein-Primakoff-Darstellung wird unter anderem in der Theorie der Spinwellen verwendet, hier betrachtet man oft den Grenzfall kleiner Bosonenzahl, , in dem die Wurzeln entwickelt werden können. Daneben gibt es noch weitere Methoden, Drehimpulsoperatoren auf Bosonen-Erzeugungs- und Vernichtungsoperatoren abzubilden (Freeman Dyson, Julian Schwinger). (de)
- The Holstein–Primakoff transformation in quantum mechanics is a mapping to the spin operators from boson creation and annihilation operators, effectively truncating their infinite-dimensional Fock space to finite-dimensional subspaces. One important aspect of quantum mechanics is the occurrence of—in general—non-commuting operators which represent observables, quantities that can be measured.A standard example of a set of such operators are the three components of the angular momentum operators, which are crucial in many quantum systems.These operators are complicated, and one would like to find a simpler representation, which can be used to generate approximate calculational schemes. The transformation was developed in 1940 by Theodore Holstein, a graduate student at the time, and Henry Primakoff. This method has found widespread applicability and has been extended in many different directions. There is a close link to other methods of boson mapping of operator algebras: in particular, the (non-Hermitian) Dyson–Maleev technique, and to a lesser extent the Jordan–Schwinger map. There is, furthermore, a close link to the theory of (generalized) coherent states in Lie algebras. (en)
- ホルシュタイン–プリマコフ変換（ホルシュタイン–プリマコフへんかん、英: Holstein–Primakoff transformation）とは、次のようなスピン演算子からボゾンの生成消滅演算子への変換のことをいう。 (ja)
- Преобразование Гольштейна — Примакова — переход от операторов спина к операторам рождения и уничтожения магнонов (являющихся бозонами). Было предложено (1915—1985, иногда фамилию пишут «Хольштейн») и Генри Примаковым (1914—1983) в оригинальной работе 1940 года. (ru)
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