About: Jordan map

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In theoretical physics, the Jordan map, often also called the Jordan–Schwinger map is a map from matrices Mij to bilinear expressions of quantum oscillators which expedites computation of representations of Lie algebras occurring in physics. It was introduced by Pascual Jordan in 1935 and was utilized by Julian Schwinger in 1952 to re-work out the theory of quantum angular momentum efficiently, given that map’s ease of organizing the (symmetric) representations of su(2) in Fock space. where is the commutator and is the Kronecker delta. ,

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  • In theoretical physics, the Jordan map, often also called the Jordan–Schwinger map is a map from matrices Mij to bilinear expressions of quantum oscillators which expedites computation of representations of Lie algebras occurring in physics. It was introduced by Pascual Jordan in 1935 and was utilized by Julian Schwinger in 1952 to re-work out the theory of quantum angular momentum efficiently, given that map’s ease of organizing the (symmetric) representations of su(2) in Fock space. The map utilizes several creation and annihilation operators and of routine use in quantum field theories and many-body problems, each pair representing a quantum harmonic oscillator.The commutation relations of creation and annihilation operators in a multiple-boson system are, where is the commutator and is the Kronecker delta. These operators change the eigenvalues of the number operator, , by one, as for multidimensional quantum harmonic oscillators. The Jordan map from a set of matrices Mij to Fock space bilinear operators M, is clearly a Lie algebra isomorphism, i.e. the operators M satisfy the same commutation relations as the matrices M. (en)
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  • In theoretical physics, the Jordan map, often also called the Jordan–Schwinger map is a map from matrices Mij to bilinear expressions of quantum oscillators which expedites computation of representations of Lie algebras occurring in physics. It was introduced by Pascual Jordan in 1935 and was utilized by Julian Schwinger in 1952 to re-work out the theory of quantum angular momentum efficiently, given that map’s ease of organizing the (symmetric) representations of su(2) in Fock space. where is the commutator and is the Kronecker delta. , (en)
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  • Jordan map (en)
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