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The Hubbard–Stratonovich (HS) transformation is an exact mathematical transformation invented by Russian physicist Ruslan L. Stratonovich and popularized by British physicist John Hubbard. It is used to convert a particle theory into its respective field theory by linearizing the density operator in the many-body interaction term of the Hamiltonian and introducing a scalar auxiliary field. It is defined via the integral identity〔 Translation available: 〕 : where the real constant . The basic idea of the HS transformation is to reformulate a system of particles interacting through two-body potentials into a system of independent particles interacting with a fluctuating field. The procedure is widely used in polymer physics, classical particle physics, spin glass theory, and electronic structure theory. ==Calculation of resulting field theories== The resulting field theories are well-suited for the application of effective approximation techniques, like the mean field approximation. A major difficulty arising in the simulation with such field theories is their highly oscillatory nature in case of strong interactions, which leads to the well-known numerical sign problem. The problem originates from the repulsive part of the interaction potential, which implicates the introduction of the complex factor via the HS transformation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hubbard–Stratonovich transformation」の詳細全文を読む スポンサード リンク
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