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In thermal quantum field theory, the Matsubara frequency (named after Takeo Matsubara) summation is the summation over discrete imaginary frequencies. It takes the following form :, where the frequencies are usually taken from either of the following two sets (with ): :first set: , bosonic frequencies, :second set: , fermionic frequencies. The summation will converge if g(z=iω) tends to 0 in z→∞ limit in a manner faster than . The summation over bosonic frequencies is denoted as SB (with η=+1), while that over fermionic frequencies is denoted as SF (with η=-1). η is the statistical sign. In addition to thermal quantum field theory, the Matsubara frequency summation method plays also an essential role in the diagrammatic approach to solid-state physics, namely, if one considers the diagrams at finite temperature.〔A. Abrikosov, L. Gor'kov, I. Dzyaloshinskii: ''Methods of Quantum Field Theory in Statistical Physics.'', New York, Dover Publ., 1975, ISBN 0-486-63228-8〕 Generally speaking, if at ''T=0'' K a certain Feynman diagram is represented by an integral , at finite temperature it is given by the sum . == Matsubara Frequency Summation == 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「Matsubara frequency」の詳細全文を読む スポンサード リンク
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