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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Auxiliary field ： ウィキペディア英語版 Auxiliary field In physics, and especially quantum field theory, an auxiliary field is one whose equations of motion admit a single solution. Therefore, the Lagrangian describing such a field $A$ contains an algebraic quadratic term and an arbitrary linear term, while it contains no kinetic terms (derivatives of the field): $\backslash mathcal\_=\backslash frac(A,A)+(f(\backslash varphi),A)$. The equation of motion for $A$ is: $A(\backslash varphi)=-f(\backslash varphi)$ and the Lagrangian becomes: $\backslash mathcal\_=-\backslash frac(f(\backslash varphi),f(\backslash varphi))$. Auxiliary fields do not propagate and hence the content of any theory remains unchanged by adding such fields by hand. If we have an initial Lagrangian $\backslash mathcal\_$ describing a field $\backslash varphi$ then the Lagrangian describing both fields is: $\backslash mathcal=\backslash mathcal\_(\backslash varphi)+\backslash mathcal\_=\backslash mathcal\_(\backslash varphi)-\backslash frac(f(\backslash varphi),f(\backslash varphi))$. Therefore, auxiliary fields can be employed to cancel quadratic terms in $\backslash varphi$ in $\backslash mathcal\_$ and linearize the action $\backslash mathcal\; =\; \backslash int.$ Examples of auxiliary fields are the complex scalar field F in a chiral superfield, the real scalar field D in a vector superfield, the scalar field B in BRST and the field in the Hubbard-Stratonovich transformation. The quantum mechanical effect of adding an auxiliary field is the same as the classical, since the path integral over such a field is Gaussian. To wit: :$\backslash int\_^\backslash infty\backslash !dA\backslash ,\; e^\; A^2\; +\; A\; f\}\; =\; \backslash sqrte^\}$. == References == * Superspace, or One thousand and one lessons in supersymmetry (arXiv:hep-th/0108200 ) 〔 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「Auxiliary field」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.