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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 Haag's theorem ： ウィキペディア英語版 Haag's theorem Rudolf Haag postulated 〔 Haag, R: ''(On quantum field theories )'', Matematisk-fysiske Meddelelser, 29, 12 (1955). 〕 that the interaction picture does not exist in an interacting, relativistic quantum field theory (QFT), something now commonly known as Haag's Theorem. Haag's original proof was subsequently generalized by a number of authors, notably Hall and Wightman,〔 Hall, D. and Wightman, A.S.: ''A theorem on invariant analytic functions with applications to relativistic quantum field theory'', Matematisk-fysiske Meddelelser, 31, 1 (1957) 〕 who reached the conclusion that a single, universal Hilbert space representation does not suffice for describing both free and interacting fields. In 1975, Reed and Simon proved 〔 Reed, M. and Simon, B.: ''Methods of modern mathematical physics'', Vol. II, 1975, ''Fourier analysis, self-adjointness'', Academic Press, New York 〕 that a Haag-like theorem also applies to free neutral scalar fields of different masses, which implies that the interaction picture cannot exist even under the absence of interactions. ==Formal description of Haag's theorem== In its modern form, the Haag theorem may be stated as follows:〔 John Earman, Doreen Fraser, ''Haag's Theorem and Its Implications for the Foundations of Quantum Field Theory'', Erkenntnis 64, 305(2006) ( online at philsci-archive ) 〕 Consider two representations of the canonical commutation relations (CCR), $(H\_1,\backslash )$ and $(H\_2,\backslash )$ (where $H\_n$ denote the respective Hilbert spaces and $\backslash$ the collection of operators in the CCR). The two representations are called unitarily equivalent if and only if there exists some unitary mapping $U$ from Hilbert space $H\_1$ to Hilbert space $H\_2$ such that for ''j'', $O^j\_2\; =\; U\; O^j\_1\; U^$. Unitary equivalence is a necessary condition for both representations to deliver the same expectation values of the corresponding observables. Haag's theorem states that, contrary to ordinary non-relativistic quantum mechanics, within the formalism of QFT such a unitary mapping does not exist, or, in other words, the two representations are unitarily inequivalent. This confronts the practitioner of QFT with the so-called ''choice problem'', namely the problem of choosing the 'right' representation among a non-denumerable set of inequivalent representations. Although there is no widely accepted solution to the choice problem, an ''unchecked'' formalism claiming to avoid it was published in 2015. The author, Ed Seidewitz, describes himself as "an amateur (but serious) theoretical physicist". 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「Haag's theorem」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.