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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 Crossing symmetry ： ウィキペディア英語版 Crossing (physics) In quantum field theory, a branch of theoretical physics, crossing is the property of scattering amplitudes that allows antiparticles to be interpreted as particles going backwards in time. Crossing states that the same formula that determines the S-matrix elements and scattering amplitudes for particle $\backslash mathrm$ to scatter with $\backslash mathrm$ and produce particle $\backslash mathrm$ and $\backslash mathrm$ will also give the scattering amplitude for $\backslash scriptstyle\; \backslash mathrm+\backslash bar$ to go into $\backslash mathrm$, or for $\backslash scriptstyle\; \backslash bar$ to produce $\backslash scriptstyle\; \backslash mathrm+\backslash bar\{\backslash mathrm\{A\}\}$. The only difference is that the value of the energy is negative for the antiparticle. The formal way to state this property is that the antiparticle scattering amplitudes are the analytic continuation of particle scattering amplitudes to negative energies. The interpretation of this statement is that the antiparticle is in every way a particle going backwards in time. Crossing was already implicit in the work of Feynman, but came to its own in the 1950s and 1960s as part of the analytic S-matrix program. ==General overview== Consider an amplitude $\backslash mathcal(\; \backslash phi\; (p)\; +\; ...\; \backslash \; \backslash rightarrow\; ...)$. We concentrate our attention on one of the incoming particles with momentum p. The quantum field $\backslash phi\; (p)$, corresponding to the particle is allowed to be either bosonic or fermionic. Crossing symmetry states that we can relate the amplitude of this process to the amplitude of a similar process with an outgoing antiparticle $\backslash bar\; (-p)$ replacing the incoming particle $\backslash phi\; (p)$: $\backslash mathcal(\; \backslash phi\; (p)\; +\; ...\; \backslash rightarrow\; ...)=\backslash mathcal(\; ...\; \backslash rightarrow\; ...\; +\; \backslash bar\; (-p)\; )$. In the bosonic case, the idea behind crossing symmetry can be understood intuitively using Feynman diagrams. Consider any process involving an incoming particle with momentum p. For the particle to give a measurable contribution to the amplitude, it has to interact with a number of different particles with momenta $k\_,\; k\_,\; ...\; ,\; k\_$ via a vertex. Conservation of momentum implies $\backslash sum\_^\; q\_=p$. In case of an outgoing particle, conservation of momentum reads as $\backslash sum\_^q\_=-p$. Thus, replacing an incoming boson with an outgoing antiboson with opposite momentum yields the same S-matrix element. In fermionic case, one can apply the same argument but now the relative phase convention for the external spinors must be taken into account. 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「Crossing (physics)」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.