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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 On shell renormalization scheme ： ウィキペディア英語版 On shell renormalization scheme In quantum field theory, and especially in quantum electrodynamics, the interacting theory leads to infinite quantities that have to be absorbed in a renormalization procedure, in order to be able to predict measurable quantities. The renormalization scheme can depend on the type of particles that are being considered. For particles that can travel asymptotically large distances, or for low energy processes, the on-shell scheme, also known as the physical scheme, is appropriate. If these conditions are not fulfilled, one can turn to other schemes, like the Minimal subtraction scheme. ==Fermion propagator in the interacting theory== Knowing the different propagators is the basis for being able to calculate Feynman diagrams which are useful tools to predict, for example, the result of scattering experiments. In a theory where the only field is the Dirac field, the Feynman propagator reads :$\backslash langle\; 0\; |\; T(\backslash psi(x)\backslash bar(0))|\; 0\; \backslash rangle\; =iS\_F(x)\; =\; \backslash int\; \backslash frac\backslash frac$ where $T$ is the time-ordering operator, $|0\backslash rangle$ the vacuum in the non interacting theory, $\backslash psi(x)$ and $\backslash bar(x)$ the Dirac field and its Dirac adjoint, and where the left-hand side of the equation is the two-point correlation function of the Dirac field. In a new theory, the Dirac field can interact with another field, for example with the electromagnetic field in quantum electrodynamics, and the strength of the interaction is measured by a parameter, in the case of QED it is the bare electron charge, $e$. The general form of the propagator should remain unchanged, meaning that if $|\backslash Omega\backslash rangle$ now represents the vacuum in the interacting theory, the two-point correlation function would now read :$\backslash langle\; \backslash Omega\; |\; T(\backslash psi(x)\backslash bar(0))|\; \backslash Omega\; \backslash rangle\; =\; \backslash int\; \backslash frac\backslash frac$ Two new quantities have been introduced. First the renormalized mass $m\_r$ has been defined as the pole in the Fourier transform of the Feynman propagator. This is the main prescription of the on-shell renormalization scheme (there is then no need to introduce other mass scales like in the minimal subtraction scheme). The quantity $Z\_2$ represents the new strength of the Dirac field. As the interaction is turned down to zero by letting $e\backslash rightarrow\; 0$, these new parameters should tend to a value so as to recover the propagator of the free fermion, namely $m\_r\backslash rightarrow\; m$ and $Z\_2\backslash rightarrow\; 1$. This means that $m\_r$ and $Z\_2$ can be defined as a series in $e$ if this parameter is small enough (in the unit system where $\backslash hbar=c=1$, $e=\backslash sqrt\backslash simeq\; 0.3$, where $\backslash alpha$ is the fine-structure constant). Thus these parameters can be expressed as :$Z\_2=1+\backslash delta\_2$ :$m\_r\; =\; m\; +\; \backslash delta\; m$ On the other hand, the modification to the propagator can be calculated up to a certain order in $e$ using Feynman diagrams. These modifications are summed up in the fermion self energy $\backslash Sigma(p)$ :$\backslash langle\; \backslash Omega\; |\; T(\backslash psi(x)\backslash bar(0))|\; \backslash Omega\; \backslash rangle\; =\; \backslash int\; \backslash frac\backslash frac$ These corrections are often divergent because they contain loops. By identifying the two expressions of the correlation function up to a certain order in $e$, the counterterms can be defined, and they are going to absorb the divergent contributions of the corrections to the fermion propagator. Thus, the renormalized quantities, such as $m\_r$, will remain finite, and will be the quantities measured in experiments. 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「On shell renormalization scheme」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.