By John R. Pierce

Книга just about all approximately Waves just about all approximately WavesКниги Физика Автор: John R. Pierce Год издания: 2006 Формат: djvu Издат.:Dover guides Страниц: 224 Размер: 1,1 ISBN: 0486453022 Язык: Английский0 (голосов: zero) Оценка:This textual content considers waves the good unifying thought of physics. With minimum arithmetic, it emphasizes the habit universal to phenomena corresponding to earthquake waves, ocean waves, sound waves, and mechanical waves. subject matters comprise speed, vector and intricate illustration, power and momentum, coupled modes, polarization, diffraction, and radiation. 1974 variation.

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Both are not symmetries of nature but redundancies in our description. The first one is gauge symmetry which arises because we use four-component fields to describe the two physical polarizations of gauge bosons. The second one is called reparameterization invariance and arises because we have introduced two reference vectors, n and nN , in the construction of the effective theory. The choice of these is not unique and physics is independent of their choice. Let us start with reparameterization invariance, which was first explored in the context of Heavy Quark Effective Theory (HQET).

X C x? 1; 1; 1= /. The scaling follows because x is conjugate to the dependence on x sum of a collinear and an anti-collinear momentum. We see that the soft interactions do not cancel, and the Sudakov form factor receives low-energy contributions which describe a long-range interaction between the fast moving ingoing and outgoing quarks. The situation is summarized in diagrammatic form in Fig. 2, where p in , l i nN , and the double lines represent the soft Wilson lines. Do the soft corrections factorize?

The simplest way to take the invariance under (III) into account is to construct all operators from building blocks which are invariant under this rescaling. The constraints from reparameterization invariance are linked to the Lorentz invariance of the underlying theory. A powerful alternative approach to dealing with Lorentz invariance in effective field theories which involve reference vectors was recently developed in [6]. While reparameterization invariance is specific to the effective theory, gauge invariance was present already in the original QCD Lagrangian.