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To grasp the relevant physics at a sloppy level, perhaps you simply need a few examples. You know a concept is commonly constructed by the manner you refer to it together with other concepts. Symmetry breaking usually results in ground state degeneracy and long range order. Order parameter field aids you in identifying degenerate sectors with the symmetries ...

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There is at least one philosopher before Plato and he is Anaximander. There are many passages in his works that relate to the concept of symmetry: The basic elements of nature (water, air, fire, earth) which the first Greek philosophers believed that constituted the universe represent in fact the primordial forces of previous thought. Their collision ...

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To start with, special relativity is necessary when describing elementary particles and hadrons composed by them. Special relativity defines the invariant mass of a particle or an ensemble of particles as the measure of the four momentum vector carried by the particle/ensemble. In the case of one elementary particle, an electron for example, it is ...

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99.9% of the mass of a hadron or a meson comes from confinement in QCD. Confinement is a special feature of QCD due to its non abelian symmetry which leads to a negative beta function. It is confinement that also leads to a breaking of the chiral symmetry at about 200 MeV or the radius of a hadron (about 1 femto meter).

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The dilaton $\sigma$ is the Goldstone boson of scale invariance. Scale transformations $x\rightarrow x/\lambda$ are generated non linearly, e.g. $$\sigma(x)\rightarrow \sigma(\lambda x)+f \log\lambda\,,\qquad \lambda>0$$ where $f$ is the dilaton decay constant (see below). An effective field theory for this Goldstone boson can be easily written with ...

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