theorems:elitzur_s_theorem
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theorems:elitzur_s_theorem [2017/10/27 13:10] jakobadmin ↷ Page moved from gauge_theory:elitzur_s_theorem to theories:gauge_theory:elitzur_s_theorem |
theorems:elitzur_s_theorem [2017/11/05 15:34] jakobadmin ↷ Links adapted because of a move operation |
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| <blockquote>"a gauge symmetry is so big, it's too big to fail."</blockquote> | <blockquote>"a gauge symmetry is so big, it's too big to fail."</blockquote> | ||
| - | A [[theories:gauge_theory|local symmetry]] means that we have an independent copy of the symmetry (of the group $G$) at each spacetime point. A spacetime point is zero-dimensional. Hence we are dealing with symmetries of zero-dimensional subsystems and | + | A [[advanced_tools:gauge_symmetry|local symmetry]] means that we have an independent copy of the symmetry (of the group $G$) at each spacetime point. A spacetime point is zero-dimensional. Hence we are dealing with symmetries of zero-dimensional subsystems and |
| <blockquote>A [[advanced_notions:symmetry_breaking:mermin-wagner_theorem|theorem due to Mermin and Wagner]] states that a continuous symmetry can only be spontaneously broken in a dimension larger than two. For a discrete symmetry this lower critical dimensionality is one. This is, in fact, well known since in quantum mechanics with finitely many degrees of freedom (corresponding to one-dimensional field theory) tunneling between degenerate classical minima allows for a unique symmetric ground state. [...] The Mermin-Wagner theorem has been restated by Coleman in the framework of field theory. <cite>page 525 in Quantum Field Theory by Claude Itzykson, Jean-Bernard Zuber </cite> </blockquote> | <blockquote>A [[advanced_notions:symmetry_breaking:mermin-wagner_theorem|theorem due to Mermin and Wagner]] states that a continuous symmetry can only be spontaneously broken in a dimension larger than two. For a discrete symmetry this lower critical dimensionality is one. This is, in fact, well known since in quantum mechanics with finitely many degrees of freedom (corresponding to one-dimensional field theory) tunneling between degenerate classical minima allows for a unique symmetric ground state. [...] The Mermin-Wagner theorem has been restated by Coleman in the framework of field theory. <cite>page 525 in Quantum Field Theory by Claude Itzykson, Jean-Bernard Zuber </cite> </blockquote> | ||
theorems/elitzur_s_theorem.txt · Last modified: 2018/05/05 12:51 by jakobadmin
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