advanced_notions:symmetry_breaking:higgs_mechanism
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advanced_notions:symmetry_breaking:higgs_mechanism [2018/05/05 12:38] jakobadmin ↷ Links adapted because of a move operation |
advanced_notions:symmetry_breaking:higgs_mechanism [2018/12/17 13:56] (current) jakobadmin [Abstract] |
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| * Great descriptions can be found in [[https://arxiv.org/pdf/0910.5167v1.pdf|Gravity from a Particle Physicists’ perspective]] by Roberto Percacci and | * Great descriptions can be found in [[https://arxiv.org/pdf/0910.5167v1.pdf|Gravity from a Particle Physicists’ perspective]] by Roberto Percacci and | ||
| * in section 3.3. of [[http://pages.physics.cornell.edu/~ajd268/Notes/QFTIII.pdf|Solitons and Instantons]] by JEFF ASAF DROR | * in section 3.3. of [[http://pages.physics.cornell.edu/~ajd268/Notes/QFTIII.pdf|Solitons and Instantons]] by JEFF ASAF DROR | ||
| - | * Another great summary can be found in https://arxiv.org/pdf/1405.5532.pdf | + | * Another great summary can be found in https://arxiv.org/pdf/1405.5532.pdf |
| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| The Higgs mechanism is a crucial ingredient of the [[models:standard_model|standard model of particle physics]]. Without the Higgs mechanism, all particles are not allowed to have a mass, because such terms would violate the [[advanced_tools:gauge_symmetry|gauge symmetry]]. (Breaking of [[advanced_tools:gauge_symmetry|gauge symmetry]] is a bad thing, because the [[advanced_tools:renormalization|renormalizability]], i.e. the removing of the infinities that pop-up in most [[theories:quantum_field_theory:canonical|quantum field theory]] calculations, depends on the existence of gauge symmetry.) | The Higgs mechanism is a crucial ingredient of the [[models:standard_model|standard model of particle physics]]. Without the Higgs mechanism, all particles are not allowed to have a mass, because such terms would violate the [[advanced_tools:gauge_symmetry|gauge symmetry]]. (Breaking of [[advanced_tools:gauge_symmetry|gauge symmetry]] is a bad thing, because the [[advanced_tools:renormalization|renormalizability]], i.e. the removing of the infinities that pop-up in most [[theories:quantum_field_theory:canonical|quantum field theory]] calculations, depends on the existence of gauge symmetry.) | ||
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| It is well known that breaking of a local gauge symmetry is impossible (see the quotes below.) | It is well known that breaking of a local gauge symmetry is impossible (see the quotes below.) | ||
| - | However, there is symmetry breaking when the Higgs field acquires a non-zero vev. It is a global part of the gauge group that gets broken. However, there are no [[advanced_notions:symmetry_breaking:goldstones_theorem|Goldstone bosons]], because these correspond to the gauge degrees of freedom and become the longitudinal polarizations of the gauge bosons that become massive. | + | However, there is symmetry breaking when the Higgs field acquires a non-zero vev. It is a global part of the gauge group that gets broken. However, there are no [[theorems:goldstones_theorem|Goldstone bosons]], because these correspond to the gauge degrees of freedom and become the longitudinal polarizations of the gauge bosons that become massive. |
| This is discussed nicely in "Quantum Field Theory - A Modern Perspective" by V. P. Nair at page 268: | This is discussed nicely in "Quantum Field Theory - A Modern Perspective" by V. P. Nair at page 268: | ||
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| <cite>[[https://arxiv.org/abs/cond-mat/0503400|Is electromagnetic gauge invariance spontaneously violated in superconductors?]] by Martin Greiter</cite></blockquote> | <cite>[[https://arxiv.org/abs/cond-mat/0503400|Is electromagnetic gauge invariance spontaneously violated in superconductors?]] by Martin Greiter</cite></blockquote> | ||
| - | The fact that spontaneous breaking of a local symmetry is impossible is the message of [[advanced_notions:elitzur_s_theorem]]. For a gauge symmetry, we have a copy of the symmetry group $G$ at each spacetime point. Thus symmetry breaking would need to happen at each spacetime point individual, i.e. in each zero-dimensional subsystem. A spacetime point is zero-dimensional and there is no symmetry breaking in systems of dimension lower than 2. This is known as the [[advanced_notions:symmetry_breaking:mermin-wagner_theorem|Mermin-Wagner theorem]]. | + | The fact that spontaneous breaking of a local symmetry is impossible is the message of [[theorems:elitzur_s_theorem]]. For a gauge symmetry, we have a copy of the symmetry group $G$ at each spacetime point. Thus symmetry breaking would need to happen at each spacetime point individual, i.e. in each zero-dimensional subsystem. A spacetime point is zero-dimensional and there is no symmetry breaking in systems of dimension lower than 2. This is known as the [[advanced_notions:symmetry_breaking:mermin-wagner_theorem|Mermin-Wagner theorem]]. |
| <blockquote> | <blockquote> | ||
| - | However, strictly speaking a //local gauge// symmetry can //never// be broken because we would want and observable to serve as an order parameter, but all such are necessarily gauge-invariant; this is the content of //[[advanced_notions:elitzur_s_theorem]]//. | + | However, strictly speaking a //local gauge// symmetry can //never// be broken because we would want and observable to serve as an order parameter, but all such are necessarily gauge-invariant; this is the content of //[[theorems:elitzur_s_theorem]]//. |
| <cite>[[https://books.google.de/books?id=LtdqCQAAQBAJ&lpg=PA30&ots=xKAr3CFF-b&dq=banks%20finite%20temperature%20behaviour%20of%20the%20lattice&hl=de&pg=PA9#v=onepage&q&f=false|Classification of topological defects and their relevance to cosmology and elsewhere]] by T.W.B. Kibble</cite> | <cite>[[https://books.google.de/books?id=LtdqCQAAQBAJ&lpg=PA30&ots=xKAr3CFF-b&dq=banks%20finite%20temperature%20behaviour%20of%20the%20lattice&hl=de&pg=PA9#v=onepage&q&f=false|Classification of topological defects and their relevance to cosmology and elsewhere]] by T.W.B. Kibble</cite> | ||
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