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'''Goldstone modes''' (also known as Nambu-Goldstone bosons)<ref>[http://dx.doi.org/10.1103/PhysRev.122.345 Y. Nambu and G. Jona-Lasinio "Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I", Physical Review '''122''' pp. 345-358 (1961)]</ref>
'''Goldstone modes''' (also known as Goldstone bosons) arise from Goldstone's conjecture; that if there is continuous symmetry transformation under which the Lagrangian is invariant, then either the vacuum state is also invariant under the transformation, or there must exist spinless particles of zero mass.
<ref>[http://dx.doi.org/10.1103/PhysRev.127.965 Jeffrey Goldstone, Abdus Salam and Steven Weinberg "Broken Symmetries", Physical Review '''127''' pp. 965-970 (1962)]</ref> arise from Goldstone's conjecture; that if there is continuous symmetry transformation under which the Lagrangian is invariant, then either the vacuum state is also invariant under the transformation, or there must exist spinless particles of zero mass.
==See also==
==See also==
*[[Mermin-Wagner theorem]]
*[[Mermin-Wagner theorem]]
==References==
==References==
<references/>
#[http://dx.doi.org/10.1103/PhysRev.122.345 Y. Nambu and G. Jona-Lasinio "Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I", Physical Review '''122''' 345-358 (1961)]
;Related reading
#[http://dx.doi.org/10.1103/PhysRev.127.965 Jeffrey Goldstone, Abdus Salam and Steven Weinberg "Broken Symmetries", Physical Review '''127''' 965-970 (1962)]
*[http://dx.doi.org/10.1007/BF01646487  Sidney Coleman "There are no Goldstone bosons in two dimensions", Communications in Mathematical Physics '''31''' pp. 259-264 (1973)]
#[http://dx.doi.org/10.1007/BF01646487  Sidney Coleman "There are no Goldstone bosons in two dimensions", Communications in Mathematical Physics '''31''' pp. 259-264 (1973)]
*[http://dx.doi.org/10.1103/PhysRevLett.108.251602 Haruki Watanabe and Hitoshi Murayama "Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance", Physical Review Letters '''108''' 251602 (2012)]
 
[[category: quantum mechanics]]
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