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These lecture notes are based on a six-hour series of lectures given at the XVII Modave summer school in mathematical physics, aimed at Ph.D.
H. Watanabe, “Counting Rules of Nambu–Goldstone Modes,” Ann. Rev. Condensed Matter Phys
1904
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1907
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1909
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R. Ruzziconi, “Asymptotic Symmetries in the Gauge Fixing Approach and the BMS Group,” PoS
1910
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P. W. Anderson, “Coherent Excited States in the Theory of Superconductivity: Gauge Invariance and the Meissner Effect,” Phys. Rev
1958
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Y. Nambu, “Quasiparticles and Gauge Invariance in the Theory of Superconductivity,” Phys. Rev
1960
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Y. Nambu and G. Jona-Lasinio, “Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. 1.,” Phys. Rev
1961
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J. Goldstone, “Field Theories with Superconductor Solutions,” Nuovo Cim
1961
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S. S. Shinozaki, “Specific heat of yttrium iron garnet from 1.5° to 4.2°k,” Phys. Rev
1961
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J. Goldstone, A. Salam, and S. Weinberg, “Broken Symmetries,” Phys. Rev
1962
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J. S. Schwinger, “Gauge Invariance and Mass,” Phys. Rev
1962
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S. A. Bludman and A. Klein, “Broken Symmetries and Massless Particles,” Phys. Rev
1963
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P. W. Anderson, “Plasmons, Gauge Invariance, and Mass,” Phys. Rev
1963
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A. Klein and B. W. Lee, “Does Spontaneous Breakdown of Symmetry Imply Zero-Mass Particles?,” Phys. Rev. Lett
1964
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W. Gilbert, “Broken Symmetries and Massless Particles,” Phys. Rev. Lett
1964
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P. W. Higgs, “Broken symmetries, massless particles and gauge fields,” Phys. Lett
1964
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G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, “Global Conservation Laws and Massless Particles,” Phys. Rev. Lett
1964
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P. W. Higgs, “Broken Symmetries and the Masses of Gauge Bosons,” Phys. Rev. Lett
1964
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F. Englert and R. Brout, “Broken Symmetry and the Mass of Gauge Vector Mesons,” Phys. Rev. Lett
1964
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R. V. Lange, “Goldstone Theorem in Nonrelativistic Theories,” Phys. Rev. Lett
1965
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R. F. Streater, “Generalized Goldstone Theorem,” Phys. Rev. Lett
1965
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E. Fabri and L. E. Picasso, “Quantum field theory and approximate symmetries,” Physical review letters
1966
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R. V. Lange, “Nonrelativistic Theorem Analogous to the Goldstone Theorem,” Phys. Rev
1966
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D. Kastler, D. W. Robinson, and A. Swieca, “Conserved currents and associated symmetries; Goldstone’s theorem,” Commun. Math. Phys
1966
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Y. Frishman and A. Katz, “Corollaries of the goldstone theorem,” Phys. Rev. Lett
1966
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N. D. Mermin and H. Wagner, “Absence of ferromagnetism or antiferromagnetism in one-dimensional or two-dimensional isotropic Heisenberg models,” Phys. Rev. Lett
1966
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S. Weinberg, “Dynamical approach to current algebra,” Phys. Rev. Lett
1967
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J. A. Cronin, “Phenomenological model of strong and weak interactions in chiral u ( 3 ) × u ( 3 ) u(3)\times u(3) ,” Phys. Rev
1967
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J. S. Schwinger, “Chiral dynamics,” Phys. Lett. B
1967
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J. Wess and B. Zumino, “Lagrangian method for chiral symmetries,” Phys. Rev
1967
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P. C. Hohenberg, “Existence of Long-Range Order in One and Two Dimensions,” Phys. Rev
1967
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G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, “Broken symmetries and the Goldstone theorem,” Adv. Part. Phys
1968
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M. Gell-Mann, R. J. Oakes, and B. Renner, “Behavior of current divergences under SU(3) x SU(3),” Phys. Rev
1968
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S. R. Coleman, J. Wess, and B. Zumino, “Structure of phenomenological Lagrangians. 1.,” Phys. Rev
1969
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C. G. Callan, Jr., S. R. Coleman, J. Wess, and B. Zumino, “Structure of phenomenological Lagrangians. 2.,” Phys. Rev
1969
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A. Salam and J. A. Strathdee, “Nonlinear realizations. 1: The Role of Goldstone bosons,” Phys. Rev
1969
Cited alongside, same era.
A. Salam and J. A. Strathdee, “Nonlinear realizations. 2. Conformal symmetry,” Phys. Rev
1969
Cited alongside, same era.
C. J. Isham, A. Salam, and J. A. Strathdee, “Nonlinear realizations of space-time symmetries. Scalar and tensor gravity,” Annals Phys
1971
Cited alongside, same era.
J. Wess and B. Zumino, “Consequences of anomalous Ward identities,” Phys. Lett. B
1971
Cited alongside, same era.
S. Weinberg, “Approximate symmetries and pseudoGoldstone bosons,” Phys. Rev. Lett
1972
Cited alongside, same era.
S. R. Coleman, “There are no Goldstone bosons in two-dimensions,” Commun. Math. Phys
I. Low and A. V. Manohar, “Spontaneously broken space-time symmetries and Goldstone’s theorem,” Phys. Rev. Lett
2002
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Y. Nambu, “Spontaneous Breaking of Lie and Current Algebras,” J. Statist. Phys
2004
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N. J. Evans and J. P. Shock, “Chiral dynamics from AdS space,” Phys. Rev. D
2004
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Cambridge University Press, 6, 2005
S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations · 2005
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T. Brauner, “Goldstone boson counting in linear sigma models with chemical potential,” Phys. Rev. D
2005
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T. Brauner, “Spontaneous symmetry breaking in the linear sigma model at finite chemical potential: One-loop corrections,” Phys. Rev. D
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1973
Cited alongside, same era.
D. V. Volkov, “Phenomenological Lagrangians,” Fiz. Elem. Chast. Atom. Yadra
1973
Cited alongside, same era.
S. R. Coleman, R. Jackiw, and H. D. Politzer, “Spontaneous Symmetry Breaking in the O(N) Model for Large N*,” Phys. Rev. D
1974
Cited alongside, same era.
D. J. Gross and A. Neveu, “Dynamical Symmetry Breaking in Asymptotically Free Field Theories,” Phys. Rev. D
1974
Cited alongside, same era.
PhD thesis, In X-th winter school of theoretical physics in Karpacz, Poland, 1974
V. I. Ogievetsky, Nonlinear realizations of internal and space-time symmetries · 1974
Cited alongside, same era.
S. Elitzur, “Impossibility of Spontaneously Breaking Local Symmetries,” Phys. Rev. D
1975
Cited alongside, same era.
H. Georgi and A. Pais, “Vacuum Symmetry and the PseudoGoldstone Phenomenon,” Phys. Rev. D
1975
Cited alongside, same era.
2006
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R. Penco, “An Introduction to Effective Field Theories,” arXiv:2006.16285 [hep-th]
2006
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T. Brauner, “Goldstone bosons in presence of charge density,” Phys. Rev. D
2007
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2010
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I. N. McArthur, “Nonlinear realizations of symmetries and unphysical Goldstone bosons,” JHEP
2010
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2011
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2012
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2012
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A. Nicolis and F. Piazza, “Spontaneous Symmetry Probing,” JHEP
2012
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Cambridge University Press, 8, 2013
S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications · 2013
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Y. Hidaka, “Counting rule for Nambu-Goldstone modes in nonrelativistic systems,” Phys. Rev. Lett
2013
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2013
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2013
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H. Watanabe, T. Brauner, and H. Murayama, “Massive Nambu-Goldstone Bosons,” Phys. Rev. Lett
2013
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H. Watanabe and H. Murayama, “Redundancies in Nambu-Goldstone Bosons,” Phys. Rev. Lett
2013
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2014
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H. Watanabe and H. Murayama, “Effective Lagrangian for Nonrelativistic Systems,” Phys. Rev. X
2014
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2014
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2014
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2015
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PhD thesis, UC Berkeley, 2015
H. Watanabe, Spontaneous Symmetry Breaking in Nonrelativistic Systems · 2015
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2015
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M. Nitta and D. A. Takahashi, “Quasi-Nambu-Goldstone modes in nonrelativistic systems,” Phys. Rev. D
2015
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S. Endlich, A. Nicolis, and R. Penco, “Spontaneously broken mass,” JHEP
2015
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R. Argurio, A. Marzolla, A. Mezzalira, and D. Musso, “Analytic pseudo-Goldstone bosons,” JHEP
2016
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2017
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2017
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D. Musso, “Simplest phonons and pseudo-phonons in field theory,” Eur. Phys. J. C
2019
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V. Lekeu, “Modave lecture notes: two useful topics in Lie algebras,” PoS
2021
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