Abstract
Broken symmetry solutions appeared in field theory when Nambu and Jona-Lasinio [1] tried to fashion a theory of strongly interacting particles analogous to the Bardeen, Cooper and Schrieffer [2] theory of superconductivity. The mass of the baryons was supposed to be completely dynamical — a result of spontaneous symmetry breakdown. The mass of the pions (analogs of the collective excitations of superconductivity) turned out to be zero. Soon afterwards Goldstone [3] conjectured that massless particles appear whenever spontaneous symmetry breakdown occurs. Arguments leading to this conclusion were later presented by Goldstone, Salam and Weinberg [4].
This is an abbreviation of a longer paper [12] by the same authors, as presented by Y. Frishman at the V. Internationalen Universitätswochen für Kernphysik, Schladming, 24 February – 9 March 1966
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References and Footnotes
Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961)
J. Bardeen, L. N. Cooper and S. R. Schrieffer, Phys. Rev. 108, 1175 (1957)
J. Goldstone, Nuovo Cim. 19, 154 (1961)
J. Goldstone, A. Salam and S. Weinberg, Phys. Rev. 127, 965 (1962)
S. A. Bludman and A. Klein, Phys. Rev. 131, 2364 (1963)
G. Jona-Lasinio, Nuovo Cim. 34, 1790 (1964)
A. Klein and B. W. Lee, Phys. Rev. Lett. 12, 266 (1964)
P. W. Higgs, Phys. Lett. 12, 132 (1964)
G. S. Guralnik, Phys. Rev. Lett. 13, 295 (1964)
J. Lopuszanski and H. Reeh, Phys. Rev. 140, B926 (1965)
W. Gilbert, Phys. Rev. Lett., 12, 713 (1964)
Y. Frishman and A. Katz, to be published
R. Haag, Nuovo Cim. 25, 287 (1962)
R. F. Streater, Proc. Roy. Soc. 287, 510 (1965)
D. Kastler, D. W. Robinson and A. Swieca, preprint (Univ. of Illinois)
J. Schwinger, Phys. Rev. Lett. 3, 296 (1959)
K. Johnson, Nuclear Physics, 25, 431 (1961)
K. Johnson, Phys. Lett. 5, 253 (1963)
G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964)
R. V. Lange, Phys. Rev. Lett. 14, 3 (1965)
R. F. Streater, Phys. Rev. Lett. 15, 475 (1965)
N. Fuchs (Phys. Rev. Lett. 15, 911 (1965)) gets, as a result of assuming a difference in the two point functions of two fields as spontaneous, that there are “states 101> with momentum and energy zero which however are not Lorentz invariant. His treatment of these 101> appears incorrect because of the points raised in ref.[4] sec. III
A. Katz: “Is the Heisenberg picture better than the Schrödinger picture?”preprint.
The Hamiltonian of the Heisenberg ferromagnet is a spin-spin interaction \( % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaiabg2 % da9iabgkHiTmaaqafabaGaamOsamaaBaaaleaacaWGPbGaamOAaaqa % baaabaGaamyAaiaadQgaaeqaniabggHiLdGcceWGtbGbaSaadaWgaa % WcbaGaamyAaaqabaGcceWGtbGbaSaadaWgaaWcbaGaamOAaaqabaaa % aa!4377! H = - \sum\limits_{ij} {J_{ij} } \vec S_i \vec S_j \) Si being the spin operator associated with the i-th point of the lattice, and Jij are positive, usually assumed to be a constant J > 0 for nearest neighbours and zero otherwise. (See W. Heisenberg, Z. Physik, 49, 619 (1928)). The ground state of this Hamiltonian is obviously a state with all spins pointing in the same direction and as such not rotationally invariant. The fact that the spectrum contains massless excitations is demonstrated in almost every book on solid state physics.
M. Baker and S. L. Glashow, Phys. Rev. 128, 2462 (1962)
Th. A. J. Maris, V. E. Herscovitz and G. Jacob, Nuovo Cim. 34, 946 (1964); a second paper by the same authors is to be published in Nuovo Cim.
R. Arnowitt and S. Deser, Phys. Lett. 13, 256 (1964); Phys. Rev. 138, B712 (1965)
G. S. Guralnik, Preprint (University of Rochester).
A. Katz and Y. Frishman: “Massless Particles rather than spurious States following broken Symmetry”, to be published in Nuovo Cimento.
Y. Frishman and A. Katz, Phys. Rev. Lett. 16, 370 (1966)
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Frishman, Y., Katz, A. (1966). Theory of Spontaneous Symmetry Breakdown and the Appearance of Massless Particles. In: Urban, P. (eds) Elementary Particle Theories. Acta Physica Austriaca, vol 3/1966. Springer, Vienna. https://doi.org/10.1007/978-3-7091-5566-0_5
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