Englert, F.; Brout, R.; Broken Symmetry and the Mass of Gauge Vector Mesons
Phys. Rev. Lett. 13 (1964) 321;
It is of interest to inquire whether gauge vector mesons acquire mass through interaction; by a gauge vector meson we mean a Yang-Mills field associated with the extension of a Lie group from global to local symmetry. The importance of this problem resides in the possibility that strong-interaction physics originates from massive gauge fields related to a system of conserved currents. In this note, we shall show that in certain cases vector mesons do indeed acquire mass when the vacuum is degenerate
with respect to a compact Lie group. Theories with degenerate vacuum (broken symmetry) have been the subject of intensive study since their inception by Namby. A characteristic feature of such theories is the possible existence of zero-mass bosons which tend to restore the symmetry. We shall show that it is precisely these singularities which maintain the gauge invariance of the theory, despite the fact that the vector meson acquires mass. We shall first treat the case where the original
fields are a set of bosons A which transform as a basis for representation of a compact Lie group. This example should be considered as a rather general phenomenological model. As such, we shall not study the particular mechanism by which the symmetry is broken but simply assume that such a mechanism exists. A calculation performed in lowest order perturbation theory indicates that those vector mesons are coupled to currents that "rotate'' the original
vacuum are the ones which acquire mass. We shall then examine a particular model based on chirality invariance which may have a more fundamental significance. Here we begin with a chirality-invariant Lagrangian and introduce both vector and pseudoscalar gauge fields, thereby guaranteeing invariance under both local phase and local 5-phase transformations. In this model the gauge fields themselves may break the 5
invariance leading to a mass for the original Fermi field. We shall show in this case that the pseudovector field acquires mass. In the last paragraph we sketch a simple argument which renders these results reasonable. (Extracted from the introductory part of the paper.).
Related references See also J. Schwinger, Phys. Rev. 125 (1962) 397;
C. N. Yang and R. L. Mills, Phys. Rev. 96 (1954) 191;
J. J. Sakurai, Ann.Phys. 11 (1960) 1;
R. Utiyama, Phys. Rev. 101 (1956) 1597;
Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961) 345;
J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127 (1962) 965;
S. A. Bludman and A. Klein, Phys. Rev. 131 (1963) 2364;
Y. Nambu, Phys. Rev. Lett. 4 (1960) 380;
Example of a field theory with spontaneous symmetry breakdown, no massless goldstone boson, and massive vector bosons.