Symmetry properties and dynamics in gauge theories with scalar fields

V. A. Matveev ; A. N. Tavkhelidze ; M. E. Shaposhnikov

Teoretičeskaâ i matematičeskaâ fizika, Tome 59 (1984) no. 3, pp. 323-344

Résumé

The possibility of spontaneous breaking of the local and global symmetries in gauge theories with scalar fields is discussed (as usual, spontaneous symmetry breaking is taken to mean that $[Q,H]=0$, $Q | \text{vac} \rangle\neq 0$, where $H$ is the Hamiltonian and $Q$ is the generator of a gauge transformation). It is shown that the standard assumption $\langle \varphi \rangle\neq 0$ in gauge theories does not mean that the symmetry is spontaneously broken. It is shown that under certain conditions the theory can be reformulated in terms of gauge-invariant (“colorless”) local fields. An example is given of a theory of eleetroweak interactions in which the occurrence of short-range forces transmitted by massive vector bosons is entirely due to the nonvanishing of the gauge-invariant order parameter of the vacuum expectation vatue $\langle\varphi^+\varphi\rangle=\eta$ (of a scalar condensate) and is not due to spontaneous breaking of the weak isospin. The mass spectrum of particles in non-Abelian gauge theories is analyzed in its dependence on the magnitude and sign of the scalar condensate. It is shown that for $\eta\gg\Lambda^2$ ($\Lambda$ is the reciprocal of the confinement radius) the spectrum contains only colorless states, and the weak coupling regime is realized, so that physical quantities can be calculated by perturbation theory. In the ease of a small $(|\eta|\ll\Lambda^2)$ or negahve $(\eta\sim-\Lambda^2)$ scalar condensate, the strong coupling regime is realized in the system. In QCD with massless scalar quarks in the ease $\eta\sim-\Lambda^2$ the possible existence of a new family of hadrons with masses of the order of several tens of GeV and containing scalars is predicted.