We extend a well-known mass-gap equation for pure gluodynamics in global colour models(formulated in equal-time quantization in Coulomb gauge)to one in which gluons are split into two sets,each exhibiting different ma...We extend a well-known mass-gap equation for pure gluodynamics in global colour models(formulated in equal-time quantization in Coulomb gauge)to one in which gluons are split into two sets,each exhibiting different masses.If the theory is SU(N)×SU(M)with gluons in both groups having identical couplings(as suggested by Grand Unification arguments at large scales)it is immediate to see that different masses are generated for each subgroup.This global symmetry is not broken,but the split masses erase accidental symmetries that might be present due to the two couplings being the same at a large scale,such as SU(N×M)or similar.We also numerically explore a couple of low-dimensional examples of simple Lie groups,but in spite of the system of equations having a form that would seem to allow spontaneous symmetry breaking,it is not triggered for these groups whose algebra has no ideal,and the dispersion relations for the various gluons converge to the same form.展开更多
基金supported by the EU under grant 824093(STRONG2020)spanish MICINN under PID2019-108655GBI00/AEI/10.13039/501100011033,PID2019-106080GB-C21 and PRX23/00225(estancias en el extranjero)Univ.Complutense de Madrid under research group 910309 and the IPARCOS institute。
文摘We extend a well-known mass-gap equation for pure gluodynamics in global colour models(formulated in equal-time quantization in Coulomb gauge)to one in which gluons are split into two sets,each exhibiting different masses.If the theory is SU(N)×SU(M)with gluons in both groups having identical couplings(as suggested by Grand Unification arguments at large scales)it is immediate to see that different masses are generated for each subgroup.This global symmetry is not broken,but the split masses erase accidental symmetries that might be present due to the two couplings being the same at a large scale,such as SU(N×M)or similar.We also numerically explore a couple of low-dimensional examples of simple Lie groups,but in spite of the system of equations having a form that would seem to allow spontaneous symmetry breaking,it is not triggered for these groups whose algebra has no ideal,and the dispersion relations for the various gluons converge to the same form.
