I am wondering if the masslessness of photons is due to the local gauge invariance of $u(1)$-gauge fields. The reason why I consider about this question is that I remember that the Proca field is not locally $u(1)$-invariant. How do I prove this explicitly in field theory?
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5Related: http://physics.stackexchange.com/q/4700/2451 and links therein. – Qmechanic Aug 17 '15 at 05:39
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Hi professor Qmechanic. Is professor Motl's answer also related with the mass gap of Yang-Mills fields? – Xiaoyi Jing Aug 17 '15 at 20:28