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- W2020145558 abstract "The invariance of a theory involving a vector field ${A}_{ensuremath{mu}}(x)$ under local gauge transformations ${A}_{ensuremath{mu}}(x)ensuremath{rightarrow}{A}_{ensuremath{mu}}(x)+{ensuremath{partial}}_{ensuremath{mu}}ensuremath{Lambda}(x)$, etc., for all $c$--number functions $ensuremath{Lambda}(x)$ in some gauge group $mathcal{G}$, does not imply that the theory contains a zero-mass gauge particle. It is shown that what is relevant to the existence of zero-mass excitations is not the existence of $mathcal{G}$ but the presence in $mathcal{G}$ of the simple gauge functions $ensuremath{Lambda}(x)=R(x)ensuremath{equiv}rifmmodecdotelsetextperiodcenteredfi{}x$, ${r}_{ensuremath{mu}}=mathrm{constants}$, under which ${A}_{ensuremath{mu}}(x)ensuremath{rightarrow}{A}_{ensuremath{mu}}(x)+{r}_{ensuremath{mu}}$. If $R(x)ensuremath{in}mathcal{G}$, then the transverse gauge particle propagator has a singularity at zero mass. This result and similar results for the other proper vertex functions are deduced by both structural and functional methods. In conventional Lorentz-gauge four-dimensional QED, $Rensuremath{in}mathcal{G}$ and so the physical photon can be interpreted as a Goldstone boson arising from the spontaneous breakdown of the $R$-transformation invariance. In two-dimensional massless QED (Schwinger model), $Rensuremath{notin}mathcal{G}$ and so there the photon can be (and is) massive. The point is further illustrated in other two-dimensional soluble models and four-dimensional perturbative models." @default.
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- W2020145558 date "1974-12-15" @default.
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- W2020145558 title "Gauge invariance and mass" @default.
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- W2020145558 doi "https://doi.org/10.1103/physrevd.10.4198" @default.
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