On the anomalous origin of masses. I

The vacuum energy density $\varepsilon$ is investigated as a function of the bare masses and the coupling constants. The form of the mass dependence of $\varepsilon$ gives indirect information about the possibility or impossibility of the spontaneous formation of mass in an original massless theory: mass can be formed spontaneously only if it is energetically advantageous – that is, when the vacuum energy density decreases with increasing mass. The model of combined weak and electromagnetic interactions of leptons with intermediate bosons is discussed; in this model all the unrenormalized masses vanish. It is shown that the photon is stable against the spontaneous formation of mass, while in the following paper [18] it will be shown that the neutrino is stable and charged leptons are unstable. It is also proved that the second derivative of $\varepsilon$ with respect to any coupling constant (“any” for the case when the interaction contains several terms) is negative, i.e. , the corresponding curve is convex. It is also shown that the “bad” scalar theories ($\lambda\varphi^3,\lambda\varphi^4$ for $\lambda>0$) are stable against the spontaneous formation of mass.