Inertial Mass and Vacuum Fluctuations in Quantum Field Theory

Motivated by recent works on the origin of inertial mass, we revisit the relationship between the mass of charged particles and zero-point electromagnetic fields. To this end we first introduce a simple model comprising a scalar field coupled to stochastic or thermal electromagnetic fields. Then we check if it is possible to start from a zero bare mass in the renormalization process and express the finite physical mass in terms of a cut-off. In scalar QED this is indeed possible, except for the problem that all conceivable cut-offs correspond to very large masses. For spin-1/2 particles (QED with fermions) the relation between bare mass and renormalized mass is compatible with the observed electron mass and with a finite cut-off, but only if the bare mass is not zero; for any value of the cut-off the radiative correction is very small. PACS: 03.20.+i; 03.50.-k; 03.65.-w; 03.70.+k 95.30 Sf In modern physics each elementary particle is characterised by a few parameters which define essentially its symmetry properties. Mass and spin define the behavior of the particle wavefunction with respect to spacetime (Poincaré) transformations; electric charge, barion or lepton number etc. define its behavior with respect to gauge transformations. These same parameters also determine the (gravitational or gauge) interactions of the particle. Unlike spin and charge, mass is a continuous parameter which spans several magnitude orders in a table of the known elementary particles. In spite of several attempts, there is no generally accepted way of expressing these masses, or at least their scale, in terms of fundamental constants. In the standard model particles acquire a mass thanks to the Higgs field, but the reproduction of the observed spectrum is only possible by choosing a different coupling for each particle. Inertia in itself is not really explained by quantum field theory; rather, it is incorporated in its formalism as an automatic consequence of the spacetime invariance of the classical Lagrangians. In turn, these Lagrangians are essentially a generalization of Newtonian dynamics. In the equations for quantum fields, like in the wave equations for single particles or in their classical limits, mass appears as a free parameter which can take zero or positive values. e-mail address: [email protected]