Remarks on the physical degrees of freedom in two-dimensional electrodynamics

A simple argument is advanced for how it happens that twodimensional electrodynamics is a theory of massive spinless bosons. (Submitted to Phys. Rev. D. Comments and Addenda) * Work supported by the TJ. S. Atomic Energy Commission. It is well-known that, once the computational dust has settled, two dimensional q;antum electrodynamics (TDED) collapses to a theory of a massive spinless non-interacting Bose field. Sophisticated arguments for why this occurs have been presented by Lowenstein and Swieca. ’ The purpose of this note is to supply a simple way of seeing why it is so. The first observation required is that, in the gauge AJ(x, t) = 0, the interaction reduces to a self-interaction of the charge density via the (two-dimensional) Coulomb potential, 2 j”(x,t) Jdy lx-YI jO(y,t) (1) Next, as is known from work on the Thirrtig model, 3 the free Dirac theory in two dimensions may equivalently be discussed in terms of the associated vector current (2) and the symmetric, traceless, conserved tensor operator constructed from the current, TPV(x,t) = g (j’“, j”l gFvjhjh . That is, H = J dx Too generates the free field equation of motion for $, given the anti-commutator { $ (x,, t) , z,6? (y, t)} = 6(x y), and the definitions Eqs. (2) and (3). The result is not obvious, however, and depends for its demonstration on the operator equation3 i7r 1 .l 5 .o ax $(x, z) = -xj-1 J + 7’ J g 14)