  The most general massless particles allowed by Poincare-invariance are
"continuous-spin" particles (CSPs) characterized by a scale \rho, which at
\rho=0 reduce to familiar helicity particles. Though known long-range forces
are adequately modeled using helicity particles, it is not known whether CSPs
can also mediate long-range forces or what consequences such forces might have.
We present sharp evidence for consistent interactions of CSPs with matter: new
CSP equations of motion, wavefunctions, and covariant radiation amplitudes. In
a companion paper, we use these results to resolve old puzzles concerning CSP
thermodynamics and exhibit a striking correspondence limit where CSP amplitudes
approach helicity-0, 1 or 2 amplitudes.
