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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 forcesare adequately modeled using helicity particles, it is not known whether CSPscan also mediate long-range forces or what consequences such forces might have.We present sharp evidence for consistent interactions of CSPs with matter: newCSP equations of motion, wavefunctions, and covariant radiation amplitudes. Ina companion paper, we use these results to resolve old puzzles concerning CSPthermodynamics and exhibit a striking correspondence limit where CSP amplitudesapproach helicity-0, 1 or 2 amplitudes.

On the Theory of Continuous-Spin Particles: Wavefunctions and Soft-Factor Scattering Amplitudes