  Following Pasterski-Shao-Strominger we construct a new basis of states in the
single-particle Hilbert space of massless particles as a linear combination of
standard Wigner states. Under Lorentz transformation the new basis states
transform in the Unitary Principal Continuous Series representation. These
states are obtained if we consider the little group of a null momentum
\textit{direction} rather than a null momentum. The definition of the states in
terms of the Wigner states makes it easier to study the action of space-time
translation in this basis. We show by taking into account the effect of
space-time translation that \textit{the dynamics of massless particles
described by these states takes place completely on the null-infinity of the
Minkowski space}. We then second quantize the theory in this basis and obtain a
unitary manifestly Poincare invariant (field) theory of free massless particles
living on null-infinity. The null-infinity arises in this case purely
group-theoretically without any reference to bulk space-time. Action of BMS on
massless particles is natural in this picture.
  As a by-product we generalize the conformal primary wave-functions for
massless particles in a way which makes the action of space-time translation
simple. Using these wave-functions we write down a modified Mellin(-Fourier)
transformation of the S-matrix elements. The resulting amplitude is Poincare
covariant. Under Poincare transformation it transforms like products of
primaries of inhomogeneous $SL(2,\mathbb{C})$ ($ISL(2,\mathbb{C})$) inserted at
various points of null-infinity. $ISL(2,\mathbb{C})$ primaries are defined in
the paper.
