tensor product of massless Poincare representations

Consider two massless representations of the connected Poincare group $$ISO_0(1,3)$$ with helicities $$s$$ and $$t$$. What is the decomposition of their tensor product into irreducibles?

Massless representations with helicity s are defined in Wigner's classification of irreducible unitary representations of the connected Poincare group, the semidirect product $$ISO_0(1,3)$$ of the connected Lorentz group $$SO_0(1,3)$$ and the 4-dimensional translation group.

• What is "massless"? what is "helicity"? representation means irreducible complex finite-dimensional representation? does "$ISO_0(3,1)$" mean the same as "$SO_0(3,1)$"? (SO stands for standard orthogonal, no idea about ISO).
– YCor
Oct 10 '18 at 8:10
• @YCor I means inhomogeneous, the semidirect product with the translation group. massless representations with helicity s are defined in Wigner's classification of irreducible unitary representations of the Poincare group. Oct 10 '18 at 9:33
• @YCor Infinite-dimensional unitary representations on a Hilbert space. Oct 10 '18 at 10:15

• +1. Also Moussa–Stora (1965), Schaaf (1970), Barut–Rączka (1977, p. 553): $$U^{0,\,J_1}\otimes U^{0,\,J_2}\cong\int_0^\infty dM\sum_{J=|J_1-J_2|}^{\infty} \oplus U^{M,\,J}.$$ Oct 10 '18 at 10:37
• @Arnold No, massive would be $U^{M_1,\,J_1}\otimes U^{M_2,\,J_2}$. Oct 10 '18 at 10:52