Timeline for tensor product of massless Poincare representations
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 10, 2018 at 11:41 | comment | added | Francois Ziegler | It is consistent. The formula (Barut–Rączka p. 553) assumes positive helicity, includes $M=0$ in the integral, and says nothing about multiplicity. For more details see the quoted papers. | |
| Oct 10, 2018 at 11:20 | comment | added | Arnold Neumaier | @FrancoisZiegler: But massless cases have positive and negative helicity for each J, and even ignoring that, the formula you gave is not consistent with that in Lomont's paper - there is an extra contribution of massless representations with inifinite multiplicity. | |
| Oct 10, 2018 at 10:52 | comment | added | Francois Ziegler | @Arnold No, massive would be $U^{M_1,\,J_1}\otimes U^{M_2,\,J_2}$. | |
| Oct 10, 2018 at 10:50 | comment | added | Arnold Neumaier | @FrancoisZiegler: But this is the massive case, whereas I had asked for the massless case. | |
| Oct 10, 2018 at 10:37 | comment | added | Francois Ziegler | +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, 2018 at 10:21 | vote | accept | Arnold Neumaier | ||
| Oct 10, 2018 at 10:20 | comment | added | Arnold Neumaier | Thanks! There is a second paper by Lomont and Moses that gives a more explicit reduction: Reduction of Reducible Representations of the Infinitesimal Generators of the Proper, Orthochronous, Inhomogeneous Lorentz Group,aip.scitation.org/doi/pdf/10.1063/1.1705287 | |
| Oct 10, 2018 at 9:12 | history | answered | Zurab Silagadze | CC BY-SA 4.0 |