# Time-reversal transformation for two-component bosonic models

Consider a two-component bosonic model $\mathcal{H}=-t\sum_{i\sigma}{b_{i\sigma}b_{i+1\sigma}^\dagger}+h.c. +\sum_{i\sigma\sigma^\prime}U_{\sigma\sigma^\prime}n_{i\sigma}n_{i\sigma^\prime}$. Here $\sigma,\sigma^\prime$ aretwo the pseudo spin, they can take $\uparrow,\downarrow$. I want to know how to define the time-reversal transformation for such two-component bosonic models. Is the definition same as fermion models?

• It is probably not the same as for fermion models (where time reversal flips the spin) – why should time reversal change the kind of boson (though if the kinds of bosons are some effective particles like right movers and left movers it probably will). I guess the correct time reversal will be independent time reversal for both boson components (but I can be wrong). – Sebastian Riese Aug 26 '15 at 20:56
• An answer can be found at physicsoverflow.org/33696 – Arnold Neumaier Oct 20 '15 at 11:16