Testing Lorentz violation using propagating UHECRs

Lorentz invariant violation (LIV) test is important for studying modem physics.All the known astrophysical constraints either have a very small examinable parameter space or are only suitable for some special theoretical models. Here, we suggest that it is possible to directly detect the time-delay of ultra-high-energy cosmic-rays (UHECRs). We discuss some difficulties in our method, including the intergalactic magnetic fields. It seems that none of them are crucial, hence this method could give a larger examinable parameter space and a stronger constraint on LIV.