A note on path integral formulism of $Z_{2}$ slave-spin representation   of Hubbard model
  This is a note on the derivation of path integral formulism for $Z_{2}$ slave-spin representation of Hubbard model and may be helpful for further study in related works. We are rather happy to receive any comments and other discussions are welcome. 
Yin Zhong, Hong-Gang Luo
cond-mat.str-el cond-mat.mes-hall hep-th