Solving local constraint condition problem in slave particle theory with the BRST quantization

With the Becchi-Rouet-Stora-Tyutin (BRST) quantization of gauge theory, we solve the longstanding difficult problem of the local constraint conditions, i.e. the single occupation of a slave particle per site, in the slave particle theory. This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier lambda(i) which ensures the constraint: in the Hamiltonian formalism of the theory,lambda(i) is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism,lambda(i)(t) becomes time-dependent and plays a role of gauge field. This implies that the redundant degrees of freedom of lambda(i)(t) are introduced and must be removed by the additional constraint, the gauge fixing condition (GFC) partial derivative(t)lambda(i)(t) = 0. In literature, this GFC was missed. We add this GFC and use the BRST quantization of gauge theory for Dirac ' s first-class constraints in the slave particle theory. This GFC endows lambda(i)(t) with dynamics and leads to important physical results. As an example, we study the Hubbard model at half-filling and find that the spinon is gapped in the weak U and the system is indeed a conventional metal, which resolves the paradox that the weak coupling state is a superconductor in the previous slave boson mean field (MF) theory. For the t-J model, we find that the dynamic effect of lambda(i)(t) substantially suppresses the d-wave pairing gap and then the superconducting critical temperature may be lowered at least a factor of one-fifth of the MF value which is of the order of 1000 K. The renormalized T-c is then close to that in cuprates.