Quantum effects in the renormalization group approach to phase transitions

The renormalization group approach to critical phenomena is developed for quantum mechanical problems with non-commuting operators. Applying the theory to the spin 1 / 2 Ising model with a transverse field Gamma it is found that the critical exponents are those of the Ising model with Gamma =0 if the transition occurs at T>0. However, for transitions at T=0 the critical behaviour of the d-dimensio…