Transfer-matrices of coherent state path integrals with the h4- and su(2)-algebra for many-body systems with contact interactions

Spatial transfer-matrices are constructed for 1D su(2)-spin and h4-bosonic many-body systems in external magnetic fields B(x) or potentials V(x). In the case of the spin system, generalized coherent states are applied to derive a path integral which can be reordered according to the spatial position of the generalized coherent state fields. The spatial generator of the transfer-matrix for the spin system consists of a so(3) Laplace operator and a term with the external magnetic field B(x). It is also demonstrated that generalized differential transfer-matrix equations can be obtained for disordered many-body systems if the ensemble-averaged coherent state path integral of the random potentials contains only contact interactions and nearest-neighbour couplings from the kinetic energy.