  It has been suggested that major transitions in evolution require the
emergence of novelties, often associated to the cooperative behaviour of
previously existing objects or agents. A key innovation involves the first
cooperative interactions among molecules in a prebiotic biosphere. One of the
simplest scenarios includes two molecular species capable of helping each other
forming a catalytic loop or hypercycle. The second order kinetics of the
hypercycle implies a hyperbolic growth dynamics, capable of overcoming some
selection barriers associated to non-cooperative molecular systems. Moreover,
it has been suggested that molecular replicators might have benefited from a
limited diffusion associated to their attachment to surfaces: evolution and
escape from extinction might have been tied to living on a surface. In this
paper we propose a field theoretical model of the hypercycle involving reaction
and diffusion through the use of a many-body Hamiltonian. This treatment allows
a characterisation of the spatially correlated dynamics of the system, where
the critical dimension is found to be $d_c=2$. We discuss the role of surface
dynamics as a selective advantage for the system's survival.
