  Reactor physics aims at studying the neutron population in a reactor core
under the influence of feedback mechanisms, such as the Doppler temperature
effect. Numerical schemes to calculate macroscopic properties emerging from
such coupled stochastic systems however require to define intermediate
quantities (e.g. the temperature field), which are bridging the gap between the
stochastic neutron field and the deterministic feedback. By interpreting the
branching random walk of neutrons in fissile media under the influence of a
feedback mechanism as a directed percolation process and by leveraging on the
statistical field theory of birth death processes, we will build a stochastic
model of neutron transport theory and of reactor physics. The critical
exponents of this model, combined to the analysis of the resulting field
equation involving a fractional Laplacian will show that the critical diffusion
equation cannot adequately describe the spatial distribution of the neutron
population and shifts instead to a critical super-diffusion equation. The
analysis of this equation will reveal that non-negligible departure from mean
field behavior might develop in reactor cores, questioning the attainable
accuracy of the numerical schemes currently used by the nuclear industry.
