  A calculational framework is proposed for phylogenetics, using nonlocal
quantum field theories in hypercubic geometry. Quadratic terms in the
Hamiltonian give the underlying Markov dynamics, while higher degree terms
represent branching events. The spatial dimension L is the number of leaves of
the evolutionary tree under consideration. Momentum conservation modulo
${\mathbb Z}_{2}^{times L}$ in $L \leftarrow 1$ scattering corresponds to tree
edge labelling using binary L-vectors. The bilocal quadratic term allows for
momentum-dependent rate constants - only the tree(s) compatible with selected
nonzero edge rates contribute to the branching probability distribution.
Applications to models of evolutionary branching processes are discussed.
