Quantum renormalization group

The observed IR and the spectator UV particles of a regulated, cutoff quantum field theory are entangled by their interactions; hence, the IR sector can be described by the help of the density matrix only. The tree-level renormalized trajectory is obtained for a self-interacting scalar field theory, containing the mixed state contributions. One needs a sharp cutoff in the momentum space as regulator to realize the true loss of information, caused by massive particles.