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 a regulator to realize the true loss of information caused by massive particles.

Figure 1

An $\mathcal{O}({\varphi }^{+3}{\varphi }^{-5})$ contribution to the right-hand side of Eq. (28) which couples the time axes by the help of a fourth and sixth order vertex. The two vertices are connected by a dashed line, standing for $D^{(k)+-}$.