Würzburg Seminar on Quantum Field Theory and Gravity

The entanglement between momentum modes of a quantum field theory at different scales is not as well studied as its counterpart in real space, despite the natural connection with the Wilsonian idea of integrating out the high-momentum degrees of freedom. In this talk we will elaborate on a novel method to calculate the Rényi and entanglement entropies between slow and fast modes, which is based on the Wilsonian effective action at a given scale.  This method is easily generalized to higher-order or nonperturbative calculations and has the advantage of avoiding matrix diagonalizations of other techniques. Further, we show that the Wilson renormalization group defines a quantum channel acting on the momentum-space density matrices of a quantum field theory. This interpretation of the RG allows us to derive a remarkable property for the vacuum of theories at a fixed point: they have no entanglement between momentum scales. Our result can be interpreted as a consequence of the scale symmetry of such theories and leads to constraints on the form of the ground state and on expectation values of momentum space operators.