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New Positive Energy Theorems in Quantum Field Theory

I review the definition of the relative modular operators in quantum field theory from a heuristic and information-theoretic point of view. I work out a few examples in conformal field theories. A special role is played by the states that correspond to the action of stress tensors on the vacuum state. I argue how and why thinking in terms of the relative modular operator in the recent years has led (and is likely to lead) to proving new generalized positive energy theorems in quantum field theory.