Corpus ID: 235694432

Modular operator for null plane algebras in free fields

  title={Modular operator for null plane algebras in free fields},
  author={Vincenzo Morinelli and Yoh Tanimoto and Benedikt Wegener},
We consider the algebras generated by observables in quantum field theory localized in regions in the null plane. For a scalar free field theory, we show that the one-particle structure can be decomposed into a continuous direct integral of lightlike fibres, and the modular operator decomposes accordingly. This implies that a certain form of QNEC is valid in free fields involving the causal completions of half-spaces on the null plane (null cuts). We also compute the relative entropy of null… Expand

Figures from this paper

Modular Nuclearity and Entanglement Entropy
In the framework of Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated to any couple of causally disjoint and distant spacetime regions SA and SB. InExpand
Modular Nuclearity and Entanglement measures
In the framework of Algebraic Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated to any couple of causally disjoint and distant spacetime regions SAExpand


Some remarks on the “null plane development” of a relativistic quantum field theory
We give conditions for the existence of field operators on so-called null planes and discuss some consequences of the necessary restriction of the test function space, concerning Haag's theorem andExpand
The CPT-theorem in two-dimensional theories of local observables
Let ℳ be a von Neumann algebra with cyclic and separating vector Ω, and letU(a) be a continuous unitary representation ofR with positive generator and Ω as fixed point. If these unitaries induce forExpand
A Lattice of Von Neumann Algebras Associated with the Quantum Theory of a Free Bose Field
Von Neumann algebras associated with the normal representation of canonical commutation relations are studied. Corresponding to each subspace of a real Hilbert space (test function space), a vonExpand
Scaling limits of integrable quantum field theories
Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-localExpand
Modular Hamiltonians on the null plane and the Markov property of the vacuum state
We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone.Expand
A general quantum field theory is considered in which the fields are assumed to be operator‐valued tempered distributions. The system of fields may include any number of boson fields and fermionExpand
Modular localization and wigner particles
We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano–Wichmann relations and a representation of the Poincare group on theExpand
On the restriction of quantum fields to a lightlike surface
To treat the front-form Hamiltonian approach to quantum field theory, called light cone quantum field theory, in a mathematically rigorous way, the existence of a well-defined restriction of theExpand
Local modular Hamiltonians from the quantum null energy condition
The vacuum modular Hamiltonian $K$ of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltoninan for more generalExpand
The Current Algebra on the Circle as a Germ of Local Field Theories
Abstract Methods of algebraic quantum field theory are used to classify all field- and observable algebras, whose common germ is the U (1)-current algebra. An elementary way is described to computeExpand