The Bisognano–Wichmann Property for Asymptotically Complete Massless QFT

Abstract

We prove the Bisognano–Wichmann property for asymptotically complete Haag–Kastler theories of massless particles. These particles should either be scalar or appear as a direct sum of two opposite integer helicities, thus, e.g., photons are covered. The argument relies on a modularity condition formulated recently by one of us (VM) and on the Buchholz’ scattering theory of massless particles.

Scaling Limits of Lattice Quantum Fields by Wavelets

“…In addition, as the Bisognano-Wichmann property (the Lorentz boosts are given by the modular group of the wedge algebra with respect to the vacuum [6]) follows in the continuum from general structural assumptions (cf. [26,60]), it would be interesting to understand what the modular groups of the lattice algebras are, and how the Bisognano-Wichmann property in the continuum is restored [54].…”

A family of non-modular covariant AQFTs

“…The BW property has been verified for large number of models (see e.g. [DM20,Mu01,BGL93]) and applied in various ways with feedback both for mathematics and for physics. For recent developments concerning entropy of QFT's we refer to [LW22, W18, Lo19, Xu20, LMo20, CLRR22] and for some new constructions exploiting geometric symmetries and modular theory to [LMPR19,MR20].…”

Scaling limits of lattice quantum fields by wavelets

“…But, the modular operator ∆ A(W 1 ),Ω also formally encapsulates the density matrix of the thermal state ω |A(W 1 ) . It is well known that (6.10) holds in any theory generated by Wightman fields [6] and it can also be derived from more general structural assumptions [60,25]. On the other hand, for a fixed state and a growing sequence of von Neumann algebras, the modular groups of the union can be approximated by the modular group of the subalgebras [53,Lemma 3].…”