17 problems

Let $\pi_0$ and $\pi_T$ denote the vacuum and infravacuum sectors, respectively. The vanishing transition-energy conjecture. The transition energy between the sectors $\pi_0$ and…

A continuous-spin massless representation gives rise, via modular localisation, to a free net $\mathcal O\mapsto\mathcal M_{\mathrm{cont}}(\mathcal O)$. The Reeh–Schlieder conjectu…

In algebraic quantum field theory, let $\mathcal O\longmapsto \mathfrak R(\mathcal O)$ be a net of local von Neumann algebras on a Hilbert space, equipped with the relevant isotony…

Let $4\mathcal{A}(\mathcal{O})4$ be a double cone algebra, and let $4O^{(2)}4$ be the two-dimensional double cone obtained by cutting $4\mathcal{O}4$ with a two-dimensional plane c…

Let $4\mathcal{A}(\mathcal{O})4$ be the algebra of a massive theory associated with a double cone $4\mathcal{O}4$, and let $4\omega_{m=0}4$ denote the conformally invariant vacuum…

An infinite tensor product of full free theories is understood as the field net formed from infinitely many free theories in the construction above. Trivial-sector conjecture. The…

Consider a massive quantum field theory and its holographic projection onto the lightcone horizon. Write the lightcone coordinates as $x_{+}=x^{0}+\left|\vec{x}\right|$ and…

Let a massive quantum field theory be localized in a double cone and let its modular objects define the corresponding modular transformations. The source considers transformations…

Localization entropy area-law conjecture. The restriction of the vacuum state to the local algebra including the collar may have finite entropy for every sufficiently small…

The Galilean and relativistic quantum field theories are distinguished by a deeper algebraic-kinematic selection of special relativity over Galilean kinematics. Structural conjectu…

Let $\{\mathcal{A}(\mathcal{O})\}$ be a Haag–Kastler net on a spacetime $\mathcal{M}$ satisfying axioms (HK1)–(HK4), with (HK2) interpreted as a sharper-than-equal-time commutation…

Essential duality conjecture. In thermal representations of the models under consideration, one should have

Møller extension conjecture. The map ${\cal R}_0$ extends to a Møller $*$-isomorphism

Let $K$ index a family of Möbius covariant nets, and let … be their free product Möbius covariant net. A subnet is a family of von Neumann subalgebras…

The discussion concerns vacuum fluctuations and entanglement in bounded open regions of spacetime, together with the thermal properties of local algebras of observables. The author…

Let the free electromagnetic field determine a Haag–Kastler net $\EuFrak{R}$, and for each sector $z\in {\bf obj\ }Z^{1,\bullet}(\EuFrak{R})$ let $G_z$ denote its gauge group. Triv…

Haag's conjecture. Local gauge groups can be explained within the algebraic formulation similarly to global gauge groups, by allowing a wider class of representations of the observ…