Related papers: Localized type I algebras and their entropy in qua…
A scalar field in the ground state, when partially hidden from observation by a spherical boundary, acquires entanglement entropy $S$ proportional to the area of the surface. This area law is well established in flat space, where it follows…
This chapter addresses the question of quantum entanglement in disordered chains, focusing on the von-Neumann and R\'enyi entropies for three important classes of random systems: Anderson localized, infinite randomness criticality, and…
Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed…
Two coalgebra structures are used in quantum field theory. The first one is the coalgebra part of a Hopf algebra leading to deformation quantization. The second one is a co-module co-algebra over the first Hopf algebra and it is used to…
We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalised condensate states, involving sums over arbitrarily refined graphs (dual to 3d triangulations). The construction relies…
In the rational cohomology of a 1-connected space a structure of $C_{\infty}$-algebra is constructed and it is shown that this object determines the rational homotopy type
In this paper we study various convolution-type algebras associated with a locally compact quantum group from cohomological and geometrical points of view. The quantum group duality endows the space of trace class operators over a locally…
In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements $x_{1}, x_{2},..., x_{k}$ of such an algebra $L$ there is finite-dimensional subalgebra $A$ which…
Various limit-free formulas are given for the computation of the algebraic and the topological entropy, respectively in the settings of endomorphisms of locally finite discrete groups and of continuous endomorphisms of totally disconnected…
We formulate gauge theories based on Leibniz(-Loday) algebras and uncover their underlying mathematical structure. Various special cases have been developed in the context of gauged supergravity and exceptional field theory. These are based…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
Quantum entanglement in 3 spatial dimensions is studied in systems with physical boundaries when an entangling surface intersects the boundary. We show that there are universal logarithmic boundary terms in the entanglement R\'{e}nyi…
In this paper, we provide a complete classification of 2-dimensional endo-commutative straight algebras of type I over any field. An endo-commutative algebra is a non-associative algebra in which the square mapping preserves multiplication.…
We establish two conditions equivalent to coamenability for type I locally compact quantum groups. The first condition is concerned with the spectra of certain convolution operators on the space…
The uncertainty principle has been established within the framework of locally compact quantum groups in recent years. This paper demonstrates that entropic uncertainty relations can be strengthened under localizations on discrete quantum…
On a manifold with boundary, the constraint algebra of general relativity may acquire a central extension, which can be computed using covariant phase space techniques. When the boundary is a (local) Killing horizon, a natural set of…
We study the apparent tension between locality and unitarity for symmetries in quantum field theory. This emerges in the context of categorical symmetries where symmetry operators are generically non-invertible. We argue that locality…
Gauge/gravity duality posits an equivalence between certain strongly coupled quantum field theories and theories of gravity with negative cosmological constant in a higher number of spacetime dimensions. The map between the degrees of…
Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as…
We give an account of the current state of the approch to quantum field theory via Hopf algebras and Hochschild cohomology. We emphasize the versatility and mathematical foundation of this algebraic structure, and collect algebraic…