Related papers: Modular dynamics in diamonds
In this work, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action…
In many gauge theories, the existence of particles in every representation of the gauge group (also known as completeness of the spectrum) is equivalent to the absence of one-form global symmetries. However, this relation does not hold, for…
Global symmetries can be generalised to transformations generated by topological operators, including cases in which the topological operator does not have an inverse. A family of such topological operators are intimately related to…
In this paper, we use the tools of nonabelian duality to formulate and prove a far-reaching generalization of the Stone-von Neumann Theorem to modular representations of actions and coactions of locally compact groups on elementary $…
Let S be the Stone space of a complete, non-atomic Boolean algebra. Let G be a countably infinite group of homeomorphisms of S. Let the action of G on S have a free dense orbit. Then we prove that, on a generic subset of S, the orbit…
Well-defined nonlinear deformations of free quantum fields are introduced as manifestly Poincar\'e invariant scaling and resonance properties of non-dynamical scale models in Minkowski space, instead of introducing nonlinear dynamical…
Recently, we have shown that von Neumann algebras form a model for Selinger and Valiron's quantum lambda calculus. In this paper, we explain our choice of interpretation of the duplicability operator "!" by studying those von Neumann…
We introduce a new formalism of differential operators for a general associative algebra A. It replaces Grothendieck's notion of differential operator on a commutative algebra in such a way that derivations of the commutative algebra are…
Classical $W$-algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel'fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension.…
The Kubo-Ando theory deals with connections for positive bounded operators. On the other hand, in various analysis related to von Neumann algebras it is impossible to avoid unbounded operators. In this article we try to extend a notion of…
We construct the phase space of a spherically symmetric causal diamond in $(d+2)$-dimensional Minkowski spacetime. Utilizing the covariant phase space formalism, we identify the relevant degrees of freedom that localize to the…
We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the…
The Stone-von Neumann Theorem is a fundamental result which unified the competing quantum mechanical models of matrix mechanics and wave mechanics. It's mechanism of proof ultimately involved the study of unitary group representations on a…
We provide a simple and explicit construction of local bulk operators that describe the interior of a black hole in the AdS/CFT correspondence. The existence of these operators is predicated on the assumption that the mapping of CFT…
For a {bounded} non-negative self-adjoint operator acting in a complex, infinite-dimensional, separable Hilbert space H and possessing a dense range R we propose a new approach to characterisation of phenomenon concerning the existence of…
We analyze the moduli space of spontaneously broken N=8 supergravity theories in 4 dimensions with classical Minkowski vacua. We find that all the known classical vacua, as well as the several new ones we construct here, can be connected by…
We study certain dynamical systems which leave invariant an indefinite quadratic form via semigroups or evolution families of complex symmetric Hilbert space operators. In the setting of bounded operators we show that a…
In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and…
We present new one loop calculations that confirm the theorems of Joglekar and Lee on the renormalization of composite operators. We do this by considering physical matrix elements with the operators inserted at non-zero momentum. The…
We use the method of the Lewis-Riesenfeld invariant to analyze the dynamical properties of the Mukhanov-Sasaki Hamiltonian and, following this approach, investigate whether we can obtain possible candidates for initial states in the context…