Related papers: Entanglement in Algebraic Quantum Field Theories
It was known long ago that quantum theory and general relativity are in sharp conflict in their foundations. Their fundamental inconsistencies render a consistent theory of quantum gravity the most challenging problem in physics. Here we…
We briefly review the current status of the algebraic approach to quantum field theory on globally hyperbolic spacetimes, both axiomatic -- for general field theories, and constructive -- for a linear Klein-Gordon model. We recall the…
We propose a novel framework for the quantum geometry of expectation values over arbitrary sets of operators and establish a link between this geometry and the eigenstates of Hamiltonian families generated by these operators. We show that…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
From the consideration of measuring bipartite mixed states by separable pure states, we introduce algebraic sets in complex projective spaces for bipartite mixed states as the degenerating locus of the measurement. These algebraic sets are…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum…
Under natural conditions (such as split property and geometric modular action of wedge algebras) it is shown that the unitary equivalence class of the net of local (von Neumann) algebras in the vacuum sector associated to double cones with…
The phenomenon of quantum entanglement is explained in a way which is fully consistent with Einstein's Special Theory of Relativity. A subtle flaw is identified in the logic supporting the view that Bell's Inequality precludes all local…
We discuss the scaling of the effective action for the interacting scalar quantum field theory on generic spacetimes with Lorentzian signature and in a generic state (including vacuum and thermal states, if they exist). This is done…
Bell's theorem reveals a profound conflict between quantum mechanics and local realism, a conflict we reinterpret through the modern lens of causal inference. We propose and computationally validate a framework where quantum entanglement…
A mathematically well-defined, manifestly covariant theory of classical and quantum field is given, based on Euclidean Poisson algebras and a generalization of the Ehrenfest equation, which implies the stationary action principle. The…
The essence of a general formulation to accommodate non-equilibrium local states in relativistic quantum field theory is explained from the viewpoint of comparison at a spacetime point between unknown generic states to be characterized as…
The formalism of nonrelativistic quantum physics was originally considered in the context of inertial frames. Here, we report on a more general framework that includes noninertial frames and arbitrarily strong gravitational fields. We…
The temporal Bell inequalities are derived from the assumptions of realism and locality in time. It is shown that quantum mechanics violates these inequalities and thus is in conflict with the two assumptions. This can be used for…
We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute…
We give an introduction for the non-expert to TQFT (Topological Quantum Field Theory), focussing especially on its role in algebraic topology. We compare the Atiyah axioms for TQFT with the Eilenberg Steenrod axioms for homology, give a few…
Equivariant localization theory is a powerful tool that has been extensively used in the past thirty years to elegantly obtain exact integration formulas, in both mathematics and physics. These integration formulas are proved within the…
Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories and quantum foundations whenever external relata are unavailable. In this work, we give a comprehensive and self-contained…
We study the relation between quantum entanglement and electron correlation in quantum chemistry calculations. We prove that the Hartree-Fock (HF) wave function does not violate Bell's inequality, thus is not entangled while the…
This thesis explores Quantum Field Theory (QFT) on curved spacetimes using a geometric Hamiltonian approach to the Schr\"odinger-like representation. In particular it studies the theory of the scalar field described through its…