Related papers: Quantum Reference Frames from Top-Down Crossed Pro…
A common feature of the extended phase space of gauge theory, the crossed product of quantum theory, and quantum reference frames (QRFs) is the adjoining of degrees of freedom followed by a constraining procedure for the resulting total…
A significant step towards a rigorous understanding of perturbative gravitational entropy was recently achieved by a series of works showing that a proper accounting of gauge invariance and observer degrees of freedom converts the Type III…
A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational…
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized…
A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The…
A reference frame F is described by the element g of the Poincare' group P which connects F with a given fixed frame F_0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have…
Recent work has highlighted the importance of crossed products in correctly elucidating the operator algebraic approach to quantum field theories. In the gravitational context, the crossed product simultaneously promotes von Neumann…
Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics…
Quantum reference frames are needed in quantum theory for much the same reasons that reference frames are in classical theories: to manifest invariance in line with fundamental relativity principles and to provide a basis for the definition…
In the context of constrained quantum mechanics, reference systems are used to construct relational observables that are invariant under the action of the symmetry group. Upon measurement of a relational observable, the reference system…
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical…
Inclusions and extensions lie at the heart of physics and mathematics. The most relevant kind of inclusion in quantum systems is that of a von Neumann subalgebra, which is the focus of this work. We propose an object intrinsic to a given…
Starting from an arbitrary endomorphism \alpha of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\alpha) but also on the choice of an ideal…
Let G be a group and let P be a subsemigroup of G. In order to describe the crossed product of a C*-algebra A by an action of P by unital endomorphisms we find that we must extend the action to the whole group G. This extension fits into a…
One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. In this work, we explore these notions in the context of quantum reference frame (QRF) covariance, in…
Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference…
We determine the quantum states and measurements that optimize the accessible information in a reference frame alignment protocol associated with the groups U(1), corresponding to a phase reference, and $\mathbb{Z}_M$, the cyclic group of…
We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…
Let P be a semigroup that admits an embedding into a group G. Assume that the embedding satisfies a certain Toeplitz condition and that the Baum-Connes conjecture holds for G. We prove a formula describing the K- theory of the reduced…
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame.…