Related papers: Classical and quantum structuralism
In hybrid classical-quantum theories, the dynamics of the classical system induce the classicality of the quantum system, meaning that such models do not necessarily require a measurement postulate to describe probabilistic measurement…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
We show that an orthogonal basis for a finite-dimensional Hilbert space can be equivalently characterised as a commutative dagger-Frobenius monoid in the category FdHilb, which has finite-dimensional Hilbert spaces as objects and continuous…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
The quantum nature of gravity remains experimentally unverified, despite recent proposals to probe it using tabletop experiments such as gravity-mediated entanglement schemes. In parallel, consistent formulations of classical--quantum…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
Classical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to interpret perceived quantum dynamics as classical. This…
It is well known that classical and quantum theories carry distinct types of representations, each type of representation corresponding to possible values of generalized charges in the classical or quantum context. This paper demonstrates a…
Conceptual analogies among statistical mechanics and classical (or quantum) mechanics often appeared in the literature. For classical two-body mean field models, an analogy develops into a proper identification between the free energy of…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
Dirac's Poisson-bracket-to-commutator analogy for the transition from classical to quantum mechanics assures that for many systems, the classical and quantum systems share the same algebraic structure. The quantum side of the analogy…
Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
Quantum and classical mechanics share a common algebraic formalism which is expressed naturally in the language of category theory. A third realization of this formalism is the so-called hyperbolic quantum mechanics where split-complex…