相关论文: Projective Limits of State Spaces III. Toy-Models

By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…

We map Spekkens' toy model to a quantum mechanics defined over the finite field $\mathbb{F}_5$. This allows us to define arbitrary linear combinations of the epistemic states in the model. For Spekkens' elementary system with only $2^2=4$…

In order to better understand a complex theory like quantum mechanics, it is sometimes useful to take a step back and create alternative theories, with more intuitive foundations, and examine which features of quantum mechanics can be…

Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…

Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…

We show that the Feynman path integral together with the Schr\"odinger representation gives rise to a rigorous and functorial quantization scheme for linear and affine field theories. Since our target framework is the general boundary…

We present a uniform framework for the treatment of a large class of toy models of quantum theory. Specifically, we will be interested in theories of wavefunctions valued in commutative involutive semirings, and which give rise to some…

The linearization of semiclassical theories of gravity is investigated in a toy model, consisting of a quantum scalar field in interaction with a second classical scalar field which plays the role of a classical background. This toy model…

Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…

I construct lowest-energy representations of non-centrally extended algebras of Noether symmetries, including diffeomorphisms and reparametrizations of the observer's trajectory. This may be viewed as a new scheme for quantization. First…

We provide two mathematical descriptions of Spekkens's toy qubit theory, an inductively one in terms of a small set of generators, as well as an explicit closed form description. It is a subcategory MSpek of the category of finite sets,…

We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…

We explore the features of gravity in its quantum regime in a mathematically rigorous way by carrying out the classical and quantum formulations of some two-Killing symmetry reductions of general relativity which admit an exact…

An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external…

The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…

We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…

Colored tensor models generalize matrix models in arbitrary dimensions yielding a statistical theory of random higher dimensional topological spaces. They admit a 1/N expansion dominated by graphs of spherical topology. The simplest tensor…

We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the…

Can quantum theory be seen as a special case of a more general probabilistic theory, similarly as classical theory is a special case of the quantum one? We study here the class of generalized probabilistic theories defined by the order of…

Quantum dynamics of the collective mode and individual particles on a ring is studied as the simplest model of projective quantum measurement. In this model, the collective mode measures an individual single quantum system. The heart of the…