Related papers: Toy Models for Quantum Field Theory
In this article, we continue our investigation on the role of non-commutativity in quantum theory. Using the method explained in "On non-commutativity in quantum theory (I): from classical to quantum probability", we analyze two toy models…
In the present work a general frame for the scattering theory of local, relativistic dipole quantum fields is presented and some models of interacting dipole fields are considered, i.e. local, relativistic quantum fields with indefinite…
We investigate the strengths and limitations of the Spekkens toy model, which is a local hidden variable model that replicates many important properties of quantum dynamics. First, we present a set of five axioms that fully encapsulate…
We construct examples of Functorial Quantum Field Theories in the Riemannian setting by quantizing free massive bosons.
The quantization of a massive spin $1/2$ field that satisfies the Klein-Gordon equation is studied. The framework is consistent, provided it is formulated as a pseudo-hermitian quantum field theory by the redefinition of the field dual and…
Toy models are highly idealized and deliberately simplified models that retain only the essential features of a system in order to explore specific theoretical questions. Long used in physics and other sciences, they have recently begun to…
The Hilbert space structure of classical field theory is proposed as a general theoretical framework to model human cognitive processes which do not often follow classical (Bayesian) probability principles. This leads to an extension of the…
A few recent innovations of applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly…
We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties, instead, locality is inferred from the…
In this paper, we consider a high-curvature limit of the varying fundamental constants toy model in which both the value of the speed of light and the value of the gravitational constant are related to the values of the two non-minimally…
We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles, which are bosons. The interaction…
We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the…
A number of writers have been attracted to the idea that some of the peculiarities of quantum theory might be manifestations of 'backward' or 'retro' causality, underlying the quantum description. This idea has been explored in the…
Electron spin-dependent chemical reactions in proteins, often discussed under the 'radical-pair mechanism', remain the leading microscopic proposal for magnetic field sensing in biology. Yet the essential physics is often obscured by the…
In a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalisation Group in order to employ it ultimately for canonical quantum gravity. The proposal was successfully tested for free scalar fields and thus…
Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field-theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich…
This note is an introduction to methods of construction for Hilbert space realizations of relativistic quantum physics. The realizations satisfy a revision to Wightman's functional analytic axioms and exhibit interaction in physical…
The geometry of two infinitely long lines of mass moving in a fixed circular orbit is considered as a toy model for the inspiral of a binary system of compact objects due to gravitational radiation. The two Killing fields in the toy model…
Explicit construction of local observable algebras in quasi-Hermitian quantum theories is derived in both the tensor product model of locality and in models of free fermions. The latter construction is applied to several cases of a…
We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science.…