Related papers: Local Quantum Theory beyond Quantization
In seeking to arrive at a theory of ``quantum gravity'', one faces several choices among alternative approaches. I list some of these ``forks in the road'' and offer reasons for taking one alternative over the other. In particular, I…
The axiomatic formulation of quantum field theory (QFT) of the 1950's in terms of fields defined as operator valued Schwartz distributions is re-examined in the light of subsequent developments. These include, on the physical side, the…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential…
Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional TQFTs from modular categories, we use surgery to derive…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
We construct local, boost covariant boundary QFT nets of von Neumann algebras on the interior of the Lorentz hyperboloid LH = {x^2 - t^2 > R^2, x>0}, in the two-dimensional Minkowski spacetime. Our first construction is canonical, starting…
We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a…
We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
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…
In a Generalised Probabilistic Theory (GPT) equipped additionally with some extra geometric structure we define the morphophoric measurements as those for which the measurement map sending states to distributions of the measurement results…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
Quantum correlations in a physical system are usually studied with respect to a unique (fixed) decomposition of the system into subsystems, without fully exploiting the rich structure of the state-space. Here, we show several examples in…
After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We…
I propose a new mathematical form for the quantum theory of gravity coupled to matter. The motivation is from the connection between CSW TQFT and the Ashtekar variables. I also connect the algebraic structure of TQFT with some thoughts…
We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate"…
We review and develop a mathematical framework for nonlocal quantum field theory (QFT) with a fundamental length. As an instructive example, we reexamine the normal ordered Gaussian function of a free field and find the primitive…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…