Related papers: Feynman geometry
Vacuum structure of a quantum field theory is a crucial property. In theories with extended symmetries, such as supersymmetric gauge theories, the vacuum is typically a continuous manifold, called the vacuum moduli space, parametrized by…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…
Since Einstein's equations $G_{ij} = 8\pi \, G \, T_{ij} \, / c^4 $ relate the metric $g_{ij}$ of spacetime to the energy-momentum tensor $T_{ij}$ which is a quantum field, the metric $g_{ij}$ must be a quantum field. And since the metric…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions…
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on…
Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…
We examine the notion of symmetry in quantum field theory from a fundamental representation theoretic point of view. This leads us to a generalization expressed in terms of quantum groups and braided categories. It also unifies the…
Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a…
We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…
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…
The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…
We introduce an alternative formalization of curved spaces in which the concept of a pointwise affine space, as defined here, replaces that of a manifold. New or modified definitions of familiar notions from differential geometry such as…
We study the behaviour of quantum field theories defined on a surface $S$ as it tends to a null surface $S_n$. In the case of a real, free scalar field theory the above limiting procedure reduces the system to one with a finite number of…
We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class…
A generalisation of Riemannian geometry is considered, based exclusively on the minimal assumptions that the line element $ds$ is a regular function of position and direction and that the distance of every point from itself is equal to…
An alternative model to describe the electronic and thermal properties of quantum dot based on triangle geometry is proposed. The model predicts characteristics and limitations of the system by controlling the magnetic field and…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…