Related papers: Scalar Quantum Field Theory on Fractals
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…
We extend our analysis for scalar fields in a Robertson-Walker metric to the electromagnetic field and Dirac fields by the method of invariants. The issue of the relation between conformal properties and particle production is re-examined…
We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension.…
We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d-dimensional coordinates (where d is less than D). By a…
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
A simple theoretical model of scalar fields in one spatial dimension with internal symmetry is considered. Assuming the existence of localized classical field configurations, the Schr\"{o}dinger picture is used to describe their quantum…
In this work we develop a re-formulation of quantum field theory through the more general weighted Lorentz invariant measures that the definition of quantum fields allows; this approach provides finite answers for the long-live problems of…
We propose a model for a power-counting renormalizable field theory living in a fractal spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The system flows, even in a classical sense, from an ultraviolet…
This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the…
We discuss scalar quantum field theories in a Lorentz-invariant three-dimensional noncommutative space-time. We first analyze the one-loop diagrams of the two-point functions, and show that the non-planar diagrams are finite and have…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive…
Fock representations are constructed for a free scalar field in the closed and quasi-Euclidean isotropic cosmological models. Invariance of their cyclic vector (vacuum) under isometries and the correspondence principle single out a class of…
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to…
We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…
We develop worldline formulations of covariant fracton gauge theories. These are a one-parameter family of gauge theories of a rank-two symmetric tensor field, invariant under a scalar gauge transformation involving a double derivative.…
Recentely, it is shown that the quantum effects of matter determine the conformal degree of freedom of the space-time metric. This was done in the framework of a scalar-tensor theory with one scalar field. A point with that theory is that…
Considering the Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) metric and the Einstein scalar field system as an underlying gravitational model to construct fractional cosmological models has interesting implications in both classical…