Related papers: Physical model of dimensional regularization
Using Dimensional Regularization (DR) for some two-point functions of a prototype Non-Comutative (NC) \phi^4 scalar theory in 4-dimensions, we explictly analyze, to one-loop, the IR and UV divergences of non-planar diagrams having quadratic…
We consider an extension of the ordinary four dimensional Minkowski space by introducing additional dimensions which have their own Lorentz transformation. Particles can transform in a different way under each Lorentz group. We show that…
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz…
A `novel' pure theory of Einstein-Gauss-Bonnet gravity in four-spacetime dimensions can be constructed by rescaling the Gauss-Bonnet coupling constant, seemingly eluding Lovelock's theorem. Recently, however, the well-posedness of this…
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…
On the basis of the results of some experiments dealing with the violation of Local Lorentz Invariance (LLI) and on the formalism of the Deformed Special Relativity (DSR), we examine the connections between the local geometrical structure…
Conventional wisdom states that Newton's force law implies only four non-compact dimensions. We demonstrate that this is not necessarily true in the presence of a non-factorizable background geometry. The specific example we study is a…
We consider compactifications of ${\cal M}$-theory to four-dimensional Minkowski space on seven-dimensional non-compact manifolds. These compactifications include a warp factor which is non-constant due to the presence of sources coming…
There is no known fundamental reason to demand as a cosmological initial condition that the bulk possess an SO(3,1) isometry. On the contrary, one expects bulk curvature terms that violate the SO(3,1) isometry at early epochs, leading to a…
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a…
Non-integer dimensions are commonplace in quantum field theories (QFTs) through dimensional regularization. In particular this affects angular calculations involving dot products. The structure of these rises from the generally accepted…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
In an extension of speculations that physical space-time is a fractal which might itself be embedded in a high-dimensional continuum, it is hypothesized to "compensate" for local variations of the fractal dimension by instead varying the…
The self-force problem---which asks how self-interaction affects a body's motion---has been poorly studied for spacetime dimensions $d \neq 4$. We remedy this for all $d \geq 3$ by nonperturbatively constructing momenta such that forces and…
Using the recently introduced parametric representation of non-commutative quantum field theory, we implement here the dimensional regularization and renormalization of the vulcanized $\Phi^{\star 4}_4$ model on the Moyal space.
A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity --…
Revisiting Einstein's gravitational theory, we build a five-dimensional braneworld. Within this framework, one announces the appearance of symmetric and asymmetric domain walls. Furthermore, it examines the emergent four-dimensional gravity…
On the basis of the relativistic symmetry of Minkowski space, we derive a Lorentz invariant equation for a spread electron. This equation slightly differs from the Dirac equation and includes additional terms originating from the spread of…
The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…