Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach

Implicit Regularization is a 4-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional Regularization does not apply. In the present contribution we extend the method to handle infrared divergences as well. We show that the essential steps which rendered Implicit Regularization adequate in the case of ultraviolet divergences have their counterpart for infrared ones. Moreover we show that a new scale appears, typically an infrared scale which is completely independent of the ultraviolet one. Examples are given.Comment: 9 pages, version to appear in Mod. Phys. Lett.

Charge Influence On Mini Black Hole's Cross Section

In this work we study the electric charge effect on the cross section production of charged mini black holes (MBH) in accelerators. We analyze the charged MBH solution using the {\it fat brane} approximation in the context of the ADD model. The maximum charge-mass ratio condition for the existence of a horizon radius is discussed. We show that the electric charge causes a decrease in this radius and, consequently, in the cross section. This reduction is negligible for protons and light ions but can be important for heavy ions.Comment: 4 pages, 0 figure. To be published in Int. J. Mod. Phys. D

Scalar Casimir Effect on a D-dimensional Einstein Static Universe

We compute the renormalised energy momentum tensor of a free scalar field coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU), RxS^n, with arbitrary low energy effective operators (up to mass dimension n+1). A generic class of regulators is used, together with the Abel-Plana formula, leading to a manifestly regulator independent result. The general structure of the divergences is analysed to show that all the gravitational couplings (not just the cosmological constant) are renormalised for an arbitrary regulator. Various commonly used methods (damping function, point-splitting, momentum cut-off and zeta function) are shown to, effectively, belong to the given class. The final results depend strongly on the parity of n. A detailed analytical and numerical analysis is performed for the behaviours of the renormalised energy density and a quantity `sigma' which determines if the strong energy condition holds for the `quantum fluid'. We briefly discuss the quantum fluid back-reaction problem, via the higher dimensional Friedmann and Raychaudhuri equations, observe that equilibrium radii exist and unveil the possibility of a `Casimir stabilisation of Einstein Static Universes'.Comment: 37 pages, 15 figures, v2: minor changes in sections 1, 2.5, 3 and 4; version published in CQ

A dynamic approach to teaching LSS at universities

Alongside the European Students of Industrial Engineering and Management (ESTIEM) a team of students from the University of Minho, in cooperation with a corporate partner, developed a free and scalable Lean Six Sigma (LSS) Green-Belt level course for Engineering students. Purpose: The authors aim to depict how free access to LSS Green-Belt knowledge before graduation can positively impact both engineering education and the students when in real-life projects. The purpose is not to build on existing literature, but to provide a practical teaching structure. Methodology: The authors chose to follow the hypothetico-deductive method which consists of formulating hypotheses and comparing them with real-life brought up from their personal experiences while teaching the course. Findings: This case study found a positive impact on both the students responsible for facilitating the training sessions, as well as the ones receiving practical and theoretical knowledge. With more than 60 course graduates, this model is generating positive results in growing awareness for LSS methods. Practical implications: This paper describes a practical application of a novel approach to teaching LSS in Universities along the obstacles surpassed to design it, blending it in the course curricula. It aims to foster similar implementations in other institutions. Originality: A teaching system built with students for students is scalable, low-cost, and highly engaging. Its deployment not only shows how it is possible to advance education by blending an existing LSS course structure but also how students can greatly benefit from a deeper LSS knowledge before their graduation.(undefined