The light-cone gauge without prescriptions

Feynman integrals in the physical light-cone gauge are harder to solve than their covariant counterparts. The difficulty is associated with the presence of unphysical singularities due to the inherent residual gauge freedom in the intermediate boson propagators constrained within this gauge choice. In order to circumvent these non-physical singularities, the headlong approach has always been to call for mathematical devices --- prescriptions --- some successful ones and others not so much so. A more elegant approach is to consider the propagator from its physical point of view, that is, an object obeying basic principles such as causality. Once this fact is realized and carefully taken into account, the crutch of prescriptions can be avoided altogether. An alternative third approach, which for practical computations could dispense with prescriptions as well as prescinding the necessity of careful stepwise watching out of causality would be of great advantage. And this third option is realizable within the context of negative dimensions, or as it has been coined, negative dimensional integration method, NDIM for short.Comment: 9 pages, PTPTeX (included

Feynman integrals with tensorial structure in the negative dimensional integration scheme

Negative dimensional integration method (NDIM) is revealing itself as a very useful technique for computing Feynman integrals, massless and/or massive, covariant and non-covariant alike. Up to now, however, the illustrative calculations done using such method are mostly covariant scalar integrals, without numerator factors. Here we show how those integrals with tensorial structures can also be handled with easiness and in a straightforward manner. However, contrary to the absence of significant features in the usual approach, here the NDIM also allows us to come across surprising unsuspected bonuses. In this line, we present two alternative ways of working out the integrals and illustrate them by taking the easiest Feynman integrals in this category that emerges in the computation of a standard one-loop self-energy diagram. One of the novel and as yet unsuspected bonus is that there are degeneracies in the way one can express the final result for the referred Feynman integral.Comment: 9 pages, revtex, no figure

Negative dimensional approach for scalar two-loop three-point and three-loop two-point integrals

The well-known $D$-dimensional Feynman integrals were shown, by Halliday and Ricotta, to be capable of undergoing analytic continuation into the domain of negative values for the dimension of space-time. Furthermore, this could be identified with Grassmannian integration in positive dimensions. From this possibility follows the concept of negative dimensional integration for loop integrals in field theories. Using this technique, we evaluate three two-loop three-point scalar integrals, with five and six massless propagators, with specific external kinematic configurations (two legs on-shell), and four three-loop two-point scalar integrals. These results are given for arbitrary exponents of propagators and dimension, in Euclidean space, and the particular cases compared to results published in the literature.Comment: 6 pages, 7 figures, Revte

Electron Beam Ion Sources

Electron beam ion sources (EBISs) are ion sources that work based on the principle of electron impact ionization, allowing the production of very highly charged ions. The ions produced can be extracted as a DC ion beam as well as ion pulses of different time structures. In comparison to most of the other known ion sources, EBISs feature ion beams with very good beam emittances and a low energy spread. Furthermore, EBISs are excellent sources of photons (X-rays, ultraviolet, extreme ultraviolet, visible light) from highly charged ions. This chapter gives an overview of EBIS physics, the principle of operation, and the known technical solutions. Using examples, the performance of EBISs as well as their applications in various fields of basic research, technology and medicine are discussed.Comment: 37 pages, contribution to the CAS-CERN Accelerator School: Ion Sources, Senec, Slovakia, 29 May - 8 June 2012, edited by R. Baile

Massless and massive one-loop three-point functions in negative dimensional approach

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time D. Our approach reproduces the known results as well as other solutions as yet unknown in the literature. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories

Infinite Infrared Regularization and a State Space for the Heisenberg Algebra

We present a method for the construction of a Krein space completion for spaces of test functions, equipped with an indefinite inner product induced by a kernel which is more singular than a distribution of finite order. This generalizes a regularization method for infrared singularities in quantum field theory, introduced by G. Morchio and F. Strocchi, to the case of singularites of infinite order. We give conditions for the possibility of this procedure in terms of local differential operators and the Gelfand- Shilov test function spaces, as well as an abstract sufficient condition. As a model case we construct a maximally positive definite state space for the Heisenberg algebra in the presence of an infinite infrared singularity.Comment: 18 pages, typos corrected, journal-ref added, reference adde