Search results for "Feynman diagram"
showing 10 items of 91 documents
From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography
2016
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman–Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman–Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the de…
K-means Clustering to Study How Student Reasoning Lines Can Be Modified by a Learning Activity Based on Feynman’s Unifying Approach
2017
Background:Research in Science Education has shown that often students need to learn how to identify differences and similarities between descriptive and explicative models. The development and use of explicative skills in the field of thermal science has always been a difficult objective to reach. A way to develop analogical reasoning is to use in Science Education unifying conceptual frameworks.Material and methods:A questionnaire containing six open-ended questions on thermally activated phenomena was administered to the students before instruction. A second one, similar but focused on different physical content was administered after instruction. Responses were analysed using k-means Cl…
Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams
2000
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams. Currently, large effort is devoted to the search for closed expressions of loop integrals, written whenever possible in terms of known - often hypergeometric-type - functions. In this work, the scalar three-point function is re-evaluated by means of generalized hypergeometric functions of two variables. Finally, use is made of the connection between such Appell functions and dilogarithms coming from a previous investigation, to recover well-known results.
A model for the γN → ππN reaction
1995
We have studied the γN→ππN reaction using a model which includes N, Δ(1232), N*(1440) and N*(1520) intermediate baryonic states and the ρ-meson as intermediate ππ resonance. The model reproduces fairly well experimental cross sections below E γ = 800 MeV and invariant-mass distributions even at higher energies. One of the interesting findings of the study is that the γ N →N*(1520) → Δπ process is very important and interferes strongly with the dominant Δ-Kroll-Ruderman term to produce the experimental peak of the cross section.
Second quantization and atomic spontaneous emission inside one-dimensional photonic crystals via a quasinormal-modes approach
2004
An extension of the second quantization scheme based on the quasinormal-modes theory to one-dimensional photonic band gap (PBG) structures is discussed. Such structures, treated as double open optical cavities, are studied as part of a compound closed system including the electromagnetic radiative external bath. The electromagnetic field inside the photonic crystal is successfully represented by a new class of modes called quasinormal modes. Starting from this representation we introduce the Feynman's propagator to calculate the decay rate of a dipole inside a PBG structure, related to the density of modes, in the presence of the vacuum fluctuations outside the one-dimensional cavity.
Ideas in the History of Nano/Miniaturization and (Quantum) Simulators: Feynman, Education and Research Reorientation in Translational Science
2015
Cultural history of nanominiaturization, computing, quantum computing and simulating is necessary to comprehend human character and place it in the whole of living beings. Ideas in the history of physics by Feynman, etc. are valued by the questions that generate. A series of questions, answers and hypothesis introduces the nature of the history of nanominiaturization, providing facts. Nanotechnology adds a third dimension to the periodic table of the elements. Thinking about computers was useful. It must do with learning computers possibilities and physics potential. Provisional conclusions follow. (1) Nature (space–time) is not classical but discrete; quantization is a different kind of ma…
Matter Dependence of the Four-Loop Cusp Anomalous Dimension
2019
We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop light-like cusp anomalous dimension in QCD, with $n_f$ fermion and $n_s$ scalar flavours. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end we first identify a set of integrals whose integrands have a dlog form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis of the soft and collinear regions of loop integration and build linear combinations of integrals w…
Weight Systems from Feynman Diagrams
1996
We find that the overall UV divergences of a renormalizable field theory with trivalent vertices fulfil a four-term relation. They thus come close to establish a weight system. This provides a first explanation of the recent successful association of renormalization theory with knot theory.
Differential equations for Feynman integrals beyond multiple polylogarithms
2017
Differential equations are a powerful tool to tackle Feynman integrals. In this talk we discuss recent progress, where the method of differential equations has been applied to Feynman integrals which are not expressible in terms of multiple polylogarithms.
JaxoDraw: A graphical user interface for drawing Feynman diagrams
2003
JaxoDraw is a Feynman graph plotting tool written in Java. It has a complete graphical user interface that allows all actions to be carried out via mouse click-and-drag operations in a WYSIWYG fashion. Graphs may be exported to postscript/EPS format and can be saved in XML files to be used in later sessions. One of the main features of JaxoDraw is the possibility to produce LaTeX code that may be used to generate graphics output, thus combining the powers of TeX/LaTeX with those of a modern day drawing program. With JaxoDraw it becomes possible to draw even complicated Feynman diagrams with just a few mouse clicks, without the knowledge of any programming language.