Feynman Diagrams for Beginners
Kumericki, Kresimir
2016-01-01
We give a short introduction to Feynman diagrams, with many exercises. Text is targeted at students who had little or no prior exposure to quantum field theory. We present condensed description of single-particle Dirac equation, free quantum fields and construction of Feynman amplitude using Feynman diagrams. As an example, we give a detailed calculation of cross-section for annihilation of electron and positron into a muon pair. We also show how such calculations are done with the aid of computer.
Feynman diagram drawing made easy
Baillargeon, Marc; Nogueira, P.
1997-02-01
We present a drawing package optimised for Feynman diagrams. These can be constructed interactively with a mouse-driven graphical interface or from a script file, more suitable to work with a diagram generator. It provides most features encountered in Feynman diagrams and allows to modify every part of a diagram after its creation. Special attention has been paid to obtain a high quality printout as easily as possible. This package is written in Tcl/Tk and in C.
The Genesis of Feynman Diagrams
Wuthrich, Adrian
2011-01-01
In a detailed reconstruction of the genesis of Feynman diagrams the author reveals that their development was constantly driven by the attempt to resolve fundamental problems concerning the uninterpretable infinities that arose in quantum as well as classical theories of electrodynamic phenomena. Accordingly, as a comparison with the graphical representations that were in use before Feynman diagrams shows, the resulting theory of quantum electrodynamics, featuring Feynman diagrams, differed significantly from earlier versions of the theory in the way in which the relevant phenomena were concep
Scattering equations and Feynman diagrams
Baadsgaard, Christian; Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-09-01
We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in φ 3-theory. We also discuss the generalization to general scalar field theories with φ p interactions, corresponding to polygonal graphs involving vertices of order p. Finally, we describe how the same graph-theoretic language can be used to provide the precise link between individual Feynman diagrams and string theory integrands.
Scattering Equations and Feynman Diagrams
Baadsgaard, Christian; Bourjaily, Jacob L; Damgaard, Poul H
2015-01-01
We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in $\\phi^3$-theory. We also discuss the generalization to general scalar field theories with $\\phi^p$ interactions, corresponding to polygonal graphs involving vertices of order $p$. Finally, we describe how the same graph-theoretic language can be used to provide the precise link between individual Feynman diagrams and string theory integrands.
Particles, Feynman Diagrams and All That
Daniel, Michael
2006-01-01
Quantum fields are introduced in order to give students an accurate qualitative understanding of the origin of Feynman diagrams as representations of particle interactions. Elementary diagrams are combined to produce diagrams representing the main features of the Standard Model.
Geometrical splitting and reduction of Feynman diagrams
Davydychev, Andrei I.
2016-10-01
A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how these results can be used to reduce the number of variables in the occurring functions.
CERN. Geneva
2013-01-01
For decades the central theoretical tool for computing scattering amplitudes has been the Feynman diagram. However, Feynman diagrams are just too slow, even on fast computers, to be able to go beyond the leading order in QCD, for complicated events with many jets of hadrons in the final state. Such events are produced copiously at the LHC, and constitute formidable backgrounds to many searches for new physics. Over the past few years, alternative methods that go beyond ...
Spin wave Feynman diagram vertex computation package
Price, Alexander; Javernick, Philip; Datta, Trinanjan
Spin wave theory is a well-established theoretical technique that can correctly predict the physical behavior of ordered magnetic states. However, computing the effects of an interacting spin wave theory incorporating magnons involve a laborious by hand derivation of Feynman diagram vertices. The process is tedious and time consuming. Hence, to improve productivity and have another means to check the analytical calculations, we have devised a Feynman Diagram Vertex Computation package. In this talk, we will describe our research group's effort to implement a Mathematica based symbolic Feynman diagram vertex computation package that computes spin wave vertices. Utilizing the non-commutative algebra package NCAlgebra as an add-on to Mathematica, symbolic expressions for the Feynman diagram vertices of a Heisenberg quantum antiferromagnet are obtained. Our existing code reproduces the well-known expressions of a nearest neighbor square lattice Heisenberg model. We also discuss the case of a triangular lattice Heisenberg model where non collinear terms contribute to the vertex interactions.
Geometrical approach to the evaluation of multileg Feynman diagrams
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Davydychev, A.I. [Department of Physics, University of Mainz, Mainz (Germany); Delbourgo, R. [Physics Department, University of Tasmania, Hobart, Tasmania (Australia)
1998-10-01
A connection between one-loop N-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (author)
On critical exponents without Feynman diagrams
Sen, Kallol; Sinha, Aninda
2016-11-01
In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov’s, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the O(n) model at the Wilson-Fisher fixed point in 4-ɛ dimensions up to O({ɛ }2). AS dedicates this work to the loving memory of his mother.
On critical exponents without Feynman diagrams
Sen, Kallol
2015-01-01
In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov's, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the $O(n)$ model at the Wilson-Fisher fixed point in $4-\\epsilon$ dimensions up to $O(\\epsilon^2)$.
Fun with higher-loop Feynman diagrams
Luthe, Thomas; Schröder, York
2016-10-01
We review recent progress that we have achieved in evaluating the class of fully massive vacuum integrals at five loops. After discussing topics that arise in classification, evaluation and algorithmic codification of this specific set of Feynman integrals, we present some selected new results for their expansions around 4 — 2ε dimensions.
Gravitational Lensing of the CMB: a Feynman Diagram Approach
Jenkins, A.E.; Manohar, A.V.; Waalewijn, W.J.; Yadav, A.P.S.
2014-01-01
We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB) in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS). We study the Hu-Okamoto quadratic estimator for extr
Electrodynamic metaphors: communicating particle physics with Feynman diagrams
Directory of Open Access Journals (Sweden)
Pietroni Massimo
2002-03-01
Full Text Available The aim of this project is to communicate the basic laws of particle physics with Feynman diagrams - visual tools which represent elementary particle processes. They were originally developed as a code to be used by physicists and are still used today for calculations and elaborations of theoretical nature. The technical and mathematical rules of Feynman diagrams are obviously the exclusive concern of physicists, but on a pictorial level they can help to popularize many concepts, ranging from matter and the antimatter; the creation, destruction and transformation of particles; the role of ‘virtual’ particles in interactions; the conservation laws, symmetries, etc. Unlike the metaphors often used to describe the microcosm, these graphic representations provide an unequivocal translation of the physical content of the underlying quantum theory. As such they are perfect metaphors, not misleading constructions. A brief introduction on Feynman diagrams will be followed by the practical realization of this project, which will be carried out with the help of an experiment based on three-dimensional manipulable objects. The Feynman rules are expressed in terms of mechanical constraints on the possible conjuctions among the various elements of the experiment. The final part of the project will present the results of this experiment, which has been conducted among high-school students.
Algorithmic calculation of two-loop Feynman diagrams
Fleischer, J; Fleischer, J; Tarasov, O V
1995-01-01
In a recent paper \\cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original diagram by differentiation and putting the external momenta equal to zero. It was demonstrated that by a certain conformal mapping and subsequent resummation by means of Pad\\'{e} approximants it is possible to obtain high precision numerical values of the Feynman integrals in the whole cut plane. The real problem in this approach is the calculation of the Taylor coefficients for the arbitrary mass case. Since their analytic evaluation by means of CA packages uses enormous CPU and yields very lengthy expressions, we develop an algorithm with the aim to set up a FORTRAN package for their numerical evaluation. This development is guided by the possibilities offered by the formulae manipulating language FORM \\cite{FORM}.
jQuery.Feyn: Drawing Feynman Diagrams with SVG
Pan, Zan
2013-01-01
jQuery.Feyn is a tool for drawing Feynman diagrams with Scalable Vector Graphics (SVG), written in JavaScript and runs in modern browsers. It features predefined propagator styles, vertex types, and symbols. Math formulae can be included as external graphics, or typeset with TeX through MathJax library. The generated SVG code can be easily modified to make fine adjustments and conveniently transferred using copy-and-paste.
Some remarks on non-planar Feynman diagrams
Energy Technology Data Exchange (ETDEWEB)
Bielas, Krzysztof; Dubovyk, Ievgen; Gluza, Janusz [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2013-12-15
Two criteria for planarity of a Feynman diagram upon its propagators (momentum ows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can planarize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.
Pictures and pedagogy: The role of diagrams in Feynman's early lectures
Gross, Ari
2012-08-01
This paper aims to give a substantive account of how Feynman used diagrams in the first lectures in which he explained his new approach to quantum electrodynamics. By critically examining unpublished lecture notes, Feynman's use and interpretation of both "Feynman diagrams" and other visual representations will be illuminated. This paper will discuss how the morphology of Feynman's early diagrams were determined by both highly contextual issues, which molded his images to local needs and particular physical characterizations, and an overarching common diagrammatic style, which facilitated Feynman's movement between different diagrams despite their divergent forms and significance.
Resistance of Feynman diagrams and the percolation backbone dimension.
Janssen, H K; Stenull, O; Oerding, K
1999-06-01
We present an alternative view of Feynman diagrams for the field theory of random resistor networks, in which the diagrams are interpreted as being resistor networks themselves. This simplifies the field theory considerably as we demonstrate by calculating the fractal dimension D(B) of the percolation backbone to three loop order. Using renormalization group methods we obtain D(B)=2+epsilon/21-172epsilon(2)/9261+2epsilon(3)[-74 639+22 680zeta(3)]/4 084 101, where epsilon=6-d with d being the spatial dimension and zeta(3)=1.202 057... .
Bubble diagram through the Symmetries of Feynman Integrals method
Kol, Barak
2016-01-01
The Symmetries of Feynman Integrals method (SFI) associates a natural Lie group with any diagram, depending only on its topology. The group acts on parameter space and the method determines the integral's dependence within group orbits. This paper analyzes the bubble diagram, namely the 1-loop propagator diagram, through the SFI method. This is the first diagram with external legs to be analyzed within SFI, and the method is generalized to include this case. The set of differential equation is obtained. In order to solve it the set is transformed into partial invariants variables. The equations are integrated to reproduce the integral's value. This value is interpreted in terms of triangle geometry partially inspired by earlier papers.
Generalized internal multiple imaging (GIMI) using Feynman-like diagrams
Zuberi, M. A. H.
2014-05-19
Single scattering events recorded in surface seismic data do not fully illuminate the subsurface structure, especially if it is complicated. In such cases, multiple internal scatterings (internal multiples) can help improve the illumination. We devise a generalized internal multiple imaging (GIMI) procedure that maps internal multiple energy to their true location with a relatively mild addition to the computational cost. GIMI theory relies heavily on seismic interferometry, which often involves cumbersome algebra, especially when one is dealing with high-order terms in the perturbation series. To make the derivations, and inference of the results easier, we introduce Feynman-like diagrams to represent different terms of the perturbation series (solution to the Lippman–Schwinger equation). The rules we define for the diagrams allow operations like convolution and cross-correlation in the series to be compressed in diagram form. The application of the theory to a double scattering example demonstrates the power of the method.
The diamond rule for multi-loop Feynman diagrams
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Ruijl, B., E-mail: benrl@nikhef.nl [Nikhef Theory Group, Science Park 105, 1098 XG Amsterdam (Netherlands); Leiden University, Niels Bohrweg 1, 2333 CA Leiden (Netherlands); Ueda, T., E-mail: tueda@nikhef.nl [Nikhef Theory Group, Science Park 105, 1098 XG Amsterdam (Netherlands); Vermaseren, J.A.M., E-mail: t68@nikhef.nl [Nikhef Theory Group, Science Park 105, 1098 XG Amsterdam (Netherlands)
2015-06-30
An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce an extensible, multi-loop version of the triangle rule, which we refer to as the diamond rule. Such a structure appears frequently in higher-loop calculations. We derive an explicit solution for the recursion, which prevents spurious poles in intermediate steps of the computations. Applications for massless propagator type diagrams at three, four, and five loops are discussed.
The diamond rule for multi-loop Feynman diagrams
Directory of Open Access Journals (Sweden)
B. Ruijl
2015-06-01
Full Text Available An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce an extensible, multi-loop version of the triangle rule, which we refer to as the diamond rule. Such a structure appears frequently in higher-loop calculations. We derive an explicit solution for the recursion, which prevents spurious poles in intermediate steps of the computations. Applications for massless propagator type diagrams at three, four, and five loops are discussed.
Gravitational lensing of the CMB: A Feynman diagram approach
Energy Technology Data Exchange (ETDEWEB)
Jenkins, Elizabeth E.; Manohar, Aneesh V. [Department of Physics, University of California at San Diego, La Jolla, CA 92093 (United States); Waalewijn, Wouter J. [Nikhef, Theory Group, Science Park 105, 1098 XG, Amsterdam (Netherlands); ITFA, University of Amsterdam, Science Park 904, 1018 XE, Amsterdam (Netherlands); Yadav, Amit P.S., E-mail: ayadav@physics.ucsd.edu [Department of Physics, University of California at San Diego, La Jolla, CA 92093 (United States)
2014-09-07
We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB) in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS). We study the Hu–Okamoto quadratic estimator for extracting lensing from the CMB and derive the noise of the estimator up to O(ϕ{sup 4}) in the lensing potential ϕ. By identifying the diagrams responsible for the previously noted large O(ϕ{sup 4}) term, we conclude that the lensing expansion does not break down. The convergence can be significantly improved by a reorganization of the ϕ expansion. Our approach makes it simple to obtain expressions for quadratic estimators based on any CMB channel, including many previously unexplored cases. We briefly discuss other applications to cosmology of this diagrammatic approach, such as distortions of the CMB due to patchy reionization, or due to Faraday rotation from primordial axion fields/.
Gravitational lensing of the CMB: A Feynman diagram approach
Directory of Open Access Journals (Sweden)
Elizabeth E. Jenkins
2014-09-01
Full Text Available We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS. We study the Hu–Okamoto quadratic estimator for extracting lensing from the CMB and derive the noise of the estimator up to O(ϕ4 in the lensing potential ϕ. By identifying the diagrams responsible for the previously noted large O(ϕ4 term, we conclude that the lensing expansion does not break down. The convergence can be significantly improved by a reorganization of the ϕ expansion. Our approach makes it simple to obtain expressions for quadratic estimators based on any CMB channel, including many previously unexplored cases. We briefly discuss other applications to cosmology of this diagrammatic approach, such as distortions of the CMB due to patchy reionization, or due to Faraday rotation from primordial axion fields.
Massless scalar Feynman diagrams: five loops and beyond
Broadhurst, David J
2016-01-01
Several powerful techniques for evaluating massless scalar Feynman diagrams are developed, viz: the solution of recurrence relations to evaluate diagrams with arbitrary numbers of loops in $n=4-2\\omega$ dimensions; the discovery and use of symmetry properties to restrict and compute Taylor series in $\\omega$; the reduction of triple sums over Chebyshev polynomials to products of Riemann zeta functions; the exploitation of conformal invariance to avoid four-dimensional Racah coefficients. As an example of the power of these techniques we evaluate all of the 216 diagrams, with 5 loops or less, which give finite contributions of order $1/k^2$ or $1/k^4$ to a propagator of momentum $k$ in massless four-dimensional scalar field theories. Remarkably, only 5 basic numbers are encountered: $\\zeta(3)$, $\\zeta(5)$, $\\zeta(7)$, $\\zeta(9)$ and the value of the most symmetrical diagram, which is calculated to 14 significant figures. It is conceivable that these are the only irrationals appearing in 6-loop beta functions. ...
ALOHA: Automatic libraries of helicity amplitudes for Feynman diagram computations
de Aquino, Priscila; Link, William; Maltoni, Fabio; Mattelaer, Olivier; Stelzer, Tim
2012-10-01
We present an application that automatically writes the HELAS (HELicity Amplitude Subroutines) library corresponding to the Feynman rules of any quantum field theory Lagrangian. The code is written in Python and takes the Universal FeynRules Output (UFO) as an input. From this input it produces the complete set of routines, wave-functions and amplitudes, that are needed for the computation of Feynman diagrams at leading as well as at higher orders. The representation is language independent and currently it can output routines in Fortran, C++, and Python. A few sample applications implemented in the MADGRAPH 5 framework are presented. Program summary Program title: ALOHA Catalogue identifier: AEMS_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: http://www.opensource.org/licenses/UoI-NCSA.php No. of lines in distributed program, including test data, etc.: 6094320 No. of bytes in distributed program, including test data, etc.: 7479819 Distribution format: tar.gz Programming language: Python2.6 Computer: 32/64 bit Operating system: Linux/Mac/Windows RAM: 512 Mbytes Classification: 4.4, 11.6 Nature of problem: An effcient numerical evaluation of a squared matrix element can be done with the help of the helicity routines implemented in the HELAS library [1]. This static library contains a limited number of helicity functions and is therefore not always able to provide the needed routine in the presence of an arbitrary interaction. This program provides a way to automatically create the corresponding routines for any given model. Solution method: ALOHA takes the Feynman rules associated to the vertex obtained from the model information (in the UFO format [2]), and multiplies it by the different wavefunctions or propagators. As a result the analytical expression of the helicity routines is obtained. Subsequently, this expression is
Energy Technology Data Exchange (ETDEWEB)
Kalmykov, Mikhail Yu.; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2012-05-15
We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equation can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master-integrals.
A Table of Third and Fourth Order Feynman Diagrams of the Interacting Fermion Green's Function
Mathar, R J
2005-01-01
The Feynman diagrams of the Green's function expansion of fermions interacting with a non-relativistic 2-body interaction are displayed in first, second and third order of the interaction as 2, 10 and 74 diagrams, respectively. A name convention for the diagrams is proposed and then used to tabulate the 706 diagrams of fourth order. The Hartree-Fock approximation summons up 2, 8, 40 and 224 of them, respectively.
Drawing theories apart the dispersion of Feynman diagrams in postwar physics
Kaiser, David
2005-01-01
Winner of the 2007 Pfizer Prize from the History of Science Society. Feynman diagrams have revolutionized nearly every aspect of theoretical physics since the middle of the twentieth century. Introduced by the American physicist Richard Feynman (1918-88) soon after World War II as a means of simplifying lengthy calculations in quantum electrodynamics, they soon gained adherents in many branches of the discipline. Yet as new physicists adopted the tiny line drawings, they also adapted the diagrams and introduced their own interpretations. Drawing Theories Apart traces how generations of young theorists learned to frame their research in terms of the diagrams—and how both the diagrams and their users were molded in the process.Drawing on rich archival materials, interviews, and more than five hundred scientific articles from the period, Drawing Theories Apart uses the Feynman diagrams as a means to explore the development of American postwar physics. By focusing on the ways young physicists learned new calcul...
New results for a two-loop massless propagator-type Feynman diagram
Kotikov, A V
2016-01-01
We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this diagram in terms of ${}_3F_2$-hypergeometric functions of argument $-1$ and $1$, respectively. We also derive new representations for this diagram which may be of importance in practical calculations.
Fermions, Gauge Theories, and the Sinc Function Representation for Feynman Diagrams
Petrov, D; Guralnik, G S; Hahn, S; Wang, W M; Petrov, Dmitri; Easther, Richard; Guralnik, Gerald; Hahn, Stephen; Wang, Wei-Mun
2001-01-01
We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc function representation for the propagators of spin-1/2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed us to derive the Sinc function representation for scalar field Feynman integrals are shared by fields with non-zero spin. We then investigate the application of the Sinc function representation to simple QED diagrams, including first order corrections to the propagators and the vertex.
Wheeler-DeWitt equation and Feynman diagrams
Barvinsky, A O
1998-01-01
We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the conventional Feynman diagrammatic technique involving graviton loops and vertices. It also reveals explicitly the back reaction effects of quantized matter and graviton vacuum polarization. This provides an explicit correspondence between the frameworks of canonical and covariant quantum gravity in the semiclassical limit.
Wheeler-DeWitt equation and Feynman diagrams
Barvinsky, Andrei O.; Kiefer, Claus
1998-08-01
We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the Feynman diagrammatic technique involving graviton loops and vertices. It also reveals explicitly the back-reaction effects of quantized matter and graviton vacuum polarization. This provides an explicit correspondence between the frameworks of canonical and covariant quantum gravity in the semiclassical limit.
Teaching Electron--Positron--Photon Interactions with Hands-on Feynman Diagrams
Kontokostas, George; Kalkanis, George
2013-01-01
Feynman diagrams are introduced in many physics textbooks, such as those by Alonso and Finn and Serway, and their use in physics education has been discussed by various authors. They have an appealing simplicity and can give insight into events in the microworld. Yet students often do not understand their significance and often cannot combine the…
Appell functions and the scalar one-loop three-point integrals in Feynman diagrams
Energy Technology Data Exchange (ETDEWEB)
Cabral-Rosetti, L G [Departamento de Posgrado, Centro Interdisciplinario de Investigacion y Docencia en Educacion Tecnica (CIIDET), Av. Universidad 282 Pte., Col. Centro, A. Postal 752, C.P. 76000, Santiago de Queretaro, Qro. (Mexico); Sanchis-Lozano, M A [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, 46100 Burjassot, Valencia (Spain)
2006-05-15
The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms coming from a previous investigation. Special cases are obtained for particular values of internal masses and external momenta.
Pascolini, A.; Pietroni, M.
2002-01-01
We report on an educational project in particle physics based on Feynman diagrams. By dropping the mathematical aspect of the method and keeping just the iconic one, it is possible to convey many different concepts from the world of elementary particles, such as antimatter, conservation laws, particle creation and destruction, real and virtual…
Appell Functions and the Scalar One-Loop Three-point Integrals in Feynman Diagrams
Cabral-Rosetti, L G; Cabral-Rosetti, Luis G.; Sanchis-Lozano, Miguel A.
2006-01-01
The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms coming from a previous investigation. Special cases are obtained for particular values of internal masses and external momenta.
Teaching Electron--Positron--Photon Interactions with Hands-on Feynman Diagrams
Kontokostas, George; Kalkanis, George
2013-01-01
Feynman diagrams are introduced in many physics textbooks, such as those by Alonso and Finn and Serway, and their use in physics education has been discussed by various authors. They have an appealing simplicity and can give insight into events in the microworld. Yet students often do not understand their significance and often cannot combine the…
Feynman diagram approach to high-energy scattering from lightest nuclei
Energy Technology Data Exchange (ETDEWEB)
Frankfurt, L. [Tel Aviv Univ. (Israel). School of Physics and Astronomy]|[Institute for Nuclear Physics, St. Petersburg (Russian Federation); Piller, G. [Physik Department, Technische Universitaet Muenchen, 85747 Garching (Germany); Sargsian, M. [Physik Department, Technische Universitaet Muenchen, 85747 Garching (Germany)]|[Yerevan Physics Institute, Yerevan 375036 (Armenia); Strikman, M. [Institute for Nuclear Physics, St. Petersburg (Russian Federation)]|[Pennsylvania Univ. (United States). American Center for the Study of Distance Education
1998-03-02
We outline a Feynman diagram approach to high-energy scattering from the lightest nuclei. It allows to describe high-energy (semi-) exclusive nuclear reactions at large recoil energies. In such processes the conventional Glauber approach is not applicable. This is demonstrated for high-Q{sup 2} nucleon knock-out processes and vector-meson electroproduction. (orig.). 12 refs.
A guide to Feynman diagrams in the many-body problem
Mattuck, Richard D
1992-01-01
Until this book, most treatments of this topic were inaccessible to nonspecialists. A superb introduction to important areas of modern physics, it covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. ""A great delight to read."" - Physics Today. 1974 edition.
Energy Technology Data Exchange (ETDEWEB)
Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Kniehl, Bernd A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik
2010-03-15
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed. (orig.)
Topologically distinct Feynman diagrams for mass operator in electron-phonon interaction
Directory of Open Access Journals (Sweden)
C.C. Tovstyuk
2009-01-01
Full Text Available The new method for designing topologically distinct Feynman diagrams for electron's mass operator in electron-phonon interaction is developed using the permutation group theory. The carried out classification of DPs allows to choose the classes, corresponding to disconnected diagrams, to singly connected diagrams, direct ("tadpole" diagrams, to diagrams corresponding to phonon Green functions. After this classification the set of considered double permutations is reduced to one class since only these are relevant to mass operator. We derive analytical expressions which allow to identify the DP, and to choose the phonon components, which are not accepted in every type. To avoid repetition of asymmetric diagrams, which correspond to the same analytical expression, we introduce the procedure of inversion in phonon component, and identify symmetric as well as a pair of asymmetric phonon components. For every type of DP (denoted by its digital encoding, taking into account its symmetry, we perform a set of transformations on this DP, list all DPs of the type and all the corresponding Feynman diagrams of mass operator automatically. It is clear that no more expressions (diagrams for the relevant order of perturbation theory for mass operator can be designed.
Academic Training Lecture | Beyond Feynman Diagrams (1/3) | 24 April
2013-01-01
by Prof. Lance Dixon (SLAC National Accelerator Laboratory (US)). Wednesday 24 April 2013, from 11 a.m. to 12 p.m. at CERN (222-R-001 - Filtration Plant) Description: The search for new physics at the LHC, and accurate measurements of Standard Model processes, all benefit from precise theoretical predictions of collider event rates, which in turn rely on higher order computations in QCD, the theory of the strong interactions. Key ingredients for such computations are scattering amplitudes, the quantum-mechanical transition amplitudes between the incoming quarks and gluons and the outgoing produced particles. To go beyond leading order, we need both classical tree amplitudes and quantum loop amplitudes. For decades the central theoretical tool for computing scattering amplitudes has been the Feynman diagram. However, Feynman diagrams are just too slow, even on fast computers, to be able to go beyond the leading order in QCD, for complicated events with many jets of hadrons in the final state. Such events ...
Threshold expansion of Feynman diagrams within a configuration space technique
Groote, S
2000-01-01
The near threshold expansion of generalized sunset-type (water melon) diagrams with arbitrary masses is constructed by using a configuration space technique. We present analytical expressions for the expansion of the spectral density near threshold and compare it with the exact expression obtained earlier using the method of the Hankel transform. We formulate a generalized threshold expansion with partial resummation of the small mass corrections for the strongly asymmetric case where one particle in the intermediate state is much lighter than the others.
Alternative method of Reduction of the Feynman Diagrams to a set of Master Integrals
Borja, Julio
2016-01-01
We propose a new set of Master Integrals which can be used as a basis for multiloop calculation in any gauge massless field theory. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The corresponding multiloop integrals may be decomposed in terms of this set of the Master Integrals. We construct a new reduction procedure which we apply to perform this decomposition.
Alternative method of Reduction of the Feynman Diagrams to a set of Master Integrals
Borja, Julio; Kondrashuk, Igor
2016-10-01
We propose a new set of Master Integrals which can be used as a basis for certain multiloop calculations in massless gauge field theories. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The corresponding multiloop integrals may be decomposed in terms of this set of the Master Integrals. We construct a new reduction procedure which we apply to perform this decomposition.
Huang, Da
2011-01-01
The consistency of loop regularization (LORE) method is explored in multiloop calculations. A key concept of the LORE method is the introduction of irreducible loop integrals (ILIs) which are evaluated from the Feynman diagrams by adopting the Feynman parametrization and ultraviolet-divergence-preserving(UVDP) parametrization. It is then inevitable for the ILIs to encounter the divergences in the UVDP-parameter space due to the generic overlapping divergences in the 4-dimensional momentum space. By computing the so-called $\\alpha\\beta\\gamma$ integrals arising from two loop Feynman diagrams, we show how to deal with the divergences in the parameter space by applying for the LORE method. By identifying the divergences in the UVDP-parameter space to those in the subdiagrams of two loop diagrams, we arrive at the Bjorken-Drell's analogy between Feynman diagrams and electrical circuits, where the UVDP parameters are associated with the conductance or resistance in the electrical circuits. In particular, the sets o...
Uses of Covariant Formalism for Analytical Computation of Feynman Diagrams with Massive Fermions
Rogalyov, R N
2003-01-01
The bilinear combination of Dirac spinors $u(p_1,n_1)\\bar u(p_2,n_2)$ is expressed in terms of Lorentz vectors in an explicit covariant form. The fact that the obtained expression involves only one auxiliary vector makes it very convenient for analytical computations with REDUCE (or FORM) package in the helicity formalism. The other advantage of the proposed formulas is that they are applicable to massive fermions as well as to massless fermions. The proposed approach is employed for the computation of one-loop Feynman diagrams and it is demonstrated that it considerably reduces the time of computations.
Huang, Da; Wu, Yue-Liang
2012-07-01
The consistency of loop regularization (LORE) method is explored in multiloop calculations. A key concept of the LORE method is the introduction of irreducible loop integrals (ILIs) which are evaluated from the Feynman diagrams by adopting the Feynman parametrization and ultraviolet-divergence-preserving (UVDP) parametrization. It is then inevitable for the ILIs to encounter the divergences in the UVDP parameter space due to the generic overlapping divergences in the four-dimensional momentum space. By computing the so-called αβγ integrals arising from two-loop Feynman diagrams, we show how to deal with the divergences in the parameter space with the LORE method. By identifying the divergences in the UVDP parameter space to those in the subdiagrams, we arrive at the Bjorken-Drell analogy between Feynman diagrams and electrical circuits. The UVDP parameters are shown to correspond to the conductance or resistance in the electrical circuits, and the divergence in Feynman diagrams is ascribed to the infinite conductance or zero resistance. In particular, the sets of conditions required to eliminate the overlapping momentum integrals for obtaining the ILIs are found to be associated with the conservations of electric voltages, and the momentum conservations correspond to the conservations of electrical currents, which are known as the Kirchhoff laws in the electrical circuits analogy. As a practical application, we carry out a detailed calculation for one-loop and two-loop Feynman diagrams in the massive scalar ϕ 4 theory, which enables us to obtain the well-known logarithmic running of the coupling constant and the consistent power-law running of the scalar mass at two-loop level. Especially, we present an explicit demonstration on the general procedure of applying the LORE method to the multiloop calculations of Feynman diagrams when merging with the advantage of Bjorken-Drell's circuit analogy.
Two-loop Feynman Diagrams in Yang-Mills Theory from Bosonic String Amplitudes
Körs, B; Kors, Boris; Schmidt, Michael G.
2000-01-01
We present intermediate results of an ongoing investigation which attempts a generalization of the well known one-loop Bern Kosower rules of Yang-Mills theory to higher loop orders. We set up a general procedure to extract the field theoretical limit of bosonic open string diagrams, based on the sewing construction of higher loop world sheets. It is tested with one- and two-loop scalar field theory, as well as one-loop and two-loop vacuum Yang-Mills diagrams, reproducing earlier results. It is then applied to two-loop two-point Yang-Mills diagrams in order to extract universal renormalization coefficients that can be compared to field theory. While developing numerous technical tools to compute the relevant contributions, we hit upon important conceptual questions: Do string diagrams reproduce Yang-Mills Feynman diagrams in a certain preferred gauge? Do they employ a certain preferred renormalization scheme? Are four gluon vertices related to three gluon vertices? Unfortunately, our investigations remained in...
Feynman diagrams sampling for quantum field theories on the QPACE 2 supercomputer
Energy Technology Data Exchange (ETDEWEB)
Rappl, Florian
2016-08-01
This work discusses the application of Feynman diagram sampling in quantum field theories. The method uses a computer simulation to sample the diagrammatic space obtained in a series expansion. For running large physical simulations powerful computers are obligatory, effectively splitting the thesis in two parts. The first part deals with the method of Feynman diagram sampling. Here the theoretical background of the method itself is discussed. Additionally, important statistical concepts and the theory of the strong force, quantum chromodynamics, are introduced. This sets the context of the simulations. We create and evaluate a variety of models to estimate the applicability of diagrammatic methods. The method is then applied to sample the perturbative expansion of the vertex correction. In the end we obtain the value for the anomalous magnetic moment of the electron. The second part looks at the QPACE 2 supercomputer. This includes a short introduction to supercomputers in general, as well as a closer look at the architecture and the cooling system of QPACE 2. Guiding benchmarks of the InfiniBand network are presented. At the core of this part, a collection of best practices and useful programming concepts are outlined, which enables the development of efficient, yet easily portable, applications for the QPACE 2 system.
Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams.
Willow, Soohaeng Yoo; Hirata, So
2014-01-14
A new, alternative set of interpretation rules of Feynman-Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mEh after 10(6) Monte Carlo steps.
Kleinert; Pelster; Kastening; Bachmann
2000-08-01
The free energy of a field theory can be considered as a functional of the free correlation function. As such it obeys a nonlinear functional differential equation that can be turned into a recursion relation. This is solved order by order in the coupling constant to find all connected vacuum diagrams with their proper multiplicities. The procedure is applied to a multicomponent scalar field theory with a straight phi(4) self-interaction and then to a theory of two scalar fields straight phi and A with an interaction straight phi2A. All Feynman diagrams with external lines are obtained from functional derivatives of the connected vacuum diagrams with respect to the free correlation function. Finally, the recursive graphical construction is automatized by computer algebra with the help of a unique matrix notation for the Feynman diagrams.
Noid, W G; Loring, Roger F
2004-10-15
Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.
Packwood, Daniel M; Oniwa, Kazuaki; Jin, Tienan; Asao, Naoki
2015-04-14
Organic crystals have unique charge transport properties that lie somewhere between delocalised band-type transport and localised hopping transport. In this paper, we use a stochastic tight-binding model to explore how dynamical disorder in organic crystals affects charge transport. By analysing the model in terms of Feynman diagrams (virtual processes), we expose the crucial role of correlated dynamical disorder to the charge transport dynamics in the model at short times in the order of a few hundred femtoseconds. Under correlated dynamical disorder, the random motions of molecules in the crystal allow for low-energy "bonding"-type interactions between neighboring molecular orbitals can persist over long periods of time. On the other hand, the dependence of charge transport on correlated dynamical disorder also tends to localize the charge, as correlated disorder cannot persist far in space. This concept of correlation may be the "missing link" for describing the intermediate regime between band transport and hopping transport that occurs in organic crystals.
Padé approximants, optimal renormalization scales, and momentum flow in Feynman diagrams
Brodsky, Stanley J.; Gardi, Einan; Karliner, Marek; Samuel, Mark.A.; Brodsky, Stanley J.; Ellis, John; Gardi, Einan; Karliner, Marek; Samuel, Mark. A.
1997-01-01
We show that the Padé Approximant (PA) approach for resummation of perturbative series in QCD provides a systematic method for approximating the flow of momentum in Feynman diagrams. In the large-$\\beta_0$ limit, diagonal PA's generalize the Brodsky-Lepage-Mackenzie (BLM) scale-setting method to higher orders in a renormalization scale- and scheme-invariant manner, using multiple scales that represent Neubert's concept of the distribution of momentum flow through a virtual gluon. If the distribution is non-negative, the PA's have only real roots, and approximate the distribution function by a sum of delta-functions, whose locations and weights are identical to the optimal choice provided by the Gaussian quadrature method for numerical integration. We show how the first few coefficients in a perturbative series can set rigorous bounds on the all-order momentum distribution function, if it is positive. We illustrate the method with the vacuum polarization function and the Bjorken sum rule computed in the large...
Non-planar Feynman diagrams and Mellin-Barnes representations with AMBRE 3.0
Energy Technology Data Exchange (ETDEWEB)
Dubovyk, Ievgen [Institute of Electrophysics and Radiation Technologies, Kharkiv (Ukraine); Gluza, Janusz [Univ. of Silesia, Katowice (Poland). Inst. of Physics; Riemann, Tord
2016-04-15
We introduce the Mellin-Barnes representation of general Feynman integrals and discuss their evaluation. The Mathematica package AMBRE has been recently extended in order to cover consistently non-planar Feynman integrals with two loops. Prospects for the near future are outlined. This write-up is an introduction to new results which have also been presented elsewhere.
Energy Technology Data Exchange (ETDEWEB)
Huang, Da; Wu, Yue-Liang [Chinese Academy of Science, State Key Laboratory of Theoretical Physics (SKLTP), Kavli Institute for Theoretical Physics China (KITPC), Institute of Theoretical Physics, Beijing (China)
2012-07-15
The consistency of loop regularization (LORE) method is explored in multiloop calculations. A key concept of the LORE method is the introduction of irreducible loop integrals (ILIs) which are evaluated from the Feynman diagrams by adopting the Feynman parametrization and ultraviolet-divergence-preserving (UVDP) parametrization. It is then inevitable for the ILIs to encounter the divergences in the UVDP parameter space due to the generic overlapping divergences in the four-dimensional momentum space. By computing the so-called {alpha}{beta}{gamma} integrals arising from two-loop Feynman diagrams, we show how to deal with the divergences in the parameter space with the LORE method. By identifying the divergences in the UVDP parameter space to those in the subdiagrams, we arrive at the Bjorken-Drell analogy between Feynman diagrams and electrical circuits. The UVDP parameters are shown to correspond to the conductance or resistance in the electrical circuits, and the divergence in Feynman diagrams is ascribed to the infinite conductance or zero resistance. In particular, the sets of conditions required to eliminate the overlapping momentum integrals for obtaining the ILIs are found to be associated with the conservations of electric voltages, and the momentum conservations correspond to the conservations of electrical currents, which are known as the Kirchhoff laws in the electrical circuits analogy. As a practical application, we carry out a detailed calculation for one-loop and two-loop Feynman diagrams in the massive scalar {phi}{sup 4} theory, which enables us to obtain the well-known logarithmic running of the coupling constant and the consistent power-law running of the scalar mass at two-loop level. Especially, we present an explicit demonstration on the general procedure of applying the LORE method to the multiloop calculations of Feynman diagrams when merging with the advantage of Bjorken-Drell's circuit analogy. (orig.)
A strategy for the off-shell analysis of collinear singularities in Feynman diagrams
Repetto, Alessandra
2011-01-01
In my PHD thesis I present a method for the off-shell singularity analysis of Feynman amplitudes based on the Speer sector decomposition of the Schwinger parametric integrals combined with the Mellin-Barnes tranform. I apply the method to one-loop corrections to Deep Inelastic Scattering.
JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes
Binosi, D.; Collins, J.; Kaufhold, C.; Theussl, L.
2009-09-01
A new version of the Feynman graph plotting tool JaxoDraw is presented. Version 2.0 is a fundamental re-write of most of the JaxoDraw core and some functionalities, in particular importing graphs, are not backward-compatible with the 1.x branch. The most prominent new features include: drawing of Bézier curves for all particle modes, on-the-fly update of edited objects, multiple undo/redo functionality, the addition of a plugin infrastructure, and a general improved memory performance. A new LaTeX style file is presented that has been written specifically on top of the original axodraw.sty to meet the needs of this new version. New version program summaryProgram title: JaxoDraw Catalogue identifier: ADUA_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUA_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL No. of lines in distributed program, including test data, etc.: 103 544 No. of bytes in distributed program, including test data, etc.: 3 745 814 Distribution format: tar.gz Programming language: Java Computer: Any Java-enabled platform Operating system: Any Java-enabled platform, tested on Linux, Windows XP, Mac OS X Classification: 14 Catalogue identifier of previous version: ADUA_v1_0 Journal reference of previous version: Comput. Phys. Comm. 161 (2004) 76 Does the new version supersede the previous version?: Yes Nature of problem: Existing methods for drawing Feynman diagrams usually require some hard-coding in one or the other programming or scripting language. It is not very convenient and often time consuming, to generate relatively simple diagrams. Solution method: A program is provided that allows for the interactive drawing of Feynman diagrams with a graphical user interface. The program is easy to learn and use, produces high quality output in several formats and runs on any operating system where a Java Runtime Environment is available. Reasons for new version: A
How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism
Gwilliam, Owen
2012-01-01
The Batalin-Vilkovisky formalism in quantum field theory was originally invented to avoid the difficult problem of finding diagrammatic descriptions of oscillating integrals with degenerate critical points. But since then, BV algebras have become interesting objects of study in their own right, and mathematicians sometimes have good understanding of the homological aspects of the story without any access to the diagrammatics. In this note we reverse the usual direction of argument: we begin by asking for an explicit calculation of the homology of a BV algebra, and from it derive Wick's Theorem and the other Feynman rules for finite-dimensional integrals.
Yang-Lee zeros of the two- and three-state Potts model defined on phi3 Feynman diagrams.
de Albuquerque, Luiz C; Dalmazi, D
2003-06-01
We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.
Haakh, Harald R; Henkel, Carsten
2011-01-01
Diagrammatic techniques are well-known in the calculation of dispersion interactions between atoms or molecules. The multipolar coupling scheme combined with Feynman ordered diagrams significantly reduces the number of graphs compared to elementary stationary perturbation theory. We review calculations of van der Waals-Casimir-Polder forces, focusing on two atoms or molecules one of which is excited. In this case, calculations of the corresponding force are notorious for mathematical issues connected to the spontaneous decay of the excitation. Treating such unstable states in a full non-equilibrium theory provides a physical interpretation of apparent contradictions in previous results and underlines the importance of decay processes for the intermolecular potential. This may have important implications on reactions in biological systems, where excited states may be relatively long-lived and the resonant intermolecular force may result in directed Brownian motion.
Kinoshita, T
2003-01-01
The $\\alpha^4$ contribution to the lepton $g-2$ from a gauge-invariant set of 18 Feynman diagrams containing a light-by-light scattering subdiagram internally has been reevaluated by a method independent of the previous approach. Comparison of two methods revealed a program error in the first version. Correcting this error, the contributions of these 18 diagrams become -0.990 72 (10)$(\\alpha/\\pi)^4$ and -4.432 43 (58)$(\\alpha/\\pi)^4$ for the electron and muon $g-2$, respectively.
Richard Feynman and computation
Hey, Tony
1999-04-01
The enormous contribution of Richard Feynman to modern physics is well known, both to teaching through his famous Feynman Lectures on Physics, and to research with his Feynman diagram approach to quantum field theory and his path integral formulation of quantum mechanics. Less well known perhaps is his long-standing interest in the physics of computation and this is the subject of this paper. Feynman lectured on computation at Caltech for most of the last decade of his life, first with John Hopfield and Carver Mead, and then with Gerry Sussman. The story of how these lectures came to be written up as the Feynman Lectures on Computation is briefly recounted. Feynman also discussed the fundamentals of computation with other legendary figures of the computer science and physics community such as Ed Fredkin, Rolf Landauer, Carver Mead, Marvin Minsky and John Wheeler. He was also instrumental in stimulating developments in both nanotechnology and quantum computing. During the 1980s Feynman re-visited long-standing interests both in parallel computing with Geoffrey Fox and Danny Hillis, and in reversible computation and quantum computing with Charles Bennett, Norman Margolus, Tom Toffoli and Wojciech Zurek. This paper records Feynman's links with the computational community and includes some reminiscences about his involvement with the fundamentals of computing.
Discontinuities, Feynman parameters and d-lines
Halliday, I G
1977-01-01
The calculation of asymptotic limits of Feynman diagrams using Feynman parameter techniques has developed a powerful and useful technology. A major gap in this armory has concerned the calculation of specific discontinuities of Feynman diagrams. The author remedies this gap and illustrates the new technique on a series of familiar situations. These include in the Regge limit, the ladder and the AFS diagrams, and the x approximately 1 deep inelastic electroproduction region. (4 refs).
Weinzierl, Stefan
2013-01-01
In these lectures I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by multiple polylogarithms. The algebraic properties of multiple polylogarithms are reviewed in the second part of these lectures. The final part of these lectures is devoted to Feynman integrals, which cannot be expressed in terms of multiple polylogarithms. Methods from algebraic geometry provide tools to tackle these integrals.
Broadhurst, D J
1999-01-01
In each of the 10 cases with propagators of unit or zero mass, the finite part of the scalar 3-loop tetrahedral vacuum diagram is reduced to 4-letter words in the 7-letter alphabet of the 1-forms $\\Omega:=dz/z$ and $\\omega_p:=dz/ yield only $\\zeta(Ømega^3ømega_0)=1/90\\pi^4$. In two cases $\\pi^4$ combines with the Euler-Zagier sum $\\zeta(Ømega^2ømega_3ømega_0)=\\sum_{m> n>0}(-1)^{m+n}/m^3n$; in three cases it combines with the square of Clausen's $Cl_2(\\pi/3)=\\Im \\zeta(Ømegaømega_1)=\\sum_{n>0}\\sin(\\pi n/3)/n^2$. The case with 6 masses involves no further constant; with 5 masses a Deligne-Euler-Zagier sum appears: $\\Re \\zeta(Ømega^2ømega_3ømega_1)= 3-loop rho-parameter of the standard model is merely $D_3=6\\zeta(3)-6 Cl_2^2(\\pi/3)-{1/24}\\pi^4$. The remarkable simplicity of these results stems from two shuffle algebras: one for nested sums; the other for iterated integrals. Each diagram evaluates to 10 000 digits in seconds, because the primitive words are transformable to exponentially convergent singl...
Virial expansion with Feynman diagrams
Energy Technology Data Exchange (ETDEWEB)
Leyronas, X. [Laboratoire de Physique Statistique, Ecole Normale Superieure, UPMC Universite Paris 06, Universite Paris Diderot, CNRS, 24 rue Lhomond, FR-75005 Paris (France)
2011-11-15
We present a field theoretic method for the calculation of the second and third virial coefficients b{sub 2} and b{sub 3} of two-species fermions interacting via a contact interaction. The method is mostly analytic. We find a closed expression for b{sub 3} in terms of the two- and three-body T matrices. We recover numerically, at unitarity, and also in the whole Bose-Einstein-condensate-BCS crossover, previous numerical results for the third virial coefficient b{sub 3}.
Kaufmann, Ralph M
2013-01-01
In this paper we give a new foundational categorical formulation for operations and relations and objects parameterizing them. This generalizes operads and all their cousins including but not limited to PROPs, modular operads, twisted (modular) operads as well as algebras over operads and an abundance of other related structures, such as FI--algebras. The usefulness of this approach is that it allows us to handle all the classical as well as more esoteric structures under a common framework and we can treat all the situations simultaneously. Many of the known constructions simply become Kan extensions. In this common framework, we also derive universal operations, such as those underlying Deligne's conjecture, construct Hopf algebras as well as perform resolutions, (co)bar transforms and Feynman transforms which are related to master equations. For these applications, we construct the relevant model category structures.
Automated generation of lattice QCD Feynman rules
Energy Technology Data Exchange (ETDEWEB)
Hart, A.; Mueller, E.H. [Edinburgh Univ. (United Kingdom). SUPA School of Physics and Astronomy; von Hippel, G.M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Horgan, R.R. [Cambridge Univ. (United Kingdom). DAMTP, CMS
2009-04-15
The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams. (orig.)
Nonabelian cut diagrams and their applications
Lam, C S
1996-01-01
A new kind of cut diagram is introduced to sum Feynman diagrams with nonabelian vertices. Unlike the Cutkosky diagrams which compute the discontinuity of single Feynman diagrams, the nonabelian cut diagrams represent a resummation of both the real and the imaginary parts of Feynman diagrams related by permutations. Several applications of the technique are reported, including a resolution of the apparent inconsistency of the baryon problem in large-N_c QCD, a simplified calculation of high-energy low-order QCD diagrams, and progress made with this technique on the unitarization of the BFKL equation.
Professor Richard Feynman colloquium
1965-01-01
Richard P. Feynman received the Nobel Prize for physics in 1965. Following the ceremony in Stockholm, Feynman gave the colloquium "Development of the space-time view of quantum electrodynamics" at CERN on 17th December.
Feynman Lectures on Computation
Feynman, Richard Phillips; Allen, Robin W
1999-01-01
"When, in 1984-86, Richard P. Feynman gave his famous course on computation at the California Institute of Technology, he asked Tony Hey to adapt his lecture notes into a book. Although led by Feynman,"
Dorlas, T. C.; Thomas, E. G. F.
2008-01-01
We construct a genuine Radon measure with values in B(l(2)(Z(d))) on the set of paths in Z(d) representing Feynman's integral for the discrete Laplacian on l(2)(Z(d)), and we prove the Feynman integral formula for the solutions of the Schrodinger equation with Hamiltonian H=-1/2 Delta+ V, where Delt
Smirnov, Vladimir A
2006-01-01
The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. `Feynman Integral Calculus' characterizes the most powerful methods in a systematic way. It concentrates on the methods that have been employed recently for most sophisticated calculations and illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples. It also shows how to choose adequate methods and combine them in a non-trivial way. This is a textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. Problems and solutions have been included, Appendix G has been added, more details have been presented, recent publications on evaluating Feynman integrals have been taken into account and the bibliography has been updated.
Feynman integrals and hyperlogarithms
Panzer, Erik
2015-01-01
We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in ...
Smirnov, Vladimir A
2004-01-01
The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. Although a great variety of methods for evaluating Feynman integrals has been developed over a span of more than fifty years, this book is a first attempt to summarize them. 'Evaluating Feynman Integrals' characterizes the most powerful methods, in particular those used for recent, quite sophisticated calculations, and then illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples.
Introduction to Feynman Integrals
Weinzierl, Stefan
2010-01-01
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced topics: Mathematical aspects of loop integrals related to periods, shuffle algebras and multiple polylogarithms are covered as well as practical algorithms for evaluating Feynman integrals.
PREFACE: Third Feynman Festival
Brandt, Howard E.; Kim, Young S.; Man'ko, Margarita A.
2007-06-01
The third Feynman Festival was held at the University of Maryland, College Park, Maryland, USA on 25-29 August 2006. This was the third meeting of the conference series entitled `Feynman Festival'. The first and second meetings were held at the same place in 2002 and 2004, respectively. The purpose of this conference was to discuss research topics initiated by Richard Feynman, who was one of the most creative physicists in the 20th Century. He produced many provocative ideas in all branches of physics. Indeed, the ideal form of confluences bearing his name would be to cover everything in physics, but this is not possible. We can cover only a small fraction of Feynman's world at a given meeting. Quantum computing, pioneered by Feynman, is one of the most popular subjects these days, and there were many papers on this subject. There were also many papers on the foundations of quantum mechanics, dealing with fundamental aspects of quantum mechanics and statistical mechanics, based on the Feynman framework. The conference format was to give equal opportunity to every participant, and 96 papers were presented from 138 participants. Not every speaker contributed to the proceedings. The proceedings were able to cover only 16 papers. There were no formal proceedings volumes for the two previous Feynman Festivals. For those earlier Festivals, we used collections of the links to archived articles as the proceedings substitutes. Also there was a Special Issue on Quantum Computing: Selected Papers from the Feynman Festival (Editors: Howard E Brandt, Young S Kim, and Margarita A Man'ko) published in Journal of Optics B: Quantum and Semiclassical Optics, Volume 5, Issue 6, pp S547-S656 (December 2003). For the third meeting, we decided to publish the proceedings as a volume of Journal of Physics: Conference Series. Every paper was thoroughly refereed according to IOP Publishing standard. Many conference papers tend to be review or preview papers, including those presented at the
Feynman diagrammatic approach to spin foams
Kisielowski, Marcin; Puchta, Jacek
2011-01-01
"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams} we introduce. Our diagrams are the spin network analogy of the Feynman diagrams. Their framework is compatible with the framework of Loop Quantum Gravity. For every operator spin network diagram we construct a corresponding operator spin foam. Admitting all the spin networks of LQG and all possible diagrams leads to a clearly defined large class of operator spin foams. In this way our framework provides a proposal for a class of 2-cell complexes that should be used in the spin foam theories of LQG. Within this class, our diagrams are just equivalent to the spin foams. The advantage, however, in the diagram framework is, that it is self contained, all the amplitudes can be calculated directly from the diagrams without explicit visualization of the corresponding spin foams. The spin network diagram operators and amplitudes are consistently defined on thei...
Lectures on configuration space methods for sunrise-type diagrams
Groote, S
2003-01-01
In this lecture series I will give a fundamental insight into configuration space techniques which are of help to calculate a broad class of Feynman diagrams, the sunrise-type diagrams. Applications are shown along with basic concepts and techniques.
Feynman integrals and hyperlogarithms
Energy Technology Data Exchange (ETDEWEB)
Panzer, Erik
2015-02-05
We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in terms of multiple polylogarithms, to all orders in the ε-expansion. These integrals can be computed effectively with the presented program. We include interesting examples of explicit results for Feynman integrals with up to 6 loops. In particular we present the first exactly computed counterterm in massless φ{sup 4} theory which is not a multiple zeta value, but a linear combination of multiple polylogarithms at primitive sixth roots of unity (and divided by the √(3)). To this end we derive a parity result on the reducibility of the real- and imaginary parts of such numbers into products and terms of lower depth.
Goodstein, David L.
1989-01-01
One of the principal purposes of this article is to consider Dick Feynman in his role as teacher. Let me not keep you in suspense about my conclusion. I think Dick was a truly great teacher, perhaps the greatest of his era and ours. That's not to say he was always completely successful, as he himself emphasized in his preface to The Feynman Lectures on Physics. I would contend that these lectures often failed at the level of their superficial intent: If his purpose in ...
Reiff, Patricia H.; Feynman, Joan; Gold, Thomas; Wasserburg, G. J.; Sheeley, Neil R., Jr.; Akasofu, S.-I.
Richard Feynman, simply put, was a genius. His quick wit and uncommon grasp of physics meant that any research area he encountered, he quickly mastered. Despite the fact that his own area of research was not geophysics, his life and work influenced almost all of us.Virtually every physics graduate student who started in the mid 60s or later was exposed to his Lectures on Physics, either by having t h em as a text for a course or by using them (as I did) to bone up for oral qualifying exams. Feynman diagrams appear in nearly every modern quantum mechanics textbook and are featured in his official Caltech portrait, which illustrates this article.
Feynman Lectures on Gravitation
Energy Technology Data Exchange (ETDEWEB)
Borcherds, P
2003-05-21
In the early 1960s Feynman lectured to physics undergraduates and, with the assistance of his colleagues Leighton and Sands, produced the three-volume classic Feynman Lectures in Physics. These lectures were delivered in the mornings. In the afternoons Feynman was giving postgraduate lectures on gravitation. This book is based on notes compiled by two students on that course: Morinigo and Wagner. Their notes were checked and approved by Feynman and were available at Caltech. They have now been edited by Brian Hatfield and made more widely available. The book has a substantial preface by John Preskill and Kip Thorne, and an introduction entitled 'Quantum Gravity' by Brian Hatfield. You should read these before going on to the lectures themselves. Preskill and Thorne identify three categories of potential readers of this book. 1. Those with a postgraduate training in theoretical physics. 2. 'Readers with a solid undergraduate training in physics'. 3. 'Admirers of Feynman who do not have a strong physics background'. The title of the book is perhaps misleading: readers in category 2 who think that this book is an extension of the Feynman Lectures in Physics may be disappointed. It is not: it is a book aimed mainly at those in category 1. If you want to get to grips with gravitation (and general relativity) then you need to read an introductory text first e.g. General Relativity by I R Kenyon (Oxford: Oxford University Press) or A Unified Grand Tour of Theoretical Physics by Ian D Lawrie (Bristol: IoP). But there is no Royal Road. As pointed out in the preface and in the introduction, the book represents Feynman's thinking about gravitation some 40 years ago: the lecture course was part of his attempts to understand the subject himself, and for readers in all three categories it is this that makes the book one of interest: the opportunity to observe how a great physicist attempts to tackle some of the hardest challenges of physics
Feynman graph solution to Wilson's exact renormalization group
Sonoda, H
2003-01-01
We introduce a new prescription for renormalizing Feynman diagrams. The prescription is similar to BPHZ, but it is mass independent, and works in the massless limit as the MS scheme with dimensional regularization. The prescription gives a diagrammatic solution to Wilson's exact renormalization group differential equation.
Feynman formulae for evolution semigroups
Directory of Open Access Journals (Sweden)
Ya. A. Butko
2014-01-01
Full Text Available The paper systematically describes an approach to solution of initial and initial-boundary value problems for evolution equations based on the representation of the corresponding evolution semigroups with the help of Feynman formulae. The article discusses some of the methods of constructing Feynman formulae for different evolution semigroups, presents specific examples of solutions of evolution equations. In particular, Feynman formula is obtained for evolution semigroups generated by multiplicative perturbations of generators of some initial semigroups. In this case semigroups on a Banach space of continuous functions defined on an arbitrary metric space are considered; Feynman formulae are constructed with the help of operator families, which are Chernoff equivalent to the initial unperturbed semigroups. The present result generalizes the author's paper \\Feynman formula for semigroups with multiplicative perturbed generators" and some of the results of the joint with O.G. Smolyanov and R.L. Schilling paper \\Lagrangian and Hamiltonian Feynman formulae for some Feller processes and their perturbations". The approach to the construction of Feynman formulae for semigroups with multiplicative and additive perturbed generators is illustrated with examples of the Cauchy problem for the Schrodinger equation, the approximation of transition probabilities of some Markov processes.Further, a wider class of additive and multiplicative perturbations of a particular generator | the Laplace operator | is considered in the paper. And Feynman formula for the solution of the Cauchy problem for a second order parabolic equation with unbounded variable coefficients is proved. In addition, the article describes a method for constructing Feynman formulae for solutions of the Cauchy | Dirichlet problem for parabolic differential equations. The method is also illustrated by a second order parabolic equation with variable coefficients. These results generalize some
The Merrifield-Simmons index of quadrangular chains%四角链的Merrifield-Simmons指标
Institute of Scientific and Technical Information of China (English)
田文文; 田双亮
2013-01-01
Quadrangular chains is a connected graph that consists of several unit square sequences and any two adjacent squares have only one cut edge .This paper presents the Merrifield-Simmons index and itscomputational formula of quadrangular chains made up by unit square sequences un-der two non-isomorphic connected positions .%四角链是由若干个单位正方形序列且任意相邻两个正方形之间只有一条割边构成的连通图。研究了n个单位正方形序列构成的四角链在两种不同构联接位下的Merrifield-Simmons指标，并给出了具体表达式。
四角链的Hosoya指标%Hosoya index of Quadrangular chains
Institute of Scientific and Technical Information of China (English)
田文文; 田双亮
2014-01-01
Quadrangular chain is a connected graph consisting of several unit square sequences, of which any two adjacent squares have only one cut edge. This paper presents the Hosoya index and its computational formula of Quadrangular chains made up by n unit square sequences under two non-isomorphic connected positions.%四角链是由若干个单位正方形序列且任意相邻两个正方形之间只有一条割边构成的连通图。文中主要研究了n个单位正方形序列构成的四角链在两种不同构联接位下的Hosoya指标，并给出了具体表达式。
Goodstein, David L.
1989-01-01
The February issue of PHYSICS TODAY celebrated the life of Richard Feynman. It seems to me appropriate to make some mention of Feynman's opinion of PHYSICS TODAY. I believe that what follows can count as the formal publication of a historically important document.
Chew, Geoffrey F
2008-01-01
Arrowed-time divergence-free rules or cosmological quantum dynamics are formulated through stepped Feynman paths across macroscopic slices of Milne spacetime. Slice boundaries house totally-relativistic rays representing elementary entities--preons. Total relativity and the associated preon Fock space, despite distinction from special relativity (which lacks time arrow), are based on the Lorentz group. Each path is a set of cubic vertices connected by straight, directed and stepped arcs that carry inertial, electromagnetic and gravitational action. The action of an arc step comprises increments each bounded by Planck's constant. Action from extremely-distant sources is determined by universe mean energy density. Identifying the arc-step energy that determines inertial action with that determining gravitational action establishes both arc-step length and universe density. Special relativity is accurate for physics at laboratory spacetime scales far below that of Hubble and far above that of Planck.
Goyal, Ketan; Kawai, Ryoichi
As nanotechnology advances, understanding of the thermodynamic properties of small systems becomes increasingly important. Such systems are found throughout physics, biology, and chemistry manifesting striking properties that are a direct result of their small dimensions where fluctuations become predominant. The standard theory of thermodynamics for macroscopic systems is powerless for such ever fluctuating systems. Furthermore, as small systems are inherently quantum mechanical, influence of quantum effects such as discreteness and quantum entanglement on their thermodynamic properties is of great interest. In particular, the quantum fluctuations due to quantum uncertainty principles may play a significant role. In this talk, we investigate thermodynamic properties of an autonomous quantum heat engine, resembling a quantum version of the Feynman Ratchet, in non-equilibrium condition based on the theory of open quantum systems. The heat engine consists of multiple subsystems individually contacted to different thermal environments.
Nanotechnology: From Feynman to Funding
Drexler, K. Eric
2004-01-01
The revolutionary Feynman vision of a powerful and general nanotechnology, based on nanomachines that build with atom-by-atom control, promises great opportunities and, if abused, great dangers. This vision made nanotechnology a buzzword and launched the global nanotechnology race. Along the way, however, the meaning of the word has shifted. A…
Analytic Tools for Feynman Integrals
Smirnov, Vladimir A
2012-01-01
The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author’s previous Springer book “Evaluating Feynman Integrals” and its textbook version “Feynman Integral Calculus.” Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added: One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, “Applied Asymptotic Expansions in Momenta and Masses,” by the author. This chapter describes, on t...
Automatic numerical integration methods for Feynman integrals through 3-loop
de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.
2015-05-01
We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.
Is Feynman's Analysis of Electrostatic Screening Correct?
Subbarao, Kris
2016-01-01
In a recent paper on electrostatic shielding, Chapman, Hewett and Trefethen present arguments that the analysis of this effect by Feynman is incorrect. Feynman analyzed shielding by a row of infinitesimally thin wires. They claim that Feynman used the wrong boundary conditions invalidating his analysis. In this paper we emphasize that Feynman's solution is a Green's function through which behavior of the potential due to finite thickness wires of arbitrary cross-section with appropriate boundary condition can be understood. This shows that the main conclusions of Feynman's treatment are indeed correct. Analogy to a parallel plate capacitor with one of the plates replaced by a row of wires provides a more intuitive understanding of Feynman's argument. The case of a finite number of wires arranged in a ring (not treated by Feynman), as a model of Faraday cage, is different. The structure of the solution in radial coordinates already suggests that one should not expect exponential behavior and further analysis c...
Mathematical aspects of Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Bogner, Christian
2009-08-15
In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals. The integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph. Starting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative
The calculation of Feynman diagrams in the superstring perturbation theory
Danilov, G S
1995-01-01
The method of the calculation of the multi-loop superstring amplitudes is proposed. The amplitudes are calculated from the equations that are none other than Ward identities. They are derived from the requirement that the discussed amplitudes are independent from a choice of gauge of both the vierbein and the gravitino field. The amplitudes are calculated in the terms of the superfields vacuum correlators on the complex (1|1) supermanifolds. The superconformal Schottky groups appropriate for this aim are built for all the spinor structures. The calculation of the multi- loop boson emission amplitudes in the closed, oriented Ramond-Neveu-Schwarz superstring theory is discussed in details. The main problem arises for those spinor structures that correspond to the Ramond fermion loops. Indeed, in this case the superfield vacuum correlators can not be derived by a simple extension of the boson string results. The method of the calculation of the above correlators is proposed. The discussed amplitudes due to all t...
The Logic Behind Feynman's Paths
García Álvarez, Edgardo T.
The classical notions of continuity and mechanical causality are left in order to reformulate the Quantum Theory starting from two principles: (I) the intrinsic randomness of quantum process at microphysical level, (II) the projective representations of symmetries of the system. The second principle determines the geometry and then a new logic for describing the history of events (Feynman's paths) that modifies the rules of classical probabilistic calculus. The notion of classical trajectory is replaced by a history of spontaneous, random and discontinuous events. So the theory is reduced to determining the probability distribution for such histories accordingly with the symmetries of the system. The representation of the logic in terms of amplitudes leads to Feynman rules and, alternatively, its representation in terms of projectors results in the Schwinger trace formula.
Selected papers of Richard Feynman with commentary
2000-01-01
These scientific papers of Richard Feynman are renowned for their brilliant content and the author's striking original style. They are grouped by topic: path integral approach to the foundations of quantum mechanics and quantum field theory, renormalized quantum electrodynamics, theory of superfluid liquid helium, theory of the Fermi interaction, polarons, gravitation, partons, computer theory, etc. Comments on Feynman's topics are provided by the editor, together with biographical notes and a complete bibliography of Feynman's publications.
Position Space Feynman quadrics and their motives
Ceyhan, Ozgur
2015-01-01
In this note, we introduce and study position space Feynman quadrics that are the loci of divergences of the position space Feynman integrals for Euclidean massless scalar quantum field theories. We prove that the Feynman quadrics define objects in the category of mixed Tate motives for complete graphs with a bound on the number of vertices. This result shows a strong contrast with the graph hypersurfaces approach which produces also non-mixed Tate examples.
Anatomical nuances of the internal carotid artery in relation to the quadrangular space.
Dolci, Ricardo L L; Ditzel Filho, Leo F S; Goulart, Carlos R; Upadhyay, Smita; Buohliqah, Lamia; Lazarini, Paulo R; Prevedello, Daniel M; Carrau, Ricardo L
2017-02-24
OBJECTIVE The aim of this study was to evaluate the anatomical variations of the internal carotid artery (ICA) in relation to the quadrangular space (QS) and to propose a classification system based on the results. METHODS A total of 44 human cadaveric specimens were dissected endonasally under direct endoscopic visualization. During the dissection, the anatomical variations of the ICA and their relationship with the QS were noted. RESULTS The space between the paraclival ICAs (i.e., intercarotid space) can be classified as 1 of 3 different shapes (i.e., trapezoid, square, or hourglass) based on the trajectory of the ICAs. The ICA trajectories also directly influence the volumetric area of the QS. Based on its geometry, the QS was classified as one of the following: 1) Type A has the smallest QS area and is associated with a trapezoid intercarotid space, 2) Type B corresponds to the expected QS area (not minimized or enlarged) and is associated with a square intercarotid space, and 3) Type C has the largest QS area and is associated with an hourglass intercarotid space. CONCLUSIONS The different trajectories of the ICAs can modify the area of the QS and may be an essential parameter to consider for preoperative planning and defining the most appropriate corridor to reach Meckel's cave. In addition, ICA trajectories should be considered prior to surgery to avoid injuring the vessels.
Application of the Feynman-tree theorem together with BCFW recursion relations
Maniatis, Markos
2016-01-01
Recently, it has been shown that on-shell scattering amplitudes can be constructed by the Feynman-tree theorem combined with the BCFW recursion relations. Since the BCFW relations are restricted to tree diagrams, the preceding application of the Feynman-tree theorem is essential. In this way amplitudes can be constructed by on-shell and gauge-invariant tree amplitudes. Here we want to apply this method to the electron-photon vertex correction. We present all the single, double, and triple phase-space tensor integrals explicitly and show that the sum of amplitudes coincides with the result of the conventional calculation of a virtual loop correction.
Motoki, Shinji; Nakasato, Naohito; Ishikawa, Tadashi; Yuasa, Fukuko; Fukushige, Toshiyuki; Kawai, Atsushi; Makino, Junichiro
2014-01-01
Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagram with multi-loop integral which may require multi-precision calculation. We developed a dedicated accelerator system for multi-precision calculation (GRAPE9-MPX). We present performance results of our system for the case of Feynman two-loop box and three-loop selfenergy diagrams with multi-precision.
A Note on the Stochastic Nature of Feynman Quantum Paths
L. Botelho, Luiz C.
2016-06-01
We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.
A Note on the Stochastic Nature of Feynman Quantum Paths
Botelho, Luiz C. L.
2016-11-01
We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.
Numerical Approach to Calculation of Feynman Loop Integrals
Yuasa, F; Kurihara, Y; Fujimoto, J; Shimizu, Y; Hamaguchi, N; de Doncker, E; Kato, K
2011-01-01
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried out in a fully numerical way, our approach is applicable to one-, two- and multi-loop diagrams. Without any analytic treatment it can compute diagrams with not only real masses but also complex masses for the internal particles. As concrete examples we present numerical results of a scalar one-loop box integral with complex masses and two-loop planar and non-planar box integrals with masses. We discuss the quality of our numerical computation by comparisons with other methods and also propose a self consistency check.
Perturbation Series in Light-Cone Diagrams of Green Function of String Field
Li, Am-Gil; Li, Chol-Man; Im, Song-Jin
2016-01-01
In this paper, we proved the correspondence between Feynman diagrams in space-time and light-cone diagrams in world-sheet by using only path integral representation on free Green function in the first quantization theory. We also obtained general representation on perturbation series of light-cone diagrams describing split and join of strings.
Feynman motives of banana graphs
Aluffi, Paolo
2008-01-01
We consider the infinite family of Feynman graphs known as the ``banana graphs'' and compute explicitly the classes of the corresponding graph hypersurfaces in the Grothendieck ring of varieties as well as their Chern--Schwartz--MacPherson classes, using the classical Cremona transformation and the dual graph, and a blowup formula for characteristic classes. We outline the interesting similarities between these operations and we give formulae for cones obtained by simple operations on graphs. We formulate a positivity conjecture for characteristic classes of graph hypersurfaces and discuss briefly the effect of passing to noncommutative spacetime.
Feynman integrals in QCD made simple
CERN. Geneva
2015-01-01
A key insight is that important properties of these functions can be predicted by inspecting the singularity structure of the Feynman integrand. Combined with the differential equations technique, this gives a powerful method for computing the necessary Feynman integrals. I will review these ideas, based on Phys.Rev.Lett. 110 (2013) 25, and present recent new results relevant for QCD scattering amplitudes.
Feynman's Entropy and Decoherence Mechanism
Kim, Y S
2000-01-01
If we reduce coherence in a given quantum system, the result is an increase in entropy. Does this necessarily convert this quantum system into a classical system? The answer to this question is No. The decrease of coherence means more uncertainty. This does not seem to make the system closer to classical system where there are no uncertainties. We examine the problem using two coupled harmonic oscillators where we make observations on one of them while the other oscillator is assumed to be unobservable or to be in Feynman's rest of the universe. Our ignorance about the rest of the universe causes an increase in entropy. However, does the system act like a classical system? The answer is again No. When and how does this system appear like a classical system? It is shown that this paradox can be resolved only if measurements are taken along the normal coordinates. It is also shown that Feynman's parton picture is one concrete physical example of this decoherence mechanism.
Poisson equation for the Mercedes diagram in string theory at genus one
Basu, Anirban
2015-01-01
The Mercedes diagram has four trivalent vertices which are connected by six links such that they form the edges of a tetrahedron. This three loop Feynman diagram contributes to the D^{12} R^4 amplitude at genus one in type II string theory, where the vertices are the points of insertion of the graviton vertex operators, and the links are the scalar propagators on the toroidal worldsheet. We obtain a modular invariant Poisson equation satisfied by the Mercedes diagram, where the source terms involve one and two loop Feynman diagrams. We calculate its contribution to the D^{12} R^4 amplitude.
EDITORIAL: Quantum Computing and the Feynman Festival
Brandt, Howard E.; Kim, Young S.; Man'ko, Margarita A.
2003-12-01
The Feynman Festival is a new interdisciplinary conference developed for studying Richard Feynman and his physics. The first meeting of this new conference series was held at the University of Maryland on 23--28 August 2002 (http://www.physics.umd.edu/robot/feynman.html) and the second meeting is scheduled for August 2004 at the same venue. According to Feynman, the different aspects of nature are different aspects of the same thing. Therefore, the ultimate purpose of the conference is to find Feynman's same thing from all different theories. For this reason, the first meeting of the Festival did not begin with a fixed formula, but composed its scientific programme based on responses from the entire physics community. The conference drew the most enthusiastic response from the community of quantum computing, the field initiated by Feynman. Encouraged by the response, we decided to edit a special issue of Journal of Optics B: Quantum and Semiclassical Optics on quantum computing in connection with the first Feynman Festival. The authorship is not restricted to the participants of the Feynman Festival, and all interested parties were encouraged to submit their papers on this subject. Needless to say, all the papers were peer reviewed according to the well-established standards of the journal. The subject of quantum computing is not restricted to building and operating computers. It requires a deeper understanding of how quantum mechanics works in materials as well as in our minds. Indeed, it covers the basic foundations of quantum mechanics, measurement theory, information theory, quantum optics, atomic physics and condensed matter physics. It may be necessary to develop new mathematical tools to accommodate the language that nature speaks. It is gratifying to note that this special issue contains papers covering all these aspects of quantum computing. As Feynman noted, we could be discussing these diversified issues to study one problem. In our case, this `one
Richard Feynman Quarks, Bombs, and Bongos
Henderson, Harry
2010-01-01
Described by his peers as the "finest physicist of his generation," Richard Feynman defied scientist stereotypes. This brash New York-born American physicist startled the more conservative giants of European physics with his endless ability to improvise. Indeed, later in life, Feynman became an accomplished bongo player. Feynman's legacy to physics was his ability to simplify complex equations and clarify fundamental principles through the use of graphs. He developed the theory of quantum electrodynamics, which illustrates the behavior of electrically charged particles, such as elect
Coupled oscillators and Feynman's three papers
Kim, Y.S.
2006-01-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the ``rest of the universe'' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference ...
Feynman Amplitudes in Mathematics and Physics
Bloch, Spencer
2015-01-01
These are notes of lectures given at the CMI conference in August, 2014 at ICMAT in Madrid. The focus is on some mathematical questions associated to Feynman amplitudes, including Hodge structures, relations with string theory, and monodromy (Cutkosky rules).
Worldline Green functions for multiloop diagrams
Schmidt, M G
1994-01-01
We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop graph, and for a loop with an arbitrary number of propagator insertions. For scalar and abelian gauge theories, the resulting integral representations allow to combine whole classes of Feynman diagrams into compact expressions.
Vous voulez rire, monsieur Feynman !
Feynman, Richard P
2000-01-01
Richard Feynman fut un scientifique hors norme. Non seulement il contribua en profondeur à la grande aventure de la physique des particules élémentaires, depuis la fabrication de la bombe atomique pendant la guerre alors qu'il n'a pas 25 ans, jusqu'à ses diagrammes qui permettent d'y voir un peu plus clair dans les processus physiques de base. Non seulement il fut un professeur génial, n'hésitant pas à faire le clown pour garder l'attention de ses étudiants et à simplifier pour aller à l'essentiel. Mais il mena une vie excentrique - collectionneur, bouffon, impertinent, joueur de bongo, amateur de strip-tease, séducteur impénitent, déchiffreur de codes secrets et de textes mayas, explorateur en Asie centrale -, qu'il raconte ici avec l'humour du gamin des rues de New York qu'il n'a jamais cessé d'être.
Block diagrams and the cancellation of divergences in energy-level perturbation theory
Michels, M.A.J.; Suttorp, L.G.
1979-01-01
The effective Hamiltonian for the degenerate energy-eigenvalue problem in adiabatic perturbation theory is cast in a form that permits an expansion in Feynman diagrams. By means of a block representation a resummation of these diagrams is carried out such that in the adiabatic limit no divergencies
From Multileg Loops to Trees (by-passing Feynman's Tree Theorem)
Energy Technology Data Exchange (ETDEWEB)
Rodrigo, German; /Valencia U., IFIC; Catani, Stefano; /INFN, Florence /Florence U.; Gleisberg, Tanju; /SLAC; Krauss, Frank; /Durham U., IPPP; Winter, Jan-Christopher; /Fermilab
2011-10-14
We illustrate a duality relation between one-loop integrals and single-cut phase-space integrals. The duality relation is realised by a modification of the customary +i0 prescription of the Feynman propagators. The new prescription regularizing the propagators, which we write in a Lorentz covariant form, compensates for the absence of multiple-cut contributions that appear in the Feynman Tree Theorem. The duality relation can be extended to generic one-loop quantities, such as Green's functions, in any relativistic, local and unitary field theories. The physics program of LHC requires the evaluation of multi-leg signal and background processes at next-to-leading order (NLO). In the recent years, important efforts have been devoted to the calculation of many 2 {yields} 3 processes and some 2 {yields} 4 processes. We have recently proposed a method to compute multi-leg one-loop cross sections in perturbative field theories. The method uses combined analytical and numerical techniques. The starting point of the method is a duality relation between one-loop integrals and phase-space integrals. In this respect, the duality relation has analogies with the Feynman's Tree Theorem (FTT). The key difference with the FTT is that the duality relation involves only single cuts of the one-loop Feynman diagrams. In this talk, we illustrate the duality relation, and discuss its correspondence, similarities, and differences with the FTT.
Covariant diagrams for one-loop matching
Zhang, Zhengkang
2016-01-01
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
Covariant diagrams for one-loop matching
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhengkang [Michigan Univ., Ann Arbor, MI (United States). Michigan Center for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2016-10-15
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
A Feynman integral via higher normal functions
Bloch, Spencer; Vanhove, Pierre
2014-01-01
We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 sur...
Grishkevich, Viktor M
2013-11-01
Axillary adduction contracture is caused by scars that tightly surround the shoulder joint impairing the function of the upper limb. Due to severe scar surface deficiency, contracture release presents a challenge for surgeons since a method of release is transfer of tissue in the form of a large pedicled or free flap(s). Thus, development of simpler, less traumatic techniques, using local tissues, persists. Anatomic studies of shoulder adduction contractures after burn (pre-operative, during surgery, post-reconstruction) were done in 346 pediatric and adult patients. All were divided into three groups according to contracture types: with edge contractures (80%), medial (6%) and total (14%). Anatomical study covered peculiarities of total contractures and possibilities for their treatment using local scarred tissue. Total contractures (48 patients) were caused by scars tightly surrounding the joint on three sides: anterior, posterior, and axillary. There were two specific forms of contracture: (a) shoulder close to the chest wall (22 of 48 patients) which was treated with thoracic pedicled or free flaps; (b) in 26 out of 48 patients a flat scar and skin graft surface laid along the shoulder and chest wall, in axillary projection, which were used for contracture release in the form of a subcutaneous pedicled quadrangular flap. The flap was mobilized only peripherally, descending to the apex of the axilla, forming the central axillary zone, and suspension of the axilla on a normal level. Wounds aside the flaps were covered with skin graft. Acceptable functional and cosmetic results were achieved in all 26 patients. Total shoulder adduction contractures have two forms: (a) shoulder close/fused with the chest wall; and (b) along the chest wall and shoulder there is a flat surface, the tissue of which can be used for reconstruction in a form of scar subcutaneous pedicled quadrangular flap. Based on this flap, a new technique is described which is relatively easy to
Colwell, Morris A
1976-01-01
Electronic Diagrams is a ready reference and general guide to systems and circuit planning and in the preparation of diagrams for both newcomers and the more experienced. This book presents guidelines and logical procedures that the reader can follow and then be equipped to tackle large complex diagrams by recognition of characteristic 'building blocks' or 'black boxes'. The goal is to break down many of the barriers that often seem to deter students and laymen in learning the art of electronics, especially when they take up electronics as a spare time occupation. This text is comprised of nin
The signed permutation group on Feynman graphs
Purkart, Julian
2016-08-01
The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalization group are small, we can expand the integral and only consider the lowest orders in the scaling. The aim of this article is to determine specific combinations of graphs in a scalar quantum field theory that lead to a remarkable simplification of the first non-trivial term in the perturbation series. It will be seen that the result is independent of the renormalization scheme and the scattering angles. To achieve that goal we will utilize the parametric representation of scalar Feynman integrals as well as the Hopf algebraic structure of the Feynman graphs under consideration. Moreover, we will present a formula which reduces the effort of determining the first-order term in the perturbation series for the specific combination of graphs to a minimum.
Characterization of qubit chains by Feynman probes
Tamascelli, Dario; Benedetti, Claudia; Olivares, Stefano; Paris, Matteo G. A.
2016-10-01
We address the characterization of qubit chains and assess the performances of local measurements compared to those provided by Feynman probes, i.e., nonlocal measurements realized by coupling a single-qubit register to the chain. We show that local measurements are suitable to estimate small values of the coupling and that a Bayesian strategy may be successfully exploited to achieve optimal precision. For larger values of the coupling Bayesian local strategies do not lead to a consistent estimate. In this regime, Feynman probes may be exploited to build a consistent Bayesian estimator that saturates the Cramér-Rao bound, thus providing an effective characterization of the chain. Finally, we show that ultimate bounds to precision, i.e., saturation of the quantum Cramér-Rao bound, may be achieved by a two-step scheme employing Feynman probes followed by local measurements.
(U) Feynman-Y calculations using PARTISN
Energy Technology Data Exchange (ETDEWEB)
Favorite, Jeffrey A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-08-31
A prescription for computing the Feynman Y as a function of coincidence gate width using a deterministic multigroup neutron transport code has been published and the results compared favorably with measurements of the BeRP ball. In this paper, we report on our project to implement the method and reproduce the results. There are several clarifications and corrections of the published prescription. We show results using two multigroup cross section libraries compared with measurements and with Monte Carlo results. Deterministic simulations of the mean count rates compare very favorably with previously published Monte Carlo results, and deterministic simulations of the Feynman Y asymptote compare somewhat favorably. In Feynman beta plots, the deterministic simulations reached the asymptotic value much sooner than did a fit to the measured data.
Remarks on the Origin of Path Integration: Einstein and Feynman
Sauer, Tilman
2008-01-01
I offer some historical comments about the origins of Feynman's path integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's thesis supervisor John Wheeler, it is argued that, contrary to what one might expect, the significance of the interaction between Einstein and Feynman pertained to a critique of classical field theory, rather than to a direct critique of quantum mechanics itself...
Quantum Man: Richard Feynman's Life in Science
CERN. Geneva
2011-01-01
It took a man who was willing to break all the rules to tame a theory that breaks all the rules. This talk will be based on my new book Quantum Man: Richard Feynman's life in science. I will try and present a scientific overview of the contributions of Richard Feynman, as seen through the arc of his fascinating life. From Quantum Mechanics to Antiparticles, from Rio de Janeiro to Los Alamos, a whirlwind tour will provide insights into the character, life and accomplishments of one of the 20th centuries most important scientists, and provide an object lesson in scientific integrity.
Rose, Matthew
2004-01-01
Matthew Rose worked at the Naval Postgraduate School as a graphic designer from February 2002-November 2011. His work for NPS included logos, brochures, business packs, movies/presentations, posters, the CyberSiege video game and many other projects. This material was organized and provided by the artist, for inclusion in the NPS Archive, Calhoun. Includes these files: Plan_ver.ai; powerline.jpg; SCADA diagram.ai; SCADA diagram.pdf; SCADA diagramsmall.pdf; SCADA2.pdf
Conditional generalized analytic Feynman integrals and a generalized integral equation
Seung Jun Chang; Soon Ja Kang; David Skoug
2000-01-01
We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various functionals. Finally we use the conditional generalized Feynman integral to derive a Schrödinger integral equation.
Delay Equations of the Wheeler-Feynman Type
Deckert, D. -A.; Dürr, D.; Vona, N.
2012-01-01
We present an approximate model of Wheeler-Feynman electrodynamics for which uniqueness of solutions is proved. It is simple enough to be instructive but close enough to Wheeler-Feynman electrodynamics such that we can discuss its natural type of initial data, constants of motion and stable orbits with regard to Wheeler-Feynman electrodynamics.
Delay Equations of the Wheeler-Feynman Type
Deckert, D -A; Vona, N
2013-01-01
We present an approximate model of Wheeler-Feynman electrodynamics for which uniqueness of solutions is proved. It is simple enough to be instructive but close enough to Wheeler-Feynman electrodynamics such that we can discuss its natural type of initial data, constants of motion and stable orbits with regard to Wheeler-Feynman electrodynamics.
Generalization of the Hellmann-Feynman theorem
Energy Technology Data Exchange (ETDEWEB)
Esteve, J.G., E-mail: esteve@unizar.e [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Falceto, Fernando [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Garcia Canal, C. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata and IFLP-CONICET (Argentina)
2010-01-25
The well-known Hellmann-Feynman theorem of quantum mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.
Hyperlogarithms and periods in Feynman amplitudes
Todorov, Ivan
2016-01-01
The role of hyperlogarithms and multiple zeta values (and their generalizations) in Feynman amplitudes is being gradually recognized since the mid 1990's. The present lecture provides a concise introduction to a fast developing subjects that attracts the attention to a wide range of specialists - from number theorists to particle physicists.
On Feynman's proof of the Maxwell equations
Noyes, H. P.
1991-03-01
Dyson has presented a derivation of the free space Maxwell Equations and the Lorentz force starting from Newton's Second Law and the commutation relations between x(sub i), x(sub j), and x(sub k). The proof is attributed to Feynman. The reason why it works is puzzling. The finite and discrete reconciliation between relativity and quantum mechanics offers a less problematic logical chain. The mass ratios are defined using deBroglie wave interference in a theory which necessarily entails the commutation relations. It is shown that this route implies Newton's Third Law. Following Mach, Newton's Second Law then becomes a definition of force, and given this the Lorentz force becomes a definition of the electromagnetic fields. The use of the relativistic Zitterbewegun with the step length h/mc consistently introduces the limiting velocity c into the calculation, and removes a puzzle about dimensions from the Feynman results. By adopting the Wheeler-Feynman point of view that the energy and momenta of massless quanta are defined by the sources and sinks, the inhomogeneous Maxwell equations are derived from quantum particle physics - which Feynman was unable to do - and hence the classical electromagnetic theory was established as a well defined continuum approximation to the fully discrete relativistic quantum mechanics. Exploration of quantum gravity along these lines appears to be promising.
Reduze - Feynman Integral Reduction in C++
Studerus, C.
2009-01-01
Reduze is a computer program for reducing Feynman Integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic prefactors in the system of equations. Reduze offers the possibility to run reductions in parallel.
On analytic formulas of Feynman propagators in position space
Institute of Scientific and Technical Information of China (English)
ZHANG Hong-Hao; FENG Kai-Xi; QIU Si-Wei; ZHAO An; LI Xue-Song
2010-01-01
We correct an inaccurate result of previous work on the Feynman propagator in position space of a free Dirac field in(3+1)-dimensional spacetime; we derive the generalized analytic formulas of both the scalar Feynman propagator and the spinor Feynman propagator in position space in arbitrary(D+1)-dimensional spacetime; and we further find a recurrence relation among the spinor Feynman propagator in(D+l)-dimensional spacetime and the scalar Feynman propagators in(D+1)-,(D-1)-and(D+3)-dimensional spacetimes.
Remarks on the Origin of Path Integration: Einstein and Feynman
Sauer, Tilman
2008-01-01
I offer some historical comments about the origins of Feynman's path integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's thesis supervisor John Wheeler, it is argued that, contrary to what one might expect, the significance of the interaction between Einstein and Feynman pertained to a critique of classical field theory, rather than to a direct critique of quantum mechanics itself. Nevertheless, the critical perspective on classical field theory became a motivation and point of departure for Feynman's space-time approach to non-relativistic quantum mechanics.
Remarks on the Origin of Path Integration:. Einstein and Feynman
Sauer, T.
2008-11-01
I offer some historical comments about the origins of Feynman's path-integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's thesis supervisor John Wheeler, it is argued that, contrary to what one might expect, the significance of the interaction between Einstein and Feynman pertained to a critique of classical field theory, rather than to a direct critique of quantum mechanics itself. Nevertheless, the critical perspective on classical field theory became a motivation and point of departure for Feynman's space-time approach to non-relativistic quantum mechanics.
Oostrom, V. van
2008-01-01
We introduce the unifying notion of delimiting diagram. Hitherto unrelated results such as: Minimality of the internal needed strategy for orthogonal first-order term rewriting systems, maximality of the limit strategy for orthogonal higher-order pattern rewrite systems (with maximality of the strat
BOOK REVIEW: Feynman Lectures on Gravitation
Feynman, Richard P.; Morinigo, Fernando B.; Wagner, William G.
2003-05-01
In the early 1960s Feynman lectured to physics undergraduates and, with the assistance of his colleagues Leighton and Sands, produced the three-volume classic Feynman Lectures in Physics. These lectures were delivered in the mornings. In the afternoons Feynman was giving postgraduate lectures on gravitation. This book is based on notes compiled by two students on that course: Morinigo and Wagner. Their notes were checked and approved by Feynman and were available at Caltech. They have now been edited by Brian Hatfield and made more widely available. The book has a substantial preface by John Preskill and Kip Thorne, and an introduction entitled 'Quantum Gravity' by Brian Hatfield. You should read these before going on to the lectures themselves. Preskill and Thorne identify three categories of potential readers of this book. 1. Those with a postgraduate training in theoretical physics. 2. 'Readers with a solid undergraduate training in physics'. 3. 'Admirers of Feynman who do not have a strong physics background'. The title of the book is perhaps misleading: readers in category 2 who think that this book is an extension of the Feynman Lectures in Physics may be disappointed. It is not: it is a book aimed mainly at those in category 1. If you want to get to grips with gravitation (and general relativity) then you need to read an introductory text first e.g. General Relativity by I R Kenyon (Oxford: Oxford University Press) or A Unified Grand Tour of Theoretical Physics by Ian D Lawrie (Bristol: IoP). But there is no Royal Road. As pointed out in the preface and in the introduction, the book represents Feynman's thinking about gravitation some 40 years ago: the lecture course was part of his attempts to understand the subject himself, and for readers in all three categories it is this that makes the book one of interest: the opportunity to observe how a great physicist attempts to tackle some of the hardest challenges of physics. However, the book was written 40
Feynman Path Integrals Over Entangled States
Green, A G; Keeling, J; Simon, S H
2016-01-01
The saddle points of a conventional Feynman path integral are not entangled, since they comprise a sequence of classical field configurations. We combine insights from field theory and tensor networks by constructing a Feynman path integral over a sequence of matrix product states. The paths that dominate this path integral include some degree of entanglement. This new feature allows several insights and applications: i. A Ginzburg-Landau description of deconfined phase transitions. ii. The emergence of new classical collective variables in states that are not adiabatically continuous with product states. iii. Features that are captured in product-state field theories by proliferation of instantons are encoded in perturbative fluctuations about entangled saddles. We develop a general formalism for such path integrals and a couple of simple examples to illustrate their utility.
General consequences of the violated Feynman scaling
Kamberov, G.; Popova, L.
1985-01-01
The problem of scaling of the hadronic production cross sections represents an outstanding question in high energy physics especially for interpretation of cosmic ray data. A comprehensive analysis of the accelerator data leads to the conclusion of the existence of breaked Feynman scaling. It was proposed that the Lorentz invariant inclusive cross sections for secondaries of a given type approaches constant in respect to a breaked scaling variable x sub s. Thus, the differential cross sections measured in accelerator energy can be extrapolated to higher cosmic ray energies. This assumption leads to some important consequences. The distribution of secondary multiplicity that follows from the violated Feynman scaling using a similar method of Koba et al is discussed.
Lectures on differential equations for Feynman integrals
Henn, Johannes M
2014-01-01
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to differential equations for Feynman integrals, we point out how they can be simplified using algorithms available in the mathematical literature. We discuss how this is related to a recent conjecture for a canonical form of the equations. We also discuss a complementary approach that allows based on properties of the space-time loop integrands, and explain how the ideas of leading singularities and d-log representations can be used to find an optimal basis for the differential equations. Finally, as an application of the differential equations method we show how single-scale integrals can be bootstrapped using the Drinfeld associator of a differential equation.
Functional analysis and the Feynman operator calculus
Gill, Tepper L
2016-01-01
This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.
Quantum gravitation the Feynman path integral approach
Hamber, Herbert W
2009-01-01
The book covers the theory of Quantum Gravitation from the point of view of Feynman path integrals. These provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. The path integral method is suitable for both perturbative as well as non-perturbative studies, and is known to already provide a framework of choice for the theoretical investigation of non-abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The ren...
Quantum Measurement and Extended Feynman Path Integral
Institute of Scientific and Technical Information of China (English)
文伟; 白彦魁
2012-01-01
Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy, but there is still no conclusion and consensus on it. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein-Gordon equation, but also the wave-function-collapse equation. It is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the ＂potential noise＂ of the apparatus or environment and ＂inner correlation＂ of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem.
Efficient Numerical Evaluation of Feynman Integral
Li, Zhao; Yan, Qi-Shu; Zhao, Xiaoran
2016-01-01
Feynman loop integral is the key ingredient of high order radiation effect, which is responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing quasi-Monte Carlo method associated with the technique of CUDA/GPU. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in physical kinematic region can be evaluated in less than half minute with $\\mathcal{O}(10^{-3})$ accuracy, which makes the direct numerical approach viable for the precise investigation on the high order effect in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with finite top quark mass.
Generalizations of polylogarithms for Feynman integrals
Bogner, Christian
2016-10-01
In this talk, we discuss recent progress in the application of generalizations of polylogarithms in the symbolic computation of multi-loop integrals. We briefly review the Maple program MPL which supports a certain approach for the computation of Feynman integrals in terms of multiple polylogarithms. Furthermore we discuss elliptic generalizations of polylogarithms which have shown to be useful in the computation of the massive two-loop sunrise integral.
Feynman amplitudes and limits of heights
Amini, O.; Bloch, S. J.; Burgos Gil, J. I.; Fresán, J.
2016-10-01
We investigate from a mathematical perspective how Feynman amplitudes appear in the low-energy limit of string amplitudes. In this paper, we prove the convergence of the integrands. We derive this from results describing the asymptotic behaviour of the height pairing between degree-zero divisors, as a family of curves degenerates. These are obtained by means of the nilpotent orbit theorem in Hodge theory.
Remarks on Wheeler-Feynman absorber theory
Gründler, Gerold
2014-01-01
The derivation of absorber theory is outlined in very detail. Absorber theory is based on classical action-at-a-distance electrodynamics, but it deviates from that theory at a crucial point. It is shown that (a) absorber theory cannot achieve any of it's essential results without this deviation, and that (b) this deviation restricts the application range of absorber theory to stationary radiation processes. Furthermore an error which crept into Wheeler's and Feynman's interpretation of their ...
Djorgovski, S.; Murdin, P.
2000-11-01
Initially introduced as a way to demonstrate the expansion of the universe, and subsequently to determine the expansion rate (the HUBBLE CONSTANT H0), the Hubble diagram is one of the classical cosmological tests. It is a plot of apparent fluxes (usually expressed as magnitudes) of some types of objects at cosmological distances, against their REDSHIFTS. It is used as a tool to measure the glob...
A complete algebraic reduction of one-loop tensor Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Fleischer, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2010-09-15
Guided by the need to eliminate inverse Gram determinants (){sub 5} from tensorial 5-point functions and sub-Gram determinants (){sub 4} from tensorial 4-point functions, we set up a new and very efficient approach for the tensor reduction of Feynman integrals. We eliminate all Gram determinants for one-loop 5-point integrals up to tensors of rank R=5 by reducing their tensor coefficients to higherdimensional 4-point tensor coefficients. These in turn are reduced to expressions which are free of inverse powers of (){sub 4}, but depend on higher-dimensional integrals I{sub 4}{sup (d)} with d{<=}2R. Their expression in terms of scalar integrals defined in the generic dimension, I{sub 4}; I{sub 3}; I{sub 2}; I{sub 1}, however, introduces coefficients [1=(){sub 4}]{sup R} for tensors of rank R. For small or vanishing (){sub 4}, an efficient expansion is found so that a stable numerical evaluation of massive and massless Feynman integrals at arbitrary values of the Gram determinants is made possible. Finally, some relations are mentioned which may be useful for analytic simplifications of the original Feynman diagrams. (orig.)
Coupled oscillators and Feynman's three papers
Kim, Y. S.
2007-05-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the "rest of the universe" contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.
Feynman graph polynomials and iterative algorithms
Energy Technology Data Exchange (ETDEWEB)
Bogner, Christian [Johannes Gutenberg-Universitaet, Mainz (Germany)
2009-07-01
I briefly report on recent work with Stefan Weinzierl, where we have proven a theorem, stating that the Laurent coefficients of scalar Feynman integrals are periods in the sense of Kontsevich and Zagier, if they are evaluated at kinematical invariants taking rational values in Euclidean momentum space. Our proof uses the (extended) sector decomposition algorithm by Binoth and Heinrich. Our result is related to the appearance of multiple zeta values in coefficients of Feynman integrals which has recently been investigated by Francis Brown, using another iterative algorithm. Both of these algorithms apply to the Feynman parametric representation of the integral and perform iterative manipulations of the polynomials in the integrand, which originate from the Symanzik polynomials. Motivated by the success of these methods I give a brief review on some more and some less well-known combinatorial properties of Symanzik polynomials. I focus on their accessibility to generalized theorems of the matrix-tree type and their relation to the multivariate Tutte polynomial.
Coupled oscillators and Feynman's three papers
Kim, Y S
2006-01-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the ``rest of the universe'' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be c...
The pointwise Hellmann-Feynman theorem
Directory of Open Access Journals (Sweden)
David Carfì
2010-02-01
Full Text Available In this paper we study from a topological point of view the Hellmann-Feynman theorem of Quantum Mechanics. The goal of the paper is twofold: On one hand we emphasize the role of the strong topology in the classic version of the theorem in Hilbert spaces, for what concerns the kind of convergence required on the space of continuous linear endomorphisms, which contains the space of (continuous observables.On the other hand we state and prove a new pointwise version of the classic Hellmann-Feynman theorem. This new version is not yet present in the literature and follows the idea of A. Bohm concerning the topology which is desiderable to use in Quantum Mechanics. It is indeed out of question that this non-trivial new version of the Hellmann-Feynman theorem is the ideal one - for what concerns the continuous observables on Hilbert spaces, both from a theoretical point of view, since it is the strongest version obtainable in this context - we recall that the pointwise topology is the coarsest one compatible with the linear structure of the space of continuous observables -, and from a practical point of view, because the pointwise topology is the easiest to use among topologies: it brings back the problems to the Hilbert space topology. Moreover, we desire to remark that this basic theorem of Quantum Mechanics, in his most desiderable form, is deeply interlaced with two cornerstones of Functional Analysis: the Banach-Steinhaus theorem and the Baire theorem.
Baikov, P A
2000-01-01
We show that the problem of solving recurrence relations for L-loop (R+1)-point Feynman integrals within the method of integration by parts is equivalent to the corresponding problem for (L+R)-loop vacuum or (L+R-1)-loop propagator-type integrals. Using this property we solve recurrence relations for two-loop massless vertex diagrams, with arbitrary numerators and integer powers of propagators in the case when two legs are on the light cone, by reducing the problem to the well-known solution of the corresponding recurrence relations for massless three-loop propagator diagrams with specific boundary conditions.
Gluza, J.; Kajda, K.; Riemann, T.
2007-12-01
The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4-2ɛ dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. The package uses a loop-by-loop approach and aims at lowest dimensions of the final MB representations. The present version works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in ɛ. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops. Program summaryProgram title:AMBRE Catalogue identifier:ADZR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZR_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:21 387 No. of bytes in distributed program, including test data, etc.:100 004 Distribution format:tar.gz Programming language:MATHEMATICA v.5.0 and later versions Computer:all Operating system:all RAM:sufficient for a typical installation of MATHEMATICA Classification:5; 11.1 External routines:The examples in the package use: MB.m [M. Czakon, Comput. Phys. Commun. 175 (2006) 559 (CPC Cat. Id. ADYG)], for expansions in ɛ; CUBA [T. Hahn, Comput. Phys. Commun. 168 (2005) 78 (CPC Cat. Id. ADVH)], for numerical evaluation of multidimensional integrals; CERNlib [CERN Program Library, http://cernlib.web.cern.ch/cernlib/], for the implementation of Γ and Ψ functions in Fortran. Nature of problem:Derivation of a representation for a Feynman diagram with L loops and N internal lines in d dimensions by Mellin-Barnes integrals; the subsequent evaluation, after an analytical continuation in ɛ=(4-d)/2, has to be done with other packages. Solution method:Introduction of N Feynman parameters x
Feynman integral and perturbation theory in quantum tomography
Fedorov, Aleksey
2013-11-01
We present a definition for tomographic Feynman path integral as representation for quantum tomograms via Feynman path integral in the phase space. The proposed representation is the potential basis for investigation of Path Integral Monte Carlo numerical methods with quantum tomograms. Tomographic Feynman path integral is a representation of solution of initial problem for evolution equation for tomograms. The perturbation theory for quantum tomograms is constructed.
Richard Feynman a life in science
Gribbin, John
1998-01-01
This text is a portrayal of one of the greatest scientists of the late 20th-century, which also provides a picture of the significant physics of the period. It combines personal anecdotes, writings and recollections with narrative. Richard Feynman's career included: war-time work on the atomic bomb at Los Alamos; a theory of quantum mechanics for which he won the Nobel prize; and major contributions to the sciences of gravity, nuclear physics and particle theory. In 1986, he was able to show that the Challenger disaster was due to the effect of cold on the booster rocket rubber sealings.
Counting statistics: a Feynman-Kac perspective.
Zoia, A; Dumonteil, E; Mazzolo, A
2012-01-01
By building upon a Feynman-Kac formalism, we assess the distribution of the number of collisions in a given region for a broad class of discrete-time random walks in absorbing and nonabsorbing media. We derive the evolution equation for the generating function of the number of collisions, and we complete our analysis by examining the moments of the distribution and their relation to the walker equilibrium density. Some significant applications are discussed in detail: in particular, we revisit the gambler's ruin problem and generalize to random walks with absorption the arcsine law for the number of collisions on the half-line.
Tempered Fractional Feynman-Kac Equation
Wu, Xiaochao; Barkai, Eli
2016-01-01
Functionals of Brownian/non-Brownian motions have diverse applications and attracted a lot of interest of scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.
Reiff, Patricia H.; Feynman, Joan; Gold, Thomas; Wasserburg, G. J.; Sheeley, Neil R., Jr.; Akasofu, S.-I.
1988-01-01
Richard Feynman, simply put, was a genius. His quick wit and uncommon grasp of physics meant that any research area he encountered, he quickly mastered. Despite the fact that his own area of research was not geophysics, his life and work influenced almost all of us. Virtually every physics graduate student who started in the mid 60s or later was exposed to his Lectures on Physics, either by having them as a text for a course or by using them (as I did) to bone up for oral qualifying exams...
An Introduction into the Feynman Path Integral
Grosche, C
1993-01-01
In this lecture a short introduction is given into the theory of the Feynman path integral in quantum mechanics. The general formulation in Riemann spaces will be given based on the Weyl- ordering prescription, respectively product ordering prescription, in the quantum Hamiltonian. Also, the theory of space-time transformations and separation of variables will be outlined. As elementary examples I discuss the usual harmonic oscillator, the radial harmonic oscillator, and the Coulomb potential. Lecture given at the graduate college ''Quantenfeldtheorie und deren Anwendung in der Elementarteilchen- und Festk\\"orperphysik'', Universit\\"at Leipzig, 16-26 November 1992.
Remarks on Wheeler-Feynman absorber theory
Gründler, Gerold
2015-01-01
The derivation of absorber theory is outlined in very detail. Absorber theory is based on classical action-at-a-distance electrodynamics, but it deviates from that theory at a crucial point. It is shown that (a) absorber theory cannot achieve any of it's essential results without this deviation, and that (b) this deviation restricts the application range of absorber theory to stationary radiation processes. Furthermore an error which crept into Wheeler's and Feynman's interpretation of their equation (19) is pointed out. These shortcomings can probably be eliminated by a quantum-theoretical formulation of absorber theory.
Modern Feynman Diagrammatic One-Loop Calculations
Reiter, Thomas; Greiner, Nicolas; Guffanti, Alberto; Guillet, Jean-Philippe; Heinrich, Gudrun; Karg, Stefan; Kauer, Nikolas; Kleinschmidt, Tobias; Koch-Janusz, Maciej; Luisoni, Gionata; Mastrolia, Pierpaolo; Ossola, Giovanni; Pilon, Eric; Rodgers, Mark; Tramontano, Francesco; Wigmore, Ioan
2010-01-01
In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation. In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation. As an application of our approach we report on the status of the calculation of the amplitude for the process $pp\\to b\\bar{b}b\\bar{b}+X$.
A Note on Dual MHV Diagrams in N=4 SYM
Brandhuber, Andreas; Travaglini, Gabriele; Yang, Gang
2010-01-01
Recently a reformulation of the MHV diagram method in N=4 supersymmetric Yang-Mills theory in momentum twistor space was presented and was shown to be equivalent to the perturbative expansion of the expectation value of a supersymmetric Wilson loop in momentum twistor space. In this note we present related explicit Feynman rules in dual momentum space, which should have the interpretation of Wilson loop diagrams in dual momentum space. We show that these novel rules are completely equivalent to ordinary spacetime MHV rules and can be naturally viewed as their graph dual representation.
Feynman's and Ohta's Models of a Josephson Junction
De Luca, R.
2012-01-01
The Josephson equations are derived by means of the weakly coupled two-level quantum system model given by Feynman. Adopting a simplified version of Ohta's model, starting from Feynman's model, the strict voltage-frequency Josephson relation is derived. The contribution of Ohta's approach to the comprehension of the additional term given by the…
A convergence theorem for asymptotic expansions of Feynman amplitudes
Energy Technology Data Exchange (ETDEWEB)
Mabouisson, A.P.C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1999-06-01
The Mellin representations of Feynman integrals is revisited. From this representation, and asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to {infinity}, may be obtained. In the case of all masses going to zero in Euclidean metric, we show that the truncated expansion has a rest compatible with convergence of the series. (author)
The Making of a Genius: Richard P. Feynman
Forstner, Christian
2012-01-01
In 1965 the Nobel Foundation honored Sin-Itiro Tomonaga, Julian Schwinger, and Richard Feynman for their fundamental work in quantum electrodynamics and the consequences for the physics of elementary particles. In contrast to both of his colleagues only Richard Feynman appeared as a genius before the public. In his autobiographies he managed to connect his behavior, which contradicted several social and scientific norms, with the American myth of the "practical man". This connection led to the image of a common American with extraordinary scientific abilities and contributed extensively to enhance the image of Feynman as genius in the public opinion. Is this image resulting from Feynman's autobiographies in accordance with historical facts? This question is the starting point for a deeper historical analysis that tries to put Feynman and his actions back into historical context. The image of a "genius" appears then as a construct resulting from the public reception of brilliant scientific research.
Le cours de physique de Feynman
Feynman, Richard; Sands, Matthew
L’ampleur du succès qu’a rencontré le « Cours de physique de Feynman » dès sa parution s’explique par son caractère fondamentalement novateur. Richard Feynman, qui fut professeur d’université dès l’âge de vingt-quatre ans, a exprimé dans ce cours, avant d’obtenir le prix Nobel de Physique, une vision expérimentale et extrêmement personnelle de l’enseignement de la physique. Cette vision a, depuis, remporté l’adhésion des physiciens du monde entier, faisant de cet ouvrage un grand classique. Ce cours en cinq volumes (Électromagnétisme 1 et 2, Mécanique 1 et 2, Mécanique quantique) s’adresse aux étudiants de tous niveaux qui y trouveront aussi bien les notions de base débarrassées de tout appareil mathématique inutile, que les avancées les plus modernes de cette science passionnante qu’est la physique. Cette nouvelle édition corrigée bénéficie d’une mise en page plus aérée pour un meilleur confort de lecture.
Efficient numerical evaluation of Feynman integrals
Li, Zhao; Wang, Jian; Yan, Qi-Shu; Zhao, Xiaoran
2016-03-01
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass. Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)
Quadratic forms for Feynman-Kac semigroups
Energy Technology Data Exchange (ETDEWEB)
Hibey, Joseph L. [Department of Electrical Engineering, University of Colorado at Denver, Campus Box 110, Denver, CO 80217 (United States)]. E-mail: joseph.hibey@cudenver.edu; Charalambous, Charalambos D. [Electrical and Computer Engineering Department, University of Cyprus, 75 Kallipoleos Avenue, Nicosia (Cyprus)]. E-mail: chadcha@ucy.ac.cy
2006-05-15
Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions.
Wheeler & Feynman's Response of the Universe, revisited
Wolff, Milo
2003-04-01
In a famous 1945 paper Wheeler and Feynman (1) sought the cause of radiation from an accelerated electron. They assumed that acceleration produced an electromagnetic wave pulse from the electron that caused responding waves from static point-particle absorbers in the universe. Problems arose with possible violation of causality by waves that begin before their cause. This paper points out that a rigorous logical solution is obtained (2) when the electron is a dynamic structure of two scalar quantum waves. The scalar wave equation produces two such inward and outward spherical waves. The two waves combined have complete properties of positrons and electrons and the natural laws. Thus the problem is resolved by replacing the point particle with a scalar quantum wave structure (3). ... The conclusion: The universe and the laws of nature are inter-connected by co-mingled matter waves. Thus if the stars did not exist, it would be meaningless to think that we could exist. 1) Wheeler & Feynman, RMP, 17, 157 (1945). 2) Wolff, Gravition and Cosmology, Kluwer Acad. Publ. (2002). 3) www.QuantumMatter.com
Algebraic renormalization and Feynman integrals in configuration spaces
Ceyhan, Ozgur
2013-01-01
This paper continues our previous study of Feynman integrals in configuration spaces and their algebro-geometric and motivic aspects. We consider here both massless and massive Feynman amplitudes, from the point of view of potential theory. We consider a variant of the wonderful compactification of configuration spaces that works simultaneously for all graphs with a given number of vertices and that also accounts for the external structure of Feynman graph. As in our previous work, we consider two version of the Feynman amplitude in configuration space, which we refer to as the real and complex versions. In the real version, we show that we can extend to the massive case a method of evaluating Feynman integrals, based on expansion in Gegenbauer polynomials, that we investigated previously in the massless case. In the complex setting, we show that we can use algebro-geometric methods to renormalize the Feynman amplitudes, so that the renormalized values of the Feynman integrals are given by periods of a mixed ...
Einstein, Wigner, and Feynman From E = mc^{2} to Feynman's decoherence via Wigner's little groups
Kim, Y S
2003-01-01
The 20th-century physics starts with Einstein and ends with Feynman. Einstein introduced the Lorentz-covariant world with E = mc^{2}. Feynman observed that fast-moving hadrons consist of partons which act incoherently with external signals. If quarks and partons are the same entities observed in different Lorentz frames, the question then is why partons are incoherent while quarks are coherent. This is the most puzzling question Feynman left for us to solve. In this report, we discuss Wigner's role in settling this question. Einstein's E = mc^{2}, which takes the form E = \\sqrt{m^{2} + p^{2}}, unifies the energy-momentum relations for massive and massless particles, but it does not take into account internal space-time structure of relativistic particles. It is pointed out Wigner's 1939 paper on the inhomogeneous Lorentz group defines particle spin and gauge degrees of freedom in the Lorentz-covariant world. Within the Wigner framework, it is shown possible to construct the internal space-time structure for h...
The Feynman Identity for Planar Graphs
da Costa, G. A. T. F.
2016-08-01
The Feynman identity (FI) of a planar graph relates the Euler polynomial of the graph to an infinite product over the equivalence classes of closed nonperiodic signed cycles in the graph. The main objectives of this paper are to compute the number of equivalence classes of nonperiodic cycles of given length and sign in a planar graph and to interpret the data encoded by the FI in the context of free Lie superalgebras. This solves in the case of planar graphs a problem first raised by Sherman and sets the FI as the denominator identity of a free Lie superalgebra generated from a graph. Other results are obtained. For instance, in connection with zeta functions of graphs.
Feynman propagator for spin foam quantum gravity.
Oriti, Daniele
2005-03-25
We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".
Unbounded random operators and Feynman formulae
Orlov, Yu. N.; Sakbaev, V. Zh.; Smolyanov, O. G.
2016-12-01
We introduce and study probabilistic interpolations of various quantization methods. To do this, we develop a method for finding the expectations of unbounded random operators on a Hilbert space by averaging (with the help of Feynman formulae) the random one-parameter semigroups generated by these operators (the usual method for finding the expectations of bounded random operators is generally inapplicable to unbounded ones). Although the averaging of families of semigroups generates a function that need not possess the semigroup property, the Chernoff iterates of this function approximate a certain semigroup, whose generator is taken for the expectation of the original random operator. In the case of bounded random operators, this expectation coincides with the ordinary one.
A Causal Alternative to Feynman's Propagator
Koksma, Jurjen F
2010-01-01
The Feynman propagator used in the conventional in-out formalism in quantum field theory is not a causal propagator as wave packets are propagated virtually instantaneously outside the causal region of the initial state. We formulate a causal in-out formalism in quantum field theory by making use of the Wheeler propagator, the time ordered commutator propagator, which is manifestly causal. Only free scalar field theories and their first quantization are considered. We identify the real Klein Gordon field itself as the wave function of a neutral spinless relativistic particle. Furthermore, we derive a probability density for our relativistic wave packet using the inner product between states that live on a suitably defined Hilbert space of real quantum fields. We show that the time evolution of our probability density is governed by the Wheeler propagator, such that it behaves causally too.
From State Diagram to Class Diagram
DEFF Research Database (Denmark)
Borch, Ole; Madsen, Per Printz
2009-01-01
UML class diagram and Java source code are interrelated and Java code is a kind of interchange format. Working with UML state diagram in CASE tools, a corresponding xml file is maintained. Designing state diagrams is mostly performed manually using design patterns and coding templates - a time...
Quantum cosmology based on discrete Feynman paths
Energy Technology Data Exchange (ETDEWEB)
Chew, Geoffrey F.
2002-10-10
Although the rules for interpreting local quantum theory imply discretization of process, Lorentz covariance is usually regarded as precluding time quantization. Nevertheless a time-discretized quantum representation of redshifting spatially-homogeneous universe may be based on discrete-step Feynman paths carrying causal Lorentz-invariant action--paths that not only propagate the wave function but provide a phenomenologically-promising elementary-particle Hilbert-space basis. In a model under development, local path steps are at Planck scale while, at a much larger ''wave-function scale'', global steps separate successive wave-functions. Wave-function spacetime is but a tiny fraction of path spacetime. Electromagnetic and gravitational actions are ''at a distance'' in Wheeler-Feynman sense while strong (color) and weak (isospin) actions, as well as action of particle motion, are ''local'' in a sense paralleling the action of local field theory. ''Nonmaterial'' path segments and ''trivial events'' collaborate to define energy and gravity. Photons coupled to conserved electric charge enjoy privileged model status among elementary fermions and vector bosons. Although real path parameters provide no immediate meaning for ''measurement'', the phase of the complex wave function allows significance for ''information'' accumulated through ''gentle'' electromagnetic events involving charged matter and ''soft'' photons. Through its soft-photon content the wave function is an ''information reservoir''.
A Model for Bilingual Physics Teaching: "The Feynman Lectures "
Metzner, Heqing W.
2006-12-01
Feynman was not only a great physicist but also a remarkably effective educator. The Feynman Lectures on Physics originally published in 1963 were designed to be GUIDES for teachers and for gifted students. More than 40 years later, his peculiar teaching ideas have special application to bilingual physics teaching in China because: (1) Each individual lecture provides a self contained unit for bilingual teaching; (2)The lectures broaden the physics understanding of students; and (3)Feynman's original thought in English is experienced through the bilingual teaching of physics.
Feynman's lost lecture the motion of planet's around the sun
Goodstein, David L
1997-01-01
On 14 March 1964 Richard Feynman, one of the greatest scientific thinkers of the 20th Century, delivered a lecture entitled 'The Motion of the Planets Around the Sun'. For thirty years this remarkable lecture was believed to be lost. But now Feynman's work has been reconstructed and explained in meticulous, accessible detail, together with a history of ideas of the planets' motions. The result is a vital and absorbing account of one of the fundamental puzzles of science, and an invaluable insight into Feynman's charismatic brilliance.
The physics and the mixed Hodge structure of Feynman integrals
Vanhove, Pierre
2014-01-01
This expository text is an invitation to the relation between quantum field theory Feynman integrals and periods. We first describe the relation between the Feynman parametrization of loop amplitudes and world-line methods, by explaining that the first Symanzik polynomial is the determinant of the period matrix of the graph, and the second Symanzik polynomial is expressed in terms of world-line Green's functions. We then review the relation between Feynman graphs and variations of mixed Hodge structures. Finally, we provide an algorithm for generating the Picard-Fuchs equation satisfied by the all equal mass banana graphs in a two-dimensional space-time to all loop orders.
Feynman rules of higher-order poles in CHY construction
Huang, Rijun; Feng, Bo; Luo, Ming-xing; Zhu, Chuan-Jie
2016-06-01
In this paper, we generalize the integration rules for scattering equations to situations where higher-order poles are present. We describe the strategy to deduce the Feynman rules of higher-order poles from known analytic results of simple CHY-integrands, and propose the Feynman rules for single double pole and triple pole as well as duplex-double pole and triplex-double pole structures. We demonstrate the validation and strength of these rules by ample non-trivial examples.
On hyperlogarithms and Feynman integrals with divergences and many scales
Erik Panzer
2014-01-01
Hyperlogarithms provide a tool to carry out Feynman integrals in Schwinger parameters. So far, this method has been applied successfully mostly to finite single-scale processes. However, it can be employed in more general situations. We give examples of integrations of three- and four-point integrals in Schwinger parameters with non-trivial kinematic dependence, including setups with off-shell external momenta and differently massive internal propagators. The full set of Feynman graphs admiss...
The Making of a Genius: Richard P. Feynman
Forstner, Christian
2012-01-01
In 1965 the Nobel Foundation honored Sin-Itiro Tomonaga, Julian Schwinger, and Richard Feynman for their fundamental work in quantum electrodynamics and the consequences for the physics of elementary particles. In contrast to both of his colleagues only Richard Feynman appeared as a genius before the public. In his autobiographies he managed to connect his behavior, which contradicted several social and scientific norms, with the American myth of the "practical man". This connection led to th...
Solutions of the Wheeler-Feynman equations with discontinuous velocities
de Souza, Daniel Câmara; De Luca, Jayme
2014-01-01
We generalize Wheeler-Feynman electrodynamics with a variational boundary-value problem with past and future boundary segments that can include velocity discontinuity points. Critical-point trajectories must satisfy the Euler-Lagrange equations of the action functional, which are neutral-differential delay equations of motion (the Wheeler-Feynman equations of motion). At velocity discontinuity points, critical-point orbits must satisfy the Weierstrass-Erdmann conditions of continuity of parti...
Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
Energy Technology Data Exchange (ETDEWEB)
Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2010-10-15
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)
Muldowney, Patrick
2012-01-01
A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. I...
Cuts and coproducts of massive triangle diagrams
Energy Technology Data Exchange (ETDEWEB)
Abreu, Samuel [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Mayfield Road, Edinburgh EH9 3JZ, Scotland (United Kingdom); Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers, F-91191 Gif-sur-Yvette (France); Britto, Ruth [Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers, F-91191 Gif-sur-Yvette (France); School of Mathematics, Trinity College,College Green, Dublin 2 (Ireland); Hamilton Mathematical Institute, Trinity College,College Green, Dublin 2 (Ireland); Grönqvist, Hanna [Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers, F-91191 Gif-sur-Yvette (France)
2015-07-21
Relations between multiple unitarity cuts and coproducts of Feynman integrals are extended to allow for internal masses. These masses introduce new branch cuts, whose discontinuities can be derived by placing single propagators on shell and identified as particular entries of the coproduct. First entries of the coproduct are then seen to include mass invariants alone, as well as threshold corrections for external momentum channels. As in the massless case, the original integral can possibly be recovered from its cuts by starting with the known part of the coproduct and imposing integrability contraints. We formulate precise rules for cuts of diagrams, and we gather evidence for the relations to coproducts through a detailed study of one-loop triangle integrals with various combinations of external and internal masses.
Kastening
2000-04-01
The free energy of a multicomponent scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys nonlinear functional differential equations which are turned into recursion relations for the connected Green's functions in a loop expansion. These relations amount to a simple proof that W[G,J] generates only connected graphs and can be used to find all such graphs with their combinatoric weights. A Legendre transformation with respect to the external current converts the functional differential equations for the free energy into those for the effective energy Gamma[G,Phi], which is considered as a functional of the free correlation function G and the field expectation Phi. These equations are turned into recursion relations for the one-particle irreducible Green's functions. These relations amount to a simple proof that Gamma[G,J] generates only one-particle irreducible graphs and can be used to find all such graphs with their combinatoric weights. The techniques used also allow for a systematic investigation into resummations of classes of graphs. Examples are given for resumming one-loop and multiloop tadpoles, both through all orders of perturbation theory. Since the functional differential equations derived are nonperturbative, they constitute also a convenient starting point for other expansions than those in numbers of loops or powers of coupling constants. We work with general interactions through four powers in the field.
Feynman Diagrams, Problem Spaces, and the Kuhnian Revolution to Come in Teacher Education
Seltzer-Kelly, Deborah
2013-01-01
A blue-ribbon panel convened by the National Council for Accreditation of Teacher Education (NCATE) concluded in 2010 that teacher education in the United States must be "turned upside down," with practical experience at its center and academic content woven around the practical. It might seem that the new clinical model based on medical…
From special relativity to Feynman diagrams a course of theoretical particle physics for beginners
D'Auria, Riccardo
2016-01-01
This book, now in its second edition, provides an introductory course on theoretical particle physics with the aim of filling the gap that exists between basic courses of classical and quantum mechanics and advanced courses of (relativistic) quantum mechanics and field theory. After a concise but comprehensive introduction to special relativity, key aspects of relativistic dynamics are covered and some elementary concepts of general relativity introduced. Basics of the theory of groups and Lie algebras are explained, with discussion of the group of rotations and the Lorentz and Poincaré groups. In addition, a concise account of representation theory and of tensor calculus is provided. Quantization of the electromagnetic field in the radiation range is fully discussed. The essentials of the Lagrangian and Hamiltonian formalisms are reviewed, proceeding from systems with a finite number of degrees of freedom and extending the discussion to fields. The final four chapters are devoted to development of the quant...
From Special Relativity to Feynman Diagrams A Course of Theoretical Particle Physics for Beginners
D'Auria, Riccardo
2012-01-01
This books aims at filling a gap between the basics courses of classical and quantum mechanics and advanced courses of (relativistic) quantum mechanics and field theory. Particular emphasis is given to the role of symmetry in modern theoretical physics. For this reason this book is particularly suited to those students who are interested in a deeper knowledge of modern developments in elementary particle physics and relativity, even if they choose not to specialize in this branch of research. This target of readers includes, besides experimental and applied physicists, also those engineers who need advanced notions of theoretical high energy physics, in view of future research activity in the field theory approach to condensed matter, in accelerator physics and in all those modern technology sectors which require a more advanced and sophisticated theoretical physics background. Courses motivated by these objectives are present in several polytechnic institutes around the world. The last chapters of this book,...
S-Matrix and Feynman Space-Time Diagrams to Quantum Brain Approach. An Extended Proposal
National Research Council Canada - National Science Library
Erol Basar
2009-01-01
.... In order to analyze scattering processes at the level of elementary particles Werner Heisenberg proposed the use of the so-called S-Matrix to understand nuclear interactions by studying ingoing at outgoing particles...
Algebraic reduction of one-loop Feynman diagrams to scalar integrals. Pt 2. [LERG-I
Energy Technology Data Exchange (ETDEWEB)
Stuart, R.G. (Centro de Investigacion y Estudios Avanzados, Dept. di Fisica, Mexico City (Mexico)); Gongora-T, A. (Universidad Nacional Autonoma de Mexico, Inst. de Fisica, Mexico City (Mexico))
1990-01-01
An extended scheme for the reduction of one-loop form factors occurring in a general gauged quantum field theory to scalar integrals is discussed and an alternative method that may be applied in the case when the scheme fails is indicated. The extensions are implemented in a new version of the package LERG-I, written in REDUCE. (orig.).
One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
Energy Technology Data Exchange (ETDEWEB)
Ellis, R. Keith [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Kunszt, Zoltan [Institute for Theoretical Physics (Switzerland); Melnikov, Kirill [Johns Hopkins Univ., Baltimore, MD (United States); Zanderighi, Giulia [Rudolf Peierls Centre for Theoretical Physics (United Kingdom)
2012-09-01
The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard scattering well. Extrapolating this observation to the LHC, we conclude that knowledge of many short-distance processes at next-to-leading order may be required to describe the physics of hard scattering. While the field of one-loop computations is quite mature, parton multiplicities in hard LHC events are so high that traditional computational techniques become inefficient. Recently new approaches based on unitarity have been developed for calculating one-loop scattering amplitudes in quantum field theory. These methods are especially suitable for the description of multi-particle processes in QCD and are amenable to numerical implementations. We present a systematic pedagogical description of both conceptual and technical aspects of the new methods.
Herzog, Franz; Ueda, Takahiro; Vermaseren, J A M; Vogt, Andreas
2016-01-01
We discuss a number of FORM features that are essential in the automatic processing of very large numbers of diagrams as used in the Forcer program for 4-loop massless propagator diagrams. Most of these features are new.
Extrinsic Curvature Embedding Diagrams
Lu, J L
2003-01-01
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\\it extrinsic} curvature (instead of the intrinsic curvature). Such an extrinsic curvature embedding diagram, when used together with the usual kind of intrinsic curvature embedding diagram, carries the information of how a surface is {\\it embedded} in the higher dimensional curved space. Simple examples are given to illustrate the idea.
Feynman's operational calculus and beyond noncommutativity and time-ordering
Johnson, George W; Nielsen, Lance
2015-01-01
This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections wi...
Mathematical theory of Feynman path integrals an introduction
Albeverio, Sergio A; Mazzucchi, Sonia
2008-01-01
Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
On Feynman's Approach to the Foundations of Gauge Theory
Land, M C; Horwitz, L P
1993-01-01
In 1948, Feynman showed Dyson how the Lorentz force and Maxwell equations could be derived from commutation relations coordinates and velocities. Several authors noted that the derived equations are not Lorentz covariant and so are not the standard Maxwell theory. In particular, Hojman and Shepley proved that the existence of commutation relations is a strong assumption, sufficient to determine the corresponding action, which for Feynman's derivation is of Newtonian form. Tanimura generalized Feynman's derivation to a Lorentz covariant form, however, this derivation does not lead to the standard Maxwell theory either. Tanimura's force equation depends on a fifth ({\\it scalar}) electromagnetic potential, and the invariant evolution parameter cannot be consistently identified with the proper time of the particle motion. Moreover, the derivation cannot be made reparameterization invariant; the scalar potential causes violations of the mass-shell constraint which this invariance should guarantee. In this paper, w...
Solutions of the Wheeler-Feynman equations with discontinuous velocities
de Souza, Daniel Câmara
2014-01-01
We generalize Wheeler-Feynman electrodynamics with a variational boundary-value problem having boundary conditions in past and future. The extended variational problem accepts trajectories with discontinuous velocities as critical points of the action functional. Critical-point trajectories must satisfy the Euler-Lagrange equations of the action functional, which are neutral-differential delay equations of motion. Moreover, at velocity discontinuity points critical-point orbits must satisfy the Weierstrass-Erdmann corner conditions of continuity of the partial momenta and partial energies. We study a special class of boundary data having the shortest time-separation between boundary segments, for which case the Wheeler-Feynman equations reduce to a two-point boundary problem for an ordinary differential equation. For this simple case we prove that solutions of the Wheeler-Feynman equations can have discontinuous velocities. We construct a numerical method to find critical-point orbits with a shooting method f...
Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction
Abreu, Samuel; Britto, Ruth; Duhr, Claude; Gardi, Einan
2017-08-01
We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It reduces to the known coaction on multiple polylogarithms, but applies more generally, e.g., to hypergeometric functions. The coaction also applies to generic one-loop Feynman integrals with any configuration of internal and external masses, and in dimensional regularization. In this case, we demonstrate that it can be given a diagrammatic representation purely in terms of operations on graphs, namely, contractions and cuts of edges. The coaction gives direct access to (iterated) discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they admit. In particular, the differential equations for any one-loop integral are determined by the diagrammatic coaction using limited information about their maximal, next-to-maximal, and next-to-next-to-maximal cuts.
Nanofabrication and the realization of Feynman's two-slit experiment
Frabboni, Stefano; Gazzadi, Gian Carlo; Pozzi, Giulio
2008-08-01
Two nanosized slits are opened by focused ion beam milling in a membrane to observe, with a transmission electron microscope, electron interference fringes. Then, on the same sample, one of the slits is closed by focused ion beam induced deposition and the corresponding transmitted intensity is recorded. The comparison between the two measurements provides an impressive experimental evidence of the probability amplitude of quantum mechanics following step by step the original idea proposed by Feynman [The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1966), Vol. 3, Chap. 1].
Deterministic Smoluchowski-Feynman ratchets driven by chaotic noise.
Chew, Lock Yue
2012-01-01
We have elucidated the effect of statistical asymmetry on the directed current in Smoluchowski-Feynman ratchets driven by chaotic noise. Based on the inhomogeneous Smoluchowski equation and its generalized version, we arrive at analytical expressions of the directed current that includes a source term. The source term indicates that statistical asymmetry can drive the system further away from thermodynamic equilibrium, as exemplified by the constant flashing, the state-dependent, and the tilted deterministic Smoluchowski-Feynman ratchets, with the consequence of an enhancement in the directed current.
Criticism of Feynman's analysis of the ratchet as an engine
Parrondo, Juan M. R.; Español, Pep
1996-09-01
The well-known discussion on an engine consisting of a ratchet and a pawl in [R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1963), Vol. 1, pp. 46.1-46.9] is shown to contain some misguided aspects: Since the engine is simultaneously in contact with reservoirs at different temperatures, it can never work in a reversible way. As a consequence, the engine can never achieve the efficiency of a Carnot cycle, not even in the limit of zero power (infinitely slow motion), in contradiction with the conclusion reached in the Lectures.
Formulation and justification of the Wheeler-Feynman absorber theory
Schulman, L. S.
1980-12-01
The “absorber theory” of Wheeler and Feynman is supposed to justify the use of retarded potentials in ordinary electromagnetic calculations despite a fundamentally time symmetric interaction. We restate the thesis of absorber theory as follows: here exist causal solutions of time symmetric electrodynamics. In our formulation, absorption need only take place in one direction of time (the future) rather than both, as seems to be required by Wheeler and Feynman. Even with complete absorption, however, the effects of advanced interactions are not entirely eliminated and a residual field may introduce a degree of indeterminacy into particle trajectories obtained using retarded potentials alone.
The asymmetry of radiation: Reinterpreting the Wheeler-Feynman argument
Price, Huw
1991-08-01
This paper suggests a novel reinterpretation of the mathematical core of Wheeler-Feynman absorber theory, and hence a new route to the conclusion that the temporal asymmetry of classical electromagnetic radiation has the same origin as that of thermodynamics. The argument begins (Sec. 2) with a careful analysis of what the apparent asymmetry of radiation actually involves. Two major flaws in the standard version of the Wheeler-Feynman treatment of radiative asymmetry are then identified (Secs. 4 5), and the proposed reinterpretation is described (Sec. 6). This avoids the two flaws previously mentioned, and also the problematic dependence of radiation on cosmological structure.
The Wheeler-Feynman absorber theory: A reinterpretation?
Ridderbos, T. M.
1997-10-01
The “reinterpretation” of the Wheeler-Feynman absorber theory of radiation, as presented by H. Price in Refs. 1 and 2, is shown not to be a reinterpretation of the mathematical framework of the theory, but an alteration of the theory, which renders it asymmetric. It is shown that Price is mistaken in accusing Wheeler and Feynman of presenting flawed arguments as to whether the advanced and retarded components are distinct; and about the reasons for excluding the time-reversed version of the absorber theory.
Phase Equilibria Diagrams Database
SRD 31 NIST/ACerS Phase Equilibria Diagrams Database (PC database for purchase) The Phase Equilibria Diagrams Database contains commentaries and more than 21,000 diagrams for non-organic systems, including those published in all 21 hard-copy volumes produced as part of the ACerS-NIST Phase Equilibria Diagrams Program (formerly titled Phase Diagrams for Ceramists): Volumes I through XIV (blue books); Annuals 91, 92, 93; High Tc Superconductors I & II; Zirconium & Zirconia Systems; and Electronic Ceramics I. Materials covered include oxides as well as non-oxide systems such as chalcogenides and pnictides, phosphates, salt systems, and mixed systems of these classes.
DEFF Research Database (Denmark)
Duijm, Nijs Jan
2007-01-01
are discussed. A simple method for quantification of safety-barrier diagrams is proposed, including situations where safety barriers depend on shared common elements. It is concluded that safety-barrier diagrams provide a useful framework for an electronic data structure that integrates information from risk......Safety-barrier diagrams and the related so-called "bow-tie" diagrams have become popular methods in risk analysis. This paper describes the syntax and principles for constructing consistent and valid safety-barrier diagrams. The relation with other methods such as fault trees and Bayesian networks...... analysis with operational safety management....
Energy Technology Data Exchange (ETDEWEB)
Butko, Yana A., E-mail: yanabutko@yandex.ru, E-mail: kinderknecht@math.uni-sb.de [Bauman Moscow State Technical University, 2nd Baumanskaya street, 5, Moscow 105005, Russia and University of Saarland, Postfach 151150, D-66041 Saarbrücken (Germany); Grothaus, Martin, E-mail: grothaus@mathematik.uni-kl.de [University of Kaiserslautern, 67653 Kaiserslautern (Germany); Smolyanov, Oleg G., E-mail: Smolyanov@yandex.ru [Lomonosov Moscow State University, Vorob’evy gory 1, Moscow 119992 (Russian Federation)
2016-02-15
Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.
Dynamic Onset of Feynman Relation in the Phonon Regime
Li, Y.; Zhu, C. J.; Hagley, E. W.; Deng, L.
2016-05-01
The Feynman relation, a much celebrated condensed matter physics gemstone for more than 70 years, predicts that the density excitation spectrum and structure factor of a condensed Bosonic system in the phonon regime drops linear and continuously to zero. Until now, this widely accepted monotonic excitation energy drop as the function of reduced quasi-momentum has never been challenged in a spin-preserving process. We show rigorously that in a light-matter wave-mixing process in a Bosonic quantum gas, an optical-dipole potential arising from the internally-generated field can profoundly alter the Feynman relation and result in a new dynamic relation that exhibits an astonishing non-Feynman-like onset and cut-off in the excitation spectrum of the ground state energy of spin-preserving processes. This is the first time that a nonlinear optical process is shown to actively and significantly alter the density excitation response of a quantum gas. Indeed, this dynamic relation with a non-Feynman onset and cut-off has no correspondence in either nonlinear optics of a normal gas or a phonon-based condensed matter Bogoliubov theory.
A Feynman-Kac formula for geometric quantization
Institute of Scientific and Technical Information of China (English)
郭懋正; 钱敏; 王正栋
1996-01-01
The geometric quantization on a homogeneous manifold is studied. For any quantizable function f, the stochastical expression for the unitary group exp(itQ (f)) generated by the quantized operator Q(f) is established. As an application, a Feynman-Kac formula for the compact semisimple Lie group is rederived.
Dynamic Onset of Feynman Relation in the Phonon Regime.
Li, Y; Zhu, C J; Hagley, E W; Deng, L
2016-05-09
The Feynman relation, a much celebrated condensed matter physics gemstone for more than 70 years, predicts that the density excitation spectrum and structure factor of a condensed Bosonic system in the phonon regime drops linear and continuously to zero. Until now, this widely accepted monotonic excitation energy drop as the function of reduced quasi-momentum has never been challenged in a spin-preserving process. We show rigorously that in a light-matter wave-mixing process in a Bosonic quantum gas, an optical-dipole potential arising from the internally-generated field can profoundly alter the Feynman relation and result in a new dynamic relation that exhibits an astonishing non-Feynman-like onset and cut-off in the excitation spectrum of the ground state energy of spin-preserving processes. This is the first time that a nonlinear optical process is shown to actively and significantly alter the density excitation response of a quantum gas. Indeed, this dynamic relation with a non-Feynman onset and cut-off has no correspondence in either nonlinear optics of a normal gas or a phonon-based condensed matter Bogoliubov theory.
On Feynman's Triangle Problem and the Routh Theorem
Man, Yiu-Kwong
2009-01-01
In this article, we give a brief history of the Feynman's Triangle problem and describe a simple method to solve a general version of this problem, which is called the Routh Theorem. This method could be found useful to school teachers, instructors or lecturers who are involved in teaching geometry.
Feynman's Relativistic Electrodynamics Paradox and the Aharonov-Bohm Effect
Caprez, Adam; Batelaan, Herman
2009-03-01
An analysis is done of a relativistic paradox posed in the Feynman Lectures of Physics involving two interacting charges. The physical system presented is compared with similar systems that also lead to relativistic paradoxes. The momentum conservation problem for these systems is presented. The relation between the presented analysis and the ongoing debates on momentum conservation in the Aharonov-Bohm problem is discussed.
Sufficient condition for the UV finiteness of Feynman graphs
Energy Technology Data Exchange (ETDEWEB)
Jian-Yuan, Cheng [Peking Univ., School of Physics, - Beijing, PRC (China)
2006-05-15
We introduce an integral expression of Euclidean-space propagators. The Euclidean-space propagators can be expressed as Fourier-Laplace transform of the free-field operator commutator. Based on the integral expression of Euclidean-space propagators, we find a sufficient condition for the ultraviolet (UV) finiteness of Feynman graphs calculated with various modified propagators. (authors)
Errors in The Feynman Lectures on Physics: Symmetry and Crystals
Indian Academy of Sciences (India)
2016-05-01
We discuss some errors in The Feynman Lectures on Physicsrelated to the concept of symmetry.We also suggest a possiblecorrection to Fig.1.4 of Vol. I. The discussion may be usefulfor students of crystallography, solid state physics and solidstate chemistry.
Rigorous time slicing approach to Feynman path integrals
Fujiwara, Daisuke
2017-01-01
This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved. The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by...
The Feynman rules for neutrinos and new neutralinos in BLMSSM
Dong, Xing-Xing; Zhang, Hai-Bin; Wang, Fang; Feng, Tai-Fu
2016-01-01
In a supersymmetric extension of the standard model where baryon and lepton numbers are local gauge symmetries(BLMSSM), we deduce the Feynman rules for neutrinos and new neutralinos. We briey introduce the mass matrices for the particles and the related couplings in this work, which are very useful to research the neutrinos and new neutralinos.
Effective fields in the Fokker-Feynman-Wheeler scheme
Bolokhov, S. V.; Kolybasova, V. V.
We discuss the possible ways to generalize the so-called action-at-a-distance principle (initially developed for the electromagnetic interactions in the works of Fokker, Feynman, and Wheeler) on the case of gravity and non-Abelian fields. Our approach is based on the relational-statistical theory of spacetime and interactions developed by Yu. S. Vladimirov.
Eubank, Jarrod F.
2011-09-14
A new blueprint network for the design and synthesis of porous, functional 3D metal-organic frameworks (MOFs) has been identified, namely, the tbo net. Accordingly, tbo-MOFs based on this unique (3,4)-connected net can be exclusively constructed utilizing a combination of well-known and readily targeted [M(R-BDC)]n MOF layers [i.e., supermolecular building layers (SBLs)] based on the edge-transitive 4,4 square lattice (sql) (i.e., 2D four-building units) and a novel pillaring strategy based on four proximal isophthalate ligands from neighboring SBL membered rings (i.e., two pairs from each layer) covalently cross-linked through an organic quadrangular core (e.g., tetrasubstituted benzene). Our strategy permits the rational design and synthesis of isoreticular structures, functionalized and/or expanded, that possess extra-large nanocapsule-like cages, high porosity, and potential for gas separation and storage, among others. Thus, tbo-MOF serves as an archetypal tunable, isoreticular MOF platform for targeting desired applications. © 2011 American Chemical Society.
Energy Technology Data Exchange (ETDEWEB)
Eubank, Jarrod F.; Mouttaki, Hasnaa; Cairns, Amy J.; Belmabkhout, Youssef; Wojtas, Lukasz; Luebke, Ryan; Alkordi, Mohamed; Eddaoudi, Mohamed (USF); (KAUST)
2011-12-09
A new blueprint network for the design and synthesis of porous, functional 3D metal-organic frameworks (MOFs) has been identified, namely, the tbo net. Accordingly, tbo-MOFs based on this unique (3,4)-connected net can be exclusively constructed utilizing a combination of well-known and readily targeted [M(R-BDC)]{sub n} MOF layers [i.e., supermolecular building layers (SBLs)] based on the edge-transitive 4,4 square lattice (sql) (i.e., 2D four-building units) and a novel pillaring strategy based on four proximal isophthalate ligands from neighboring SBL membered rings (i.e., two pairs from each layer) covalently cross-linked through an organic quadrangular core (e.g., tetrasubstituted benzene). Our strategy permits the rational design and synthesis of isoreticular structures, functionalized and/or expanded, that possess extra-large nanocapsule-like cages, high porosity, and potential for gas separation and storage, among others. Thus, tbo-MOF serves as an archetypal tunable, isoreticular MOF platform for targeting desired applications.
Eubank, Jarrod F; Mouttaki, Hasnaa; Cairns, Amy J; Belmabkhout, Youssef; Wojtas, Lukasz; Luebke, Ryan; Alkordi, Mohamed; Eddaoudi, Mohamed
2011-09-14
A new blueprint network for the design and synthesis of porous, functional 3D metal-organic frameworks (MOFs) has been identified, namely, the tbo net. Accordingly, tbo-MOFs based on this unique (3,4)-connected net can be exclusively constructed utilizing a combination of well-known and readily targeted [M(R-BDC)](n) MOF layers [i.e., supermolecular building layers (SBLs)] based on the edge-transitive 4,4 square lattice (sql) (i.e., 2D four-building units) and a novel pillaring strategy based on four proximal isophthalate ligands from neighboring SBL membered rings (i.e., two pairs from each layer) covalently cross-linked through an organic quadrangular core (e.g., tetrasubstituted benzene). Our strategy permits the rational design and synthesis of isoreticular structures, functionalized and/or expanded, that possess extra-large nanocapsule-like cages, high porosity, and potential for gas separation and storage, among others. Thus, tbo-MOF serves as an archetypal tunable, isoreticular MOF platform for targeting desired applications.
Penguin-like Diagrams from the Standard Model
Chia, Swee-Ping
2015-01-01
The Standard Model is highly successful in describing the interactions of leptons and quarks. There are, however, rare processes that involve higher order effects in electroweak interactions. One specific class of processes is the penguin-like diagram. Such class of diagrams involves the neutral change of quark flavours accompanied by the emission of a gluon (gluon penguin), a photon (photon penguin), a gluon and a photon (gluon-photon penguin), a Z-boson (Z penguin), or a Higgs-boson (Higgs penguin). Such diagrams do not arise at the tree level in the Standard Model. They are, however, induced by one-loop effects. In this paper, we present an exact calculation of the penguin diagram vertices in the tHooft-Feynman gauge. Renormalization of the vertex is effected by a prescription by Chia and Chong which gives an expression for the counter term identical to that obtained by employing Ward-Takahashi identity. The on-shell vertex functions for the penguin diagram vertices are obtained. The various penguin diagra...
Institute of Scientific and Technical Information of China (English)
LI Shichun
2004-01-01
Based on the Thomas-Fermi-Dirac-Cheng model, atomic phase diagram or electron density versus atomic radius diagram describing the interaction properties of atoms of different kinds in equilibrium state is developed. Atomic phase diagram is established based on the two-atoms model. Besides atomic radius, electron density and continuity condition for electron density on interfaces between atoms, the lever law of atomic phase diagram involving other physical parameters is taken into account, such as the binding energy, for the sake of simplicity.
A note on dual MHV diagrams in mathcal{N} = 4 SYM
Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele; Yang, Gang
2010-12-01
Recently a reformulation of the MHV diagram method in mathcal{N} = 4 supersymmetric Yang-Mills theory in momentum twistor space was presented and was shown to be equivalent to the perturbative expansion of the expectation value of a supersymmetric Wilson loop in momentum twistor space. In this note we present related explicit Feynman rules in dual momentum space, which should have the interpretation of Wilson loop diagrams in dual momentum space. We show that these novel rules are completely equivalent to ordinary spacetime MHV rules and can be naturally viewed as their graph dual representation.
DEFF Research Database (Denmark)
Moeller, Jesper; Lichtenberg, Jacob; Andersen, Henrik Reif;
1999-01-01
This paper describes a new data structure, difference decision diagrams (DDDs), for representing a Boolean logic over inequalities of the form $x-y......This paper describes a new data structure, difference decision diagrams (DDDs), for representing a Boolean logic over inequalities of the form $x-y...
Hockney, Roger
1987-01-01
Algorithmic phase diagrams are a neat and compact representation of the results of comparing the execution time of several algorithms for the solution of the same problem. As an example, the recent results are shown of Gannon and Van Rosendale on the solution of multiple tridiagonal systems of equations in the form of such diagrams. The act of preparing these diagrams has revealed an unexpectedly complex relationship between the best algorithm and the number and size of the tridiagonal systems, which was not evident from the algebraic formulae in the original paper. Even so, for a particular computer, one diagram suffices to predict the best algorithm for all problems that are likely to be encountered the prediction being read directly from the diagram without complex calculation.
A Feynman integral and its recurrences and associators
Puhlfürst, Georg; Stieberger, Stephan
2016-05-01
We determine closed and compact expressions for the ɛ-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This ɛ-expansion is identified with the normalized solution of the underlying Fuchs system of four regular singular points. We compute its regularized zeta series (giving rise to two independent associators) whose ratio gives the ɛ-expansion at a specific value. Furthermore, we use the well known one-loop massive bubble integral as an example to demonstrate how to obtain all-order ɛ-expansions for Feynman integrals and how to construct representations for Feynman integrals in terms of generalized hypergeometric functions. We use the method of differential equations in combination with the recently established general solution for recurrence relations with non-commutative coefficients.
A Feynman integral and its recurrences and associators
Directory of Open Access Journals (Sweden)
Georg Puhlfürst
2016-05-01
Full Text Available We determine closed and compact expressions for the ϵ-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This ϵ-expansion is identified with the normalized solution of the underlying Fuchs system of four regular singular points. We compute its regularized zeta series (giving rise to two independent associators whose ratio gives the ϵ-expansion at a specific value. Furthermore, we use the well known one-loop massive bubble integral as an example to demonstrate how to obtain all-order ϵ-expansions for Feynman integrals and how to construct representations for Feynman integrals in terms of generalized hypergeometric functions. We use the method of differential equations in combination with the recently established general solution for recurrence relations with non-commutative coefficients.
Quantenmechanik im Kalten Krieg David Bohm und Richard Feynman
Forstner, Christian
2007-01-01
Mitte des 20. Jahrhunderts entwickelten David Bohm und Richard Feynman zwei grundlegend verschiedene Ansätze der moderne Quantenmechanik: Bohm eine realistische Deutung mit Hilfe verborgener Parameter und Feynman den Pfadintegralformalismus. Dies ist umso bemerkenswerter, weil beide Physiker von ähnlichen Voraussetzungen ausgingen und aus ähnlichen Zusammenhängen stammten. Durch ihren vergleichenden Ansatz bietet diese Studie mehr als einen Beitrag zur Geschichte der Quantentheorie. Mit der Frage nach den sozialen und kulturellen Bedingungen der Theoriebildung ist sie darüberhinaus von wissenschaftssoziologischem und wissenschaftstheoretischem Interesse. Die anfangs ähnliche und später unterschiedliche Einbindung der beiden Wissenschaftler in die Scientific Community erlaubt es überdies zu untersuchen, welchen Anpassungsdruck die jeweilige Gruppe auf den individuellen Wissenschaftler und die Kernbestandteile seiner Forschungen ausübt und welche neuen Freiheitsgrade für die Theoriebildung entstehen, ...
Some properties of the Feynman-Kac functional
Directory of Open Access Journals (Sweden)
S. Graversen
1995-01-01
Full Text Available The Feynman-Kac formula and its connections with classical analysis were initiated in the now celebrated paper [6] of M. Kac. It soon became obvious that the formula provides a powerful tool for solving partial differential equations by running the Brownian motion process. K.L. Chung and K.M. Rao in [4] used it to characterize solutions of the Schrödinger equation. In this paper we study some properties of the Feynman-Kac functional using the Brownian motion process. In particular, we are going to use it in connection with the gauge function in order to obtain an energy formula similar to one obtained by G. Dal Maso and U. Mosco in [5].
Advanced computer algebra algorithms for the expansion of Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Round, Mark; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2012-10-15
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+{epsilon}-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.
Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals
Ablinger, J; Round, M; Schneider, C
2012-01-01
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in $4+\\ep$-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter $n$. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist--Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in $n$. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all $n$ solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.
Inductively generating Euler diagrams.
Stapleton, Gem; Rodgers, Peter; Howse, John; Zhang, Leishi
2011-01-01
Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In all of their application areas, the ability to automatically layout Euler diagrams brings considerable benefits. In this paper, we present a novel approach to Euler diagram generation. We develop certain graphs associated with Euler diagrams in order to allow curves to be added by finding cycles in these graphs. This permits us to build Euler diagrams inductively, adding one curve at a time. Our technique is adaptable, allowing the easy specification, and enforcement, of sets of well-formedness conditions; we present a series of results that identify properties of cycles that correspond to the well-formedness conditions. This improves upon other contributions toward the automated generation of Euler diagrams which implicitly assume some fixed set of well-formedness conditions must hold. In addition, unlike most of these other generation methods, our technique allows any abstract description to be drawn as an Euler diagram. To establish the utility of the approach, a prototype implementation has been developed.
A test of the Feynman scaling in the fragmentation region
Doke, T.; Innocente, V.; Kasahara, K.; Kikuchi, J.; Kashiwagi, T.; Lanzano, S.; Masuda, K.; Murakami, H.; Muraki, Y.; Nakada, T.
1985-01-01
The result of the direct measurement of the fragmentation region will be presented. The result will be obtained at the CERN proton-antiproton collider, being exposured the Silicon calorimeters inside beam pipe. This experiment clarifies a long riddle of cosmic ray physics, whether the Feynman scaling does villate at the fragmentation region or the Iron component is increasing at 10 to the 15th power eV.
FIESTA4: Optimized Feynman integral calculations with GPU support
Smirnov, A. V.
2016-07-01
This paper presents a new major release of the program FIESTA (Feynman Integral Evaluation by a Sector decomposiTion Approach). The new release is mainly aimed at optimal performance at large scales when one is increasing the number of sampling points in order to reduce the uncertainty estimates. The release now supports graphical processor units (GPUs) for the numerical integration, methods to optimize cluster-usage, as well as other speed, memory, and stability improvements.
Wheeler-Feynman Absorbers on the Light Horizon
Lear, C. W.
2016-01-01
Early Wheeler-Feynman absorber theories invoke both retarded and advanced electromagnetic waves for photon emission and absorption in order to remove problems involving lack of radiative damping during electron acceleration. Subsequent inquiries have suggested that only certain cosmologies would allow such a retarded-advanced wave mechanism to exist. These include quasi-steady state cosmologies and exclude flat, expanding Friedman-type cosmologies. Key to the exclusion process is a diminishin...
Wheeler-Feynman dynamics of spin-1/2 particles
Energy Technology Data Exchange (ETDEWEB)
Van Alstine, P.; Crater, H.W.
1986-02-15
By combining a supersymmetric description of a spinning particle in an external field with an appropriate modification of the ''adjunct field'' of Wheeler and Feynman, we construct a many-time relativistic dynamics for arbitrary numbers of spin-(1/2) and spinless particles in mutual scalar or vector interaction. Quantization of the slow-motion approximation to the dynamics of two spinning particles reproduces the corresponding field-theoretic (Bethe-Salpeter) dynamics through order U.
Wheeler-Feynman dynamics of spin-1/2 particles
van Alstine, Peter; Crater, Horace W.
1986-02-01
By combining a supersymmetric description of a spinning particle in an external field with an appropriate modification of the ``adjunct field'' of Wheeler and Feynman, we construct a many-time relativistic dynamics for arbitrary numbers of spin-(1/2) and spinless particles in mutual scalar or vector interaction. Quantization of the slow-motion approximation to the dynamics of two spinning particles reproduces the corresponding field-theoretic (Bethe-Salpeter) dynamics through order α4.
FIESTA 4: optimized Feynman integral calculations with GPU support
Smirnov, Alexander V
2015-01-01
This paper presents a new major release of the program FIESTA (Feynman Integral Evaluation by a Sector decomposiTion Approach). The new release is mainly aimed at optimal performance at large scales when one is increasing the number of sampling points in order to reduce the uncertainty estimates. The release now supports graphical processor units (GPU) for the numerical integration, methods to optimize cluster-usage, as well as other speed, memory, and stability improvements.
Generalization of the hypervirial and Feynman-Hellman theorems
Nadareishvili, Teimuraz
2013-01-01
Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is carried on for most general second order differential equation, which involves all physically interesting cases, such as Schr\\"odinger and two-body Klein-Gordon equations with singular potentials. Some physical consequences are discussed. The connection with Feynman-Hellmann like theorems are also considered and some relevant differences are underlined.
Destructive interferences results in bosons anti bunching: refining Feynman's argument
Marchewka, Avi; Granot, Er'el
2014-09-01
The effect of boson bunching is frequently mentioned and discussed in the literature. This effect is the manifestation of bosons tendency to "travel" in clusters. One of the core arguments for boson bunching was formulated by Feynman in his well-known lecture series and has been frequently used ever since. By comparing the scattering probabilities of two bosons and of two distinguishable particles, he concluded: "We have the result that it is twice as likely to find two identical Bose particles scattered into the same state as you would calculate assuming the particles were different" [R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics: Quantum mechanics (Addison-Wesley, 1965)]. This argument was rooted in the scientific community (see for example [C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics (John Wiley & Sons, Paris, 1977); W. Pauli, Exclusion Principle and Quantum Mechanics, Nobel Lecture (1946)]), however, while this sentence is completely valid, as is proved in [C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics (John Wiley & Sons, Paris, 1977)], it is not a synonym of bunching. In fact, as it is shown in this paper, wherever one of the wavefunctions has a zero, bosons can anti-bunch and fermions can bunch. It should be stressed that zeros in the wavefunctions are ubiquitous in Quantum Mechanics and therefore the effect should be common. Several scenarios are suggested to witness the effect.
Constructive Representation Theory for the Feynman Operator Calculus
Gill, T L
2006-01-01
In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. We first develop an operator version of the Henstock-Kurzweil integral, and a new Hilbert space that allows us to construct the elementary path integral in the manner originally envisioned by Feynman. After developing our time-ordered operator theory we extend a few of the important theorems of semigroup theory, including the Hille-Yosida theorem. As an application, we unify and extend the theory of time-dependent parabolic and hyperbolic evolution equations. We then develop a general perturbation theory and use it to prove that all theories generated by semigroups are asympotic in the operator-valued sense of Poincar e. This allows us to provide a general theory for the interaction representation of relativistic quantum theory. We then show that our theory can be reformulated as a physically motivated sum over paths, and use this version to extend the Feynman path integral to include more general interaction...
Fractional Feynman-Kac equation for weak ergodicity breaking.
Carmi, Shai; Barkai, Eli
2011-12-01
The continuous-time random walk (CTRW) is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, ψ(τ) ~ τ(-(1+α)), leads to subdiffusion (x(2) ~ t(α)) for 0 Feynman-Kac equation if the motion is Brownian. Here, we derive forward and backward fractional Feynman-Kac equations for functionals of CTRW in a binding potential. We use our equations to study two specific time averages: the fraction of time spent by a particle in half-box, and the time average of the particle's position in a harmonic field. In both cases, we obtain the probability density function of the time averages for t → ∞ and the first two moments. Our results show that both the occupation fraction and the time-averaged position are random variables even for long times, except for α = 1, when they are identical to their ensemble averages. Using our fractional Feynman-Kac equation, we also study the dynamics leading to weak ergodicity breaking, namely the convergence of the fluctuations to their asymptotic values.
Feynman-Kac formula for stochastic hybrid systems
Bressloff, Paul C.
2017-01-01
We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.
Solutions of the Wheeler-Feynman equations with discontinuous velocities.
de Souza, Daniel Câmara; De Luca, Jayme
2015-01-01
We generalize Wheeler-Feynman electrodynamics with a variational boundary value problem for continuous boundary segments that might include velocity discontinuity points. Critical-point orbits must satisfy the Euler-Lagrange equations of the action functional at most points, which are neutral differential delay equations (the Wheeler-Feynman equations of motion). At velocity discontinuity points, critical-point orbits must satisfy the Weierstrass-Erdmann continuity conditions for the partial momenta and the partial energies. We study a special setup having the shortest time-separation between the (infinite-dimensional) boundary segments, for which case the critical-point orbit can be found using a two-point boundary problem for an ordinary differential equation. For this simplest setup, we prove that orbits can have discontinuous velocities. We construct a numerical method to solve the Wheeler-Feynman equations together with the Weierstrass-Erdmann conditions and calculate some numerical orbits with discontinuous velocities. We also prove that the variational boundary value problem has a unique solution depending continuously on boundary data, if the continuous boundary segments have velocity discontinuities along a reduced local space.
Feynman-Kac formula for stochastic hybrid systems.
Bressloff, Paul C
2017-01-01
We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.
Feynman formulas for semigroups generated by an iterated Laplace operator
Buzinov, M. S.
2017-04-01
In the present paper, we find representations of a one-parameter semigroup generated by a finite sum of iterated Laplace operators and an additive perturbation (the potential). Such semigroups and the evolution equations corresponding to them find applications in the field of physics, chemistry, biology, and pattern recognition. The representations mentioned above are obtained in the form of Feynman formulas, i.e., in the form of a limit of multiple integrals as the multiplicity tends to infinity. The term "Feynman formula" was proposed by Smolyanov. Smolyanov's approach uses Chernoff's theorems. A simple form of representations thus obtained enables one to use them for numerical modeling the dynamics of the evolution system as a method for the approximation of solutions of equations. The problems considered in this note can be treated using the approach suggested by Remizov (see also the monograph of Smolyanov and Shavgulidze on path integrals). The representations (of semigroups) obtained in this way are more complicated than those given by the Feynman formulas; however, it is possible to bypass some analytical difficulties.
Solutions of the Wheeler-Feynman equations with discontinuous velocities
de Souza, Daniel Câmara; De Luca, Jayme
2015-01-01
We generalize Wheeler-Feynman electrodynamics with a variational boundary value problem for continuous boundary segments that might include velocity discontinuity points. Critical-point orbits must satisfy the Euler-Lagrange equations of the action functional at most points, which are neutral differential delay equations (the Wheeler-Feynman equations of motion). At velocity discontinuity points, critical-point orbits must satisfy the Weierstrass-Erdmann continuity conditions for the partial momenta and the partial energies. We study a special setup having the shortest time-separation between the (infinite-dimensional) boundary segments, for which case the critical-point orbit can be found using a two-point boundary problem for an ordinary differential equation. For this simplest setup, we prove that orbits can have discontinuous velocities. We construct a numerical method to solve the Wheeler-Feynman equations together with the Weierstrass-Erdmann conditions and calculate some numerical orbits with discontinuous velocities. We also prove that the variational boundary value problem has a unique solution depending continuously on boundary data, if the continuous boundary segments have velocity discontinuities along a reduced local space.
Local mirror symmetry and the sunset Feynman integral
Bloch, Spencer; Vanhove, Pierre
2016-01-01
We study the sunset Feynman integral defined as the scalar two-point self-energy at two-loop order in a two dimensional space-time. We firstly compute the Feynman integral, for arbitrary internal masses, in terms of the regulator of a class in the motivic cohomology of a 1-parameter family of open elliptic curves. Using an Hodge theoretic (B-model) approach, we show that the integral is given by a sum of elliptic dilogarithms evaluated at the divisors determined by the punctures. Secondly we associate to the sunset elliptic curve a local non-compact Calabi-Yau 3-fold, obtained as a limit of elliptically fibered compact Calabi-Yau 3-folds. By considering the limiting mixed Hodge structure of the Batyrev dual A-model, we arrive at an expression for the sunset Feynman integral in terms of the local Gromov-Witten prepotential of the del Pezzo surface of degree 6. This expression is obtained by proving a strong form of local mirror symmetry which identifies this prepotential with the second regulator period of the...
Baaquie, Belal E
2007-01-01
European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.
Engineering holographic phase diagrams
Chen, Jiunn-Wei; Dai, Shou-Huang; Maity, Debaprasad; Zhang, Yun-Long
2016-10-01
By introducing interacting scalar fields, we tried to engineer physically motivated holographic phase diagrams which may be interesting in the context of various known condensed matter systems. We introduce an additional scalar field in the bulk which provides a tunable parameter in the boundary theory. By exploiting the way the tuning parameter changes the effective masses of the bulk interacting scalar fields, desired phase diagrams can be engineered for the boundary order parameters dual to those scalar fields. We give a few examples of generating phase diagrams with phase boundaries which are strikingly similar to the known quantum phases at low temperature such as the superconducting phases. However, the important difference is that all the phases we have discussed are characterized by neutral order parameters. At the end, we discuss if there exists any emerging scaling symmetry associated with a quantum critical point hidden under the dome in this phase diagram.
Borwein, J M
1998-01-01
We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers $a$ and $b$ giving $a/b vol(M)=(-D)^{3/2}/(2\\pi)^{2n-4} (\\zeta_K(2))/(2\\zeta(2))$ for a manifold M whose invariant trace field $K$ has a single complex place, discriminant $D$, degree $n$, and Dedekind zeta value $\\zeta_K(2)$. The largest numerator of the 998 invariants of Hodgson-Weeks manifolds is, astoundingly, $a=2^4\\times23\\times37\\times691 =9,408,656$; the largest denominator is merely b=9. We also study the rational invariant a/b for single-complex-place cusped manifolds, complementary to knots and links, both within and beyond the Hildebrand-Weeks census. Within the censi, we identify 152 distinct Dedekind zetas rationally related to volumes. Moreover, 91 census manifolds have volumes reducible to pairs of these zeta values. Motivated by studies of Feynman diagrams, we find a 10-component 24-crossing link in the case n=2 and D=-20. It is one of 5 alternating platonic links,...
两类广义Feynman-Kac半群强连续性的探讨%Topics on Strong Continuity of Two Generalized Feynman-Kac Semigroups
Institute of Scientific and Technical Information of China (English)
梁青
2015-01-01
研究两类广义Feynman-Kac半群的强连续性问题，这些半群是由一些特定的函数和狄氏过程产生的。得到了广义Feynman-Kac半群强连续，不强连续以及能量测度不在Kato类中的充分条件；构造了一个带跳狄氏型相应的广义Feynman-Kac半群强连续的实例。%In this paper the strongly continuous character of two classes of generalized Feynman-Kac semigroups is stud⁃ied. These semigroups are produced by some special functions and Dirichlet processes. We obtain the sufficient condition for some particular Feynman-Kac semigroups to be strongly continuous or not. We also obtain the sufficient condition for the energy measures of the functions which produce strongly continuous generalizd Feynman-Kac semigroups to be not in the Kato class. We construct a generalized Feynman-Kac semigroup related with a Dirichlet form with jump that is strongly con⁃tinuous.
Feynman rules for neutrinos and new neutralinos in the BLMSSM
Dong, Xing-Xing; Zhao, Shu-Min; Zhang, Hai-Bin; Wang, Fang; Feng, Tai-Fu
2016-09-01
In a supersymmetric extension of the Standard Model where baryon and lepton numbers are local gauge symmetries (BLMSSM), we deduce the Feynman rules for neutrinos and new neutralinos. We briefly introduce the mass matrices for the particles and the related couplings in this work, which are very useful to research the neutrinos and new neutralinos. Supported by Major Project of NNSFC (11535002) and NNSFC (11275036), Natural Science Foundation of Hebei Province (A2016201010), and Foundation of Hebei Province (BR2-201), and the Natural Science Fund of Hebei University (2011JQ05, 2012-242), Hebei Key Lab of Optic-Electronic Information and Materials, Midwest Universities Comprehensive Strength Promotion Project
Fractional Feynman-Kac equation for non-brownian functionals.
Turgeman, Lior; Carmi, Shai; Barkai, Eli
2009-11-06
We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [Phys. Rev. Lett. 96, 230601 (2006)10.1103/PhysRevLett.96.230601] provide the correct fractional framework for the problem. For applications, we calculate the distribution of occupation times in half space and show how the statistics of anomalous functionals is related to weak ergodicity breaking.
Tempered fractional Feynman-Kac equation: Theory and examples.
Wu, Xiaochao; Deng, Weihua; Barkai, Eli
2016-03-01
Functionals of Brownian and non-Brownian motions have diverse applications and attracted a lot of interest among scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.
Feynman propagator for an arbitrary half-integral spin
Institute of Scientific and Technical Information of China (English)
黄时中; 张鹏飞; 阮图南; 祝玉灿; 郑志鹏
2003-01-01
Based on the solution to Bargmann-Wigner equation for a particle with arbitrary half-integral spin, a directderivation of the projection operator and propagator for a particle with arbitrary half-integral spin is worked out. Theprojection operator constructed by Behrends and Fronsdal is re-deduced and confirmed and simplified, the generalcommutation rules and Feynman propagator with additional non-covariant terms for a free particle with arbitraryhalf-integral spin are derived, and explicit expressions for the propagators for spins 3/2, 5/2 and 7/2 are provided.
Feynman propagator for an arbitrary half-integral spin
Institute of Scientific and Technical Information of China (English)
黄时中; 张鹏飞; 阮图南; 祝玉灿; 郑志鹏
2003-01-01
Based on the solution to Bargmann-Wigner equation for a particle with arbitrary half-integral spin, a direct derivation of the projection operator and propagator for a particle with arbitrary half-integral spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed and simplified, the general commutation rules and Feynman propagator with additional non-covariant terms for a free particle with arbitrary half-inteRzal spin are derived, and explicit expressions for the propagators for spins 3/2, 5/2 and 7/2 are provided.
Towards the automatized evaluation of Feynman integrals with differential equations
Energy Technology Data Exchange (ETDEWEB)
Meyer, Christoph; Uwer, Peter [HU Berlin, Berlin (Germany)
2016-07-01
In the past years the method of differential equations has proven itself to be a powerful tool for the computation of multi-loop Feynman integrals. This method relies on the choice of a basis of master integrals in which the dependence on the dimensional regulator factorizes. We present an algorithm which automatizes the transformation to such a basis, starting from a given reduction basis. The algorithm only requires some mild assumptions about the basis. It applies to problems with multiple scales of which we will present some examples.
Extensions of the Feynman-Hellman theorem and applications
Singh, S. Brajamani; Singh, C. A.
1989-10-01
Epstein's [Am. J. Phys. 22, 613 (1954)] off-diagonal and higher-order extensions of the Feynman-Hellmann theorem, obtained by using the basic technique of parameter differentiation under the integral sign, are further pursued. Epstein's rederivation of the Rayleigh-Schrödinger perturbation expansion is also extended to include the degenerate case. The same approach is also used to obtain the Lennard-Jones-Brillouin-Wigner perturbation theory. The quantum virial theorem and its off-diagonal generalization is deduced and its application is illustrated by taking the example of the linear harmonic oscillator. The semiclassical expression for the kinetic energy is obtained directly from the quantization condition.
Wheeler and Feynman electrodynamics within the framework of retarded causality
Energy Technology Data Exchange (ETDEWEB)
Yaremko, Yu [Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv (Ukraine)
2002-11-08
A frontal collision of two point-like charged particles which are asymptotically free in the remote past and in the distant future is considered. Ten conserved quantities corresponding to the symmetry of a closed system of particles and electromagnetic field under the Poincare group are expressed in terms of particle variables. It is shown that an interference of outgoing electromagnetic waves (retarded Lienard-Wiechert solutions) ensures the action of the field of one source on another (mutual interaction). The combination of wave motions accords with the modified Wheeler and Feynman absorber theory of radiation where (acausal) 'perfect absorption' is replaced by an interference phenomenon.
On the Existence of Dynamics of Wheeler-Feynman Electromagnetism
Bauer, G.; Deckert, D. -A.; Dürr, D.
2010-01-01
We study the equations of Wheeler-Feynman electrodynamics which is an action-at-a-distance theory about world-lines of charges that interact through their corresponding advanced and retarded Li\\'enard-Wiechert field terms. The equations are non-linear, neutral, and involve time-like advanced as well as retarded arguments of unbounded delay. Using a reformulation in terms of Maxwell-Lorentz electrodynamics without self-interaction, which we have introduced in a preceding work, we are able to e...
Wheeler and Feynman electrodynamics within the framework of retarded causality
Yaremko, Yu
2002-01-01
A frontal collision of two point-like charged particles which are asymptotically free in the remote past and in the distant future is considered. Ten conserved quantities corresponding to the symmetry of a closed system of particles and electromagnetic field under the Poincare group are expressed in terms of particle variables. It is shown that an interference of outgoing electromagnetic waves (retarded Lienard-Wiechert solutions) ensures the action of the field of one source on another (mutual interaction). The combination of wave motions accords with the modified Wheeler and Feynman absorber theory of radiation where (acausal) 'perfect absorption' is replaced by an interference phenomenon.
Wheeler and Feynman electrodynamics within the framework of retarded causality
Yaremko, Yu
2002-11-01
A frontal collision of two point-like charged particles which are asymptotically free in the remote past and in the distant future is considered. Ten conserved quantities corresponding to the symmetry of a closed system of particles and electromagnetic field under the Poincaré group are expressed in terms of particle variables. It is shown that an interference of outgoing electromagnetic waves (retarded Liénard-Wiechert solutions) ensures the action of the field of one source on another (mutual interaction). The combination of wave motions accords with the modified Wheeler and Feynman absorber theory of radiation where (acausal) 'perfect absorption' is replaced by an interference phenomenon.
Aoyama, T; Kinoshita, T; Nio, M
2006-01-01
Among 12672 Feynman diagrams contributing to the electron anomalous magnetic moment at the tenth order, 6354 are the diagrams having no lepton loops, i.e., those of quenched type. Because the renormalization structure of these diagrams is very complicated, some automation scheme is inevitable to calculate them. We developed an algorithm to write down FORTRAN programs for numerical evaluation of these diagrams, where the necessary counterterms to subtract out ultraviolet subdivergence are generated according to Zimmermann's forest formula. Thus far we have evaluated crudely integrals of 2232 tenth-order vertex diagrams which require vertex renormalization only. Remaining 4122 diagrams, which have ultraviolet-divergent self-energy subdiagrams and infrared-divergent subdiagrams, are being evaluated by giving small mass lambda to photons to control the infrared problem.
Institute of Scientific and Technical Information of China (English)
QIAN Shang-Wu; CHAN King-Man; GU Zhi-Yu
2002-01-01
This article revisits Feynman's characteristic function, and points out the insight and usefulness of hisphysical interpretation. As an example, the tedious and rather long derivation of the propagator in polar coordinatescan be easily and clearly obtained by merely using Feynman's physical intepretation of the characteristic function andsome well-known results of central force problem.
A DISCUSSION OF THE WHEELER-FEYNMAN ABSORBER THEORY OF RADIATION.
The Wheeler - Feynman absorber theory of radiation is reviewed. A proof is offered to show that a sum of advanced and retarded effects from the...absorber can provide the origin of radiative reaction. This proof is different from and perhaps simpler than that of Wheeler and Feynman . From arguments
Particle diagrams and embedded many-body random matrix theory.
Small, R A; Müller, S
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ≤ m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k = m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k = m,3 k = m,...,nk = m.
Particle diagrams and embedded many-body random matrix theory
Small, R. A.; Müller, S.
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ≤m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k=m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k=m,3k=m,...,nk=m.
Equational binary decision diagrams
Groote, J.F.; Pol, J.C. van de
2000-01-01
We incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tautology checkin
Lindenbergh, R.C.
2002-01-01
The classic Voronoi diagram of a configuration of distinct points in the plane associates to each point that part of the plane that is closer to the point than to any other point in the configuration. In this thesis we no longer require all points to be distinct. After the introduction in
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Compressing Binary Decision Diagrams
DEFF Research Database (Denmark)
Hansen, Esben Rune; Satti, Srinivasa Rao; Tiedemann, Peter
2008-01-01
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and compression will in many cases reduce the size of the BDD to 1...
Compressing Binary Decision Diagrams
DEFF Research Database (Denmark)
Rune Hansen, Esben; Srinivasa Rao, S.; Tiedemann, Peter
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and compression will in many cases reduce the size of the BDD to 1...
Kneupper, Charles W.
1978-01-01
Responds to Charles Willard's recommendations (in an article in "Communication Monographs," November 1976) that argument be viewed as an attempt to establish formal relationships among symbolic structures. Demonstrates flaws in this redefinition and shows argument diagrams to be theoretically and practically justifiable. (JMF)
Compressing Binary Decision Diagrams
DEFF Research Database (Denmark)
Hansen, Esben Rune; Satti, Srinivasa Rao; Tiedemann, Peter
2008-01-01
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and compression will in many cases reduce the size of the BDD to 1...
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tauto
Lagrangian and Hamiltonian Feynman formulae for some Feller semigroups and their perturbations
Butko, Yana A; Smolyanov, Oleg G
2012-01-01
A Feynman formula is a representation of a solution of an initial (or initial-boundary) value problem for an evolution equation (or, equivalently, a representation of the semigroup resolving the problem) by a limit of $n$-fold iterated integrals of some elementary functions as $n\\to\\infty$. In this note we obtain some Feynman formulae for a class of semigroups associated with Feller processes. Finite dimensional integrals in the Feynman formulae give approximations for functional integrals in some Feynman--Kac formulae corresponding to the underlying processes. Hence, these Feynman formulae give an effective tool to calculate functional integrals with respect to probability measures generated by these Feller processes and, in particular, to obtain simulations of Feller processes.
Hellmann–Feynman connection for the relative Fisher information
Energy Technology Data Exchange (ETDEWEB)
Venkatesan, R.C., E-mail: ravi@systemsresearchcorp.com [Systems Research Corporation, Aundh, Pune 411007 (India); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [IFLP, National University La Plata & National Research (CONICET) C. C., 727 1900, La Plata (Argentina)
2015-08-15
The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS link and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided. - Highlights: • Legendre transform structure for the RFI is obtained with the Hellmann–Feynman theorem. • Inference of the energy-eigenvalues of the SWE-like equation for the RFI is accomplished. • Basis for reconstruction of the RFI framework from the FIM-case is established. • Substantial qualitative and quantitative distinctions with prior studies are discussed.
High Performance and Increased Precision Techniques for Feynman Loop Integrals
Kato, K.; de Doncker, E.; Ishikawa, T.; Kapenga, J.; Olagbemi, O.; Yuasa, F.
2016-10-01
For the investigation of physics within and beyond the Standard Model, a precise evaluation of higher order corrections in perturbative quantum field theory is required. We have worked on the development of a computational method for Feynman loop integrals with a fully numerical approach. It is based on numerical integration and extrapolation techniques. In this paper, we describe the status and new developments in our techniques for the numerical computation of Feynman loop integrals. Separation of ultra-violet divergences is important for the renormalization procedure. In our analyses, the separation can be done numerically. For 2-loop integrals we have performed the calculations for up to 4-point functions, and for 2-point functions we can handle up to 4- loop integrals. We report the status and accuracy of the computations with detailed numerical comparisons to results in the literature, in order to demonstrate that our method will evolve into an important component of automated systems for the study of higher-order radiative corrections.
Feynman integrals, L-series and Kloosterman moments
Broadhurst, David
2016-01-01
This work lies at an intersection of three subjects: quantum field theory, algebraic geometry and number theory, in a situation where dialogue between practitioners has revealed rich structure. It contains a theorem and 7 conjectures, tested deeply by 3 optimized algorithms, on relations between Feynman integrals and L-series defined by products, over the primes, of data determined by moments of Kloosterman sums in finite fields. There is an extended introduction, for readers who may not be familiar with all three of these subjects. Notable new results include conjectural evaluations of non-critical L-series of modular forms of weights 3, 4 and 6, by determinants of Feynman integrals, an evaluation for the weight 5 problem, at a critical integer, and formulas for determinants of arbitrary size, tested up to 30 loops. It is shown that the functional equation for Kloosterman moments determines much but not all of the structure of the L-series. In particular, for problems with odd numbers of Bessel functions, it...
Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations
Boulahoual, A
2003-01-01
The main focus of the present work is to study the Feynman's proof of the Maxwell equations using the NC geometry framework. To accomplish this task, we consider two kinds of noncommutativity formulations going along the same lines as Feynman's approach. This allows us to go beyond the standard case and discover non-trivial results. In fact, while the first formulation gives rise to the static Maxwell equations, the second formulation is based on the following assumption $m[x_{j},\\dot{x_{k}}]=i\\hbar \\delta_{jk}+im\\theta_{jk}f.$ The results extracted from the second formulation are more significant since they are associated to a non trivial $\\theta $-extension of the Bianchi-set of Maxwell equations. We find $div_{\\theta}B=\\eta_{\\theta}$ and $\\frac{\\partial B_{s}}{\\partial t}+\\epsilon_{kjs}\\frac{\\partial E_{j}}{\\partial x_{k}}=A_{1}\\frac{d^{2}f}{dt^{2}}+A_{2}\\frac{df}{dt}+A_{3},$ where $\\eta_{\\theta}$, $A_{1}$, $A_{2}$ and $A_{3}$ are local functions depending on the NC $\\theta $-parameter. The novelty of this...
Dirac Matrices and Feynman's Rest of the Universe
Kim, Young S
2012-01-01
There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four $\\gamma$ matrices. These fifteen matrices can also serve as the generators of the group $SL(4,r)$. The second set consists of ten generators of the $Sp(4)$ group which he derived from two coupled harmonic oscillators. In classical mechanics, it is possible to extend the symmetry of the coupled oscillators to the SL(4,r) regime with fifteen Majorana matrices, while quantum mechanics allows only ten generators. This difference can serve as an illustrative example of Feynman's rest of the universe. The universe of the coupled oscillators consists of fifteen generators, and the ten generators are for the world where quantum mechanics is valid. The remaining five generators belong to the rest of the universe. It is noted that the groups $SL(4,r)$ and $Sp(4)$ are locally isomorphic to the Lorentz groups O(3,3) and O(3,2) respectively. This allows us to interpret Feynman's rest...
DEFF Research Database (Denmark)
Andersen, Henrik Reif; Hulgaard, Henrik
2002-01-01
This paper presents a new data structure called boolean expression diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of binary decision diagrams (BDDs) which can represent any Boolean circuit in linear space. Two algorithms are described for transforming...... a BED into a reduced ordered BDD. One is a generalized version of the BDD apply-operator while the other can exploit the structural information of the Boolean expression. This ability is demonstrated by verifying that two different circuit implementations of a 16-bit multiplier implement the same...... Boolean function. Using BEDs, this verification problem is solved efficiently, while using standard BDD techniques this problem is infeasible. Generally, BEDs are useful in applications, for example tautology checking, where the end-result as a reduced ordered BDD is small. Moreover, using operators...
DEFF Research Database (Denmark)
Andersen, Henrik Reif; Hulgaard, Henrik
1997-01-01
This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable...... properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One closely mimics the BDD apply-operator while the other can exploit the structural information of the Boolean expression. The efficacy of the BED representation is demonstrated by verifying...... that the redundant and non-redundant versions of the ISCAS 85 benchmark circuits are identical. In particular, it is verified that the two 16-bit multiplication circuits (c6288 and c6288nr) implement the same Boolean functions. Using BEDs, this verification problem is solved in less than a second, while using...
DEFF Research Database (Denmark)
Øhrstrøm, Peter
2011-01-01
Some very good arguments can be given in favor of the Augustinean wisdom, according to which it is impossible to provide a satisfactory definition of the concept of time. However, even in the absence of a proper definition, it is possible to deal with conceptual problems regarding time. It can...... be done in terms of analogies and metaphors. In particular, it is attractive to make use of Peirce's diagrams by means of which various kinds of conceptual experimentation can be carried out. This paper investigates how Peircean diagrams can be used within the study of time. In particular, we discuss 1......) the topological properties of time, 2) the implicative structure in tense logic, 3) the notions of open future and branching time models, and finally 4) tenselogical alternatives to branching time models....
Energy Technology Data Exchange (ETDEWEB)
Wilms, R Scott [Los Alamos National Laboratory; Carlson, Bryan [Los Alamos National Laboratory; Coons, James [Los Alamos National Laboratory; Kubic, William [Los Alamos National Laboratory
2008-01-01
This presentation describes the development of the proposed Process Flow Diagram (PFD) for the Tokamak Exhaust Processing System (TEP) of ITER. A brief review of design efforts leading up to the PFD is followed by a description of the hydrogen-like, air-like, and waterlike processes. Two new design values are described; the mostcommon and most-demanding design values. The proposed PFD is shown to meet specifications under the most-common and mostdemanding design values.
Energy Technology Data Exchange (ETDEWEB)
Rudin, M.J. [Univ. of Nevada, Las Vegas NV (United States); O`Brien, M.C. [Univ. of Arizona, Tucson, AZ (United States)
1995-04-01
A planning and management tool was developed that relates environmental restoration and waste management problems to technologies that can be used to remediate these problems. Although the Technology Logic Diagram has been widely used within the US Department of Energy`s Office of Environmental Restoration and Waste Management, it can be modified for use during the planning of any waste management and environmental cleanup effort.
The Massive Thermal Basketball Diagram
Andersen, J O; Strickland, Michael T; Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-01-01
The "basketball diagram" is a three-loop vacuum diagram for a scalar fieldtheory that cannot be expressed in terms of one-loop diagrams. We calculatethis diagram for a massive scalar field at nonzero temperature, reducing it toexpressions involving three-dimensional integrals that can be easily evaluatednumerically. We use this result to calculate the free energy for a massivescalar field with a phi^4 interaction to three-loop order.
Voronoi diagrams on the sphere
Na, H.-S.; Lee, C.-N.; Cheong, O.
2001-01-01
Given a set of compact sites on a sphere, we show that their spherical Voronoi diagram can be computed by computing two planar Voronoi diagrams of suitably transformed sites in the plane. We also show that a planar furthest-site Voronoi diagram can always be obtained as a portion of a
Towards a Realistic Parsing of the Feynman Path Integral
Directory of Open Access Journals (Sweden)
Ken Wharton
2016-01-01
Full Text Available The Feynman path integral does not allow a one real path interpretation, because the quantum amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, all paths happen, is not a useful or informative account. In this paper it is shown that an intermediate parsing of the path integral, into realistic non-interfering possibilities, is always available. Each realistic possibility formally corresponds to numerous particle paths, but is arguably best interpreted as a spacetime-valued field. Notably, one actual field history can always be said to occur, although it will generally not have an extremized action. The most obvious concerns with this approach are addressed, indicating necessary follow-up research. But without obvious showstoppers, it seems plausible that the path integral might be reinterpreted to explain quantum phenomena in terms of Lorentz covariant field histories.Quanta 2016; 5: 1–11.
Jensen-Feynman approach to the statistics of interacting electrons.
Pain, Jean-Christophe; Gilleron, Franck; Faussurier, Gérald
2009-08-01
Faussurier [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions. It consists of a decomposition into a reference electron system and a first-order correction. The procedure appears to be very efficient in order to evaluate the free energy and the orbital populations. In this work, we present numerical applications of the method and propose to extend it using a reference energy which includes the interaction between two electrons inside a given orbital. This is possible, thanks to our efficient recursion relation for the calculation of partition functions. We also show that a linear reference energy, however, is usually sufficient to achieve a good precision and that the most promising way to improve the approach of Faussurier is to apply Jensen's inequality to a more convenient convex function.
Hellman-Feynman operator sampling in diffusion Monte Carlo calculations.
Gaudoin, R; Pitarke, J M
2007-09-21
Diffusion Monte Carlo (DMC) calculations typically yield highly accurate results in solid-state and quantum-chemical calculations. However, operators that do not commute with the Hamiltonian are at best sampled correctly up to second order in the error of the underlying trial wave function once simple corrections have been applied. This error is of the same order as that for the energy in variational calculations. Operators that suffer from these problems include potential energies and the density. This Letter presents a new method, based on the Hellman-Feynman theorem, for the correct DMC sampling of all operators diagonal in real space. Our method is easy to implement in any standard DMC code.
Parametric representation of Feynman amplitudes in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Sars, Matthias Christiaan Bernhard
2015-09-01
In this thesis a systematic method is given for writing the amplitudes in (scalar) quantum electrodynamics and non-Abelian gauge theories in Schwinger parametric form. This is done by turning the numerator of the Feynman rules in momentum space into a differential operator. It acts then on the parametric integrand of the scalar theory. For QED it is the most straightforward, because the Leibniz rule is not involved here. In the case of sQED and non-Abelian gauge theories, the contributions from the Leibniz rule are satisfyingly related to 4-valent vertices. Another feature of this method is that in the used renormalization scheme, the subtractions for 1-scale graphs cause significant simplifications. Furthermore, the Ward identities for mentioned three theories are studied.
Calculations in the Wheeler-Feynman Absorber Theory of Radiation.
Balaji, Kalathur Sreenivasan
One dimensional computer aided calculations were done to find the self-consistent solutions for various absorber configurations in the context of the Wheeler-Feynman Absorber theory, wherein every accelerating charge is assumed to produce a time symmetric combination of advanced and retarded fields. These calculations picked out the so called "outerface" solution for incomplete absorbers and showed that advanced as well as retarded signals interact with matter in the same manner as in the full retarded theory. Based on these calculations the Partridge experiment and the Schmidt-Newman experiment were ruled out as tests of the Absorber theory. An experiment designed to produce and detect advanced effects is proposed, based on more one-dimensional calculations.
Tachyons and the Wheeler-Feynman Absorber Theory
Tomaschitz, R
2001-01-01
The Proca equation with negative mass-square is studied in a refractive and absorptive spacetime. The generation of superluminal radiation fields by subluminal currents is discussed. The possibility of time-symmetric wave propagation is analysed in the context of the Wheeler-Feynman absorber theory; it is shown how advanced modes of the Proca field can be turned into retarded ones in a permeable spacetime capable of producing an absorber field. A microscopic oscillator model for the permeability is suggested. Tachyonic Lienard-Wiechert potentials are studied and strictly causal retarded wave solutions are obtained. Energy transfer by superluminal radiation is discussed, and explicit formulae for the spectral energy density and intensity are derived. Superluminal radiation fields generated by classical damped oscillators carrying tachyonic charge are investigated, including the tachyonic analogue to Thomson and Rayleigh cross sections. The Maxwell equations for negative mass-square are derived, their non-local...
Calculations in the Wheeler-Feynman absorber theory of radiation
Energy Technology Data Exchange (ETDEWEB)
Balaji, K.S.
1986-01-01
One dimensional computer aided calculations were done to find the self consistent solutions for various absorber configurations in the context of the Wheeler-Feynman absorber theory, wherein every accelerating charge is assumed to produce a time symmetric combination of advanced and retarded fields. These calculations picked out the so called outerface solution for incomplete absorbers and showed that advanced as well as retarded signals interact with matter in the same manner as in the full retarded theory. Based on these calculations, the Partridge experiment and the Schmidt-Newman experiment were ruled out as tests of the absorber theory. An experiment designed to produce and detect advanced effects is proposed, based on more one-dimensional calculations.
Applications of the Feynman-Hellmann theorem in hadron structure
Chambers, A J; Nakamura, Y; Perlt, H; Pleiter, D; Rakow, P E L; Schierholz, G; Schiller, A; Stüben, H; Young, R D; Zanotti, J M
2015-01-01
The Feynman-Hellmann (FH) relation offers an alternative way of accessing hadronic matrix elements through artificial modifications to the QCD Lagrangian. In particular, a FH-motivated method provides a new approach to calculations of disconnected contributions to matrix elements and high-momentum nucleon and pion form factors. Here we present results for the total nucleon axial charge, including a statistically significant non-negative total disconnected quark contribution of around $-5\\%$ at an unphysically heavy pion mass. Extending the FH relation to finite-momentum transfers, we also present calculations of the pion and nucleon electromagnetic form factors up to momentum transfers of around 7-8 GeV$^2$. Results for the nucleon are not able to confirm the existence of a sign change for the ratio $\\frac{G_E}{G_M}$, but suggest that future calculations at lighter pion masses will provide fascinating insight into this behaviour at large momentum transfers.
Beam spread functions calculated using Feynman path integrals
Kilgo, Paul; Tessendorf, Jerry
2017-07-01
A method of solving the radiative transfer equation using Feynman path integrals (FPIs) is discussed. The FPI approach is a mathematical framework for computing multiple scattering in participating media. Its numerical behavior is not well known, and techniques are being developed to solve the FPI approach numerically. A missing numerical technique is detailed and used to calculate beam spread functions (BSFs), a commonly studied experimental property of many types of media. The calculations are compared against measured BSFs of sea ice. Analysis shows differently-shaped BSFs, and suggests the width parameter of the calculated BSF's Gaussian fit approaches a value in the limit of the number of path segments. A projection is attempted, but suggests a larger number of path segments would not increase the width of the calculated BSF. The trial suggests the approach is numerically stable, but requires further testing to ensure scientific accuracy.
A recursive approach to the reduction of tensor Feynman integrals
Diakonidis, Theodoros; Riemann, Tord; Tausk, Bas
2010-01-01
We describe a new, convenient, recursive tensor integral reduction scheme for one-loop $n$-point Feynman integrals. The reduction is based on the algebraic Davydychev-Tarasov formalism where the tensors are represented by scalars with shifted dimensions and indices, and then expressed by conventional scalars with generalized recurrence relations. The scheme is worked out explicitly for up to $n=6$ external legs and for tensor ranks $R\\leq n$. The tensors are represented by scalar one- to four-point functions in $d$ dimensions. For the evaluation of them, the Fortran code for the tensor reductions has to be linked with a package like QCDloop or LoopTools/FF. Typical numerical results are presented.
Wheeler-Feynman Absorbers on the Light Horizon
Lear, C W
2016-01-01
Early Wheeler-Feynman absorber theories invoke both retarded and advanced electromagnetic waves for photon emission and absorption in order to remove problems involving lack of radiative damping during electron acceleration. Subsequent inquiries have suggested that only certain cosmologies would allow such a retarded-advanced wave mechanism to exist. These include quasi-steady state cosmologies and exclude flat, expanding Friedman-type cosmologies. Key to the exclusion process is a diminishing density of future absorbers in an ever-expanding universe. Such absorbers would be expected to be real electromagnetically interacting particles. However future virtual absorber sites, if they exist, would not be so diminished. Such sites would be plentiful on the future light horizon, receding from the source at the speed of light. The present treatment proposes that virtual absorption sites are present at every point in spacetime, and are characterized by the Fresnel-Kirchhoff diffraction integral. On the future light...
Steiner, E.
1973-01-01
The use of the electrostatic Hellmann-Feynman theorem for the calculation of the leading term in the 1/R expansion of the force of interaction between two well-separated hydrogen atoms is discussed. Previous work has suggested that whereas this term is determined wholly by the first-order wavefunction when calculated by perturbation theory, the use of the Hellmann-Feynman theorem apparently requires the wavefunction through second order. It is shown how the two results may be reconciled and that the Hellmann-Feynman theorem may be reformulated in such a way that only the first-order wavefunction is required.
LanHEP - a package for automatic generation of Feynman rules in gauge models
Semenov, A Yu
1996-01-01
We consider the general problem of derivation of the Feynman rules for the matrix elements in momentum representation from the given Lagrangian in coordinate space invariant under the transformation of some gauge group. LanHEP package presented in this paper allows to define in a convenient way the gauge model Lagrangian in canonical form and then to generate automatically the Feynman rules that can be used in the following calculation of the physical processes by means of CompHEP package. The detailed description of LanHEP commands is given and several examples of LanHEP applications (QED, QCD, Standard Model in the t'Hooft-Feynman gauge) are presented.
Knot probabilities in random diagrams
Cantarella, Jason; Chapman, Harrison; Mastin, Matt
2016-10-01
We consider a natural model of random knotting—choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to compute exact probabilities for knots in this model. As expected, most diagrams with 10 and fewer crossings are unknots (about 78% of the roughly 1.6 billion 10 crossing diagrams). For these crossing numbers, the unknot fraction is mostly explained by the prevalence of ‘tree-like’ diagrams which are unknots for any assignment of over/under information at crossings. The data shows a roughly linear relationship between the log of knot type probability and the log of the frequency rank of the knot type, analogous to Zipf’s law for word frequency. The complete tabulation and all knot frequencies are included as supplementary data.
Collective neurodynamics: Phase diagram
Ovchinnikov, Igor V.; Li, Wenyuan; Schwartz, Robert N.; Hudson, Andrew E.; Meier, Karlheinz; Wang, Kang L.
2016-01-01
Here, we conceptualize the phase diagram of collective short-term bio-chemo-electric component of neurodynamics (S-ND) on the parameter space of externally, e.g., pharmacologically, controllable single-neuron parameters such as the resting potential and/or firing threshold, repolarization time, etc. This concept may become a useful tool for the systematization of knowledge in anesthesiology and provide a fruitful venue for future studies of the high-level S-ND functionalities such as short-te...
Diagramming Complex Activities
DEFF Research Database (Denmark)
Andersen, Peter Bøgh
2005-01-01
We increasingly live in heterogeneous ever-changing webs of activities where human actions are intertwined with events created by automatic machines. In order to make such webs understandable to its human participants, their structure should be represented by displays emphasizing their action as...... aspect. The paper suggests thematic roles as a semantics for actions, argues that a selection of well-known diagramming techniques can be defined within this theory, and uses the theory to discuss new issues related to process control and mobile technology....
Smolec, Radoslaw; Dziembowski, Wojciech; Moskalik, Pawel; Netzel, Henryka; Prudil, Zdenek; Skarka, Marek; Soszynski, Igor
2017-09-01
Over the recent years, the Petersen diagram for classical pulsators, Cepheids and RR Lyr stars, populated with a few hundreds of new multiperiodic variables. We review our analyses of the OGLE data, which resulted in a significant extension of the known, and in the discovery of a few new and distinct forms of multiperiodic pulsation. The showcase includes not only radial mode pulsators, but also radial-non-radial pulsators and stars with significant modulation observed on top of the beat pulsation. First theoretical models explaining the new forms of stellar variability are briefly discussed.
Kowalczyk, Piotr; Brualla, Lorenzo; Gauden, Piotr A; Terzyk, Artur P
2009-10-28
We study the applicability of the semiclassical Feynman and Hibbs (FH) (second-order or fourth-order) effective potentials to the description of the thermodynamic properties of quantum fluids at finite temperatures. First, we use path integral Monte Carlo (PIMC) simulations to estimate the thermodynamic/static properties of our model quantum fluid, i.e. low-density 4He at 10 K. With PIMC we obtain the experimental equation of state, the single-particle mean kinetic energy, the single-particle density matrix and the single-particle momentum distribution of this system at low densities. We show that our PIMC results are in full agreement with experimental data obtained with deep inelastic neutron scattering at high momentum transfers (D. Colognesi, C. Andreani, R. Senesi, Europhys. Lett., 2000, 50, 202). As expected, in this region of the 4He phase diagram, quantum effects modify the width of the single-particle momentum distribution but do not alter its Gaussian shape. Knowing the exact values of density, pressure and single-particle mean kinetic energy for our model quantum fluid, we investigate the limitations of the semiclassical FH effective potentials. We show that commonly used 'short-time' approximations to the high-temperature density matrix due to Feynman and Hibbs can only be applied in a very limited range of the 4He phase diagram. We found that FH effective potentials reproduce the experimental densities of 4He at 10 K for Lambda/a < 0.45 (Lambda = 2.73 A denotes the thermal de Broglie wavelength, a = rho(-1/3) is the mean nearest-neighbor distance in the fluid and rho denotes fluid density). Moreover, semiclassical FH effective potentials are able to correctly predict the single-particle mean kinetic energy of 4He at 10 K in a very limited range of fluid densities, i.e.Lambda/a < 0.17. We show that the ad hoc application of the semiclassical FH effective potentials for the calculation of the thermodynamic properties of dense liquid-like para
Wheeler-Feynman Absorber Theory Viewed by Model of Expansive Nondecelerative Universe
Sukenik, Miroslav; Sima, Jozef
2001-01-01
The present contribution documents the harmony of postulates and conclusions of Wheeler-Feynman absorber theory and the model of Expansive Nondecelerative Universe. A relationship connecting advanced electromagnetic waves and gravitational field quanta is rationalized.
Why Professor Richard Feynman was upset solving the Laplace equation for spherical waves?
Khelashvili, Anzor
2013-01-01
We take attention to the singular behavior of the Laplace operator in spherical coordinates, which was established in our earlier work. This singularity has many non-trivial consequences. In this article we consider only the simplest ones, which are connected to the solution of Laplace equation in Feynman classical books and Lectures. Feynman was upset looking in his derived solutions, which have a fictitious singular behavior at the origin. We show how these inconsistencies can be avoided.
A partial solution for Feynman's problem: A new derivation of the Weyl equation
Directory of Open Access Journals (Sweden)
Atsushi Inoue
2000-07-01
Full Text Available Associating classical mechanics to a system of partial differential equations, we give a procedure for Feynman-type quantization of a "Schrodinger-type equation with spin." Mathematically, we construct a "good parametrix" for the Weyl equation with an external electromagnetic field. Main ingredients are (i a new interpretation of the matrix structure using superanalysis and (ii another interpretation of the method of characteristics as a quantization procedure of Feynman type.
Feynman-Kac-type theorems and Gibbs measures on path space
Lörinczi, József; Betz, Volker
2018-01-01
This is the second updated and extended edition of the successful book on Feynman-Kac Theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. Thefirst volume concentrates on Feynman-Kac-type formulae and Gibbs measures. In the second volume, these ideas are applied principally to a rigorous treatment of some fundamental models of quantum field theory.
Program Synthesizes UML Sequence Diagrams
Barry, Matthew R.; Osborne, Richard N.
2006-01-01
A computer program called "Rational Sequence" generates Universal Modeling Language (UML) sequence diagrams of a target Java program running on a Java virtual machine (JVM). Rational Sequence thereby performs a reverse engineering function that aids in the design documentation of the target Java program. Whereas previously, the construction of sequence diagrams was a tedious manual process, Rational Sequence generates UML sequence diagrams automatically from the running Java code.
Mass divergence power counting for QCD in the Feynman gauge
Energy Technology Data Exchange (ETDEWEB)
Tucci, R.
1986-03-01
We present a mass divergence power counting technique for QCD in the Feyman gauge. For the process ..gamma..sup(*)->qanti q, we find the leading regions of integration and show that single diagrams are at worst logarithmically divergent. Using the Weyl representation facilitates the ..gamma.. matrix manipulations necessary for power counting and adds much physical insight. (orig.).
Evaluating multiloop Feynman integrals by Mellin-Barnes representation
Smirnov, V A
2004-01-01
The status of analytical evaluation of double and triple box diagrams is characterized. The method of Mellin-Barnes representation as a tool to evaluate master integrals in these problems is advocated. New MB representations for massive on-shell double boxes with general powers of propagators are presented.
Institute of Scientific and Technical Information of China (English)
杨晓玲; 潘爽
2009-01-01
研究带跳狄氏型相应的广义Feynman-Kac半群的强连续性问题,这个广义Feynman-Kac半群是由α-stable like过程和与此过程联系的狄氏型其定义域中的一个特殊函数产生,证明出由此函数产生的广义Feynman-Kac半群具有强连续性.
New results for algebraic tensor reduction of Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Fleischer, Jochem [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, Valery [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center
2012-02-15
We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2{epsilon}. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)
Finding new relationships between hypergeometric functions by evaluating Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Kniehl, Bernd A. [Santa Barbara Univ., CA (United States). Kavli Inst. for Theoretical Physics; Tarasov, Oleg V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2011-08-15
Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and arbitrary powers of propagators is derived in terms of only one Appell hypergeometric function F{sub 1}. From the comparison of this expression with a previously known one, a new relation between the Appell functions F{sub 1} and F{sub 4} is found. By comparing this new expression for the case of equal masses with another known result, a new formula for reducing the F{sub 1} function with particular arguments to the hypergeometric function {sub 3}F{sub 2} is derived. By comparing results for a particular one-loop vertex integral obtained using different methods, a new relationship between F{sub 1} functions corresponding to a quadratic transformation of the arguments is established. Another reduction formula for the F{sub 1} function is found by analysing the imaginary part of the two-loop self-energy integral on the cut. An explicit formula relating the F{sub 1} function and the Gaussian hypergeometric function {sub 2}F{sub 1} whose argument is the ratio of polynomials of degree six is presented. (orig.)
Gluon saturation and Feynman scaling in leading neutron production
Directory of Open Access Journals (Sweden)
F. Carvalho
2016-01-01
Full Text Available In this paper we extend the color dipole formalism for the study of leading neutron production in e+p→e+n+X collisions at high energies and estimate the related observables which were measured at HERA and could be analyzed in future electron–proton (ep colliders. In particular, we calculate the Feynman xF distribution of leading neutrons, which is expressed in terms of the pion flux and the photon–pion total cross section. In the color dipole formalism, the photon–pion cross section is described in terms of the dipole–pion scattering amplitude, which contains information about the QCD dynamics at high energies and gluon saturation effects. We consider different models for the scattering amplitude, which have been used to describe the inclusive and diffractive ep HERA data. Moreover, the model dependence of our predictions with the description of the pion flux is analyzed in detail. We demonstrate the recently released H1 leading neutron spectra can be described using the color dipole formalism and that these spectra could help us to observe more clearly gluon saturation effects in future ep colliders.
New results for algebraic tensor reduction of Feynman integrals
Fleischer, Jochem; Yundin, Valery
2012-01-01
We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5-point Gram determinants, and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a $(d+2)$-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension $d=4-2 \\epsilon$. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the $(d+2)$-dimensional 5...
Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman
Kim, Y S; Noz, Marilyn E.
2004-01-01
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called $SL(2,c)$...
On the existence of dynamics in Wheeler-Feynman electromagnetism
Bauer, G.; Deckert, D.-A.; Dürr, D.
2013-08-01
Wheeler-Feynman electrodynamics (WF) is an action-at-a-distance theory about world-lines of charges that in contrary to the textbook formulation of classical electrodynamics is free of ultraviolet singularities and is capable of explaining the irreversible nature of radiation. In WF, the world-lines of charges obey the so-called Fokker-Schwarzschild-Tetrode (FST) equations, a coupled set of nonlinear and neutral differential equations that involve time-like advanced as well as retarded arguments of unbounded delay. Using a reformulation of this theory in terms of Maxwell-Lorentz electrodynamics without self-interaction that we have introduced in a preceding work, we are able to establish the existence of conditional solutions. These conditional solutions solve the FST equations on any finite time interval with prescribed continuations outside of this interval. As a byproduct, we also prove existence and uniqueness of solutions to the Synge equations on the time half-line for a given history of charge world-lines.
Tachyons and the Wheeler-Feynman absorber theory
Tomaschitz, Roman
2001-11-01
The Proca equation with negative mass-square is studied in a refractive and absorptive spacetime. The generation of superluminal radiation fields by subluminal currents is discussed. The possibility of time-symmetric wave propagation is analysed in the context of the Wheeler-Feynman absorber theory; it is shown how advanced modes of the Proca field can be turned into retarded ones in a permeable spacetime capable of producing an absorber field. A microscopic oscillator model for the permeability is suggested. Tachyonic Liénard-Wiechert potentials are studied and strictly causal retarded wave solutions are obtained. Energy transfer by superluminal radiation is discussed, and explicit formulae for the spectral energy density and intensity are derived. Superluminal radiation fields generated by classical damped oscillators carrying tachyonic charge are investigated, including the tachyonic analogue to Thomson and Rayleigh cross sections. The Maxwell equations for negative mass-square are derived, their non-local generalization to frequency-dependent permeabilities, as well as the Poynting theorem for superluminal radiation in an absorptive spacetime.
Modified Feynman ratchet with velocity-dependent fluctuations
Directory of Open Access Journals (Sweden)
Jack Denur
2004-03-01
Full Text Available Abstract: The randomness of Brownian motion at thermodynamic equilibrium can be spontaneously broken by velocity-dependence of fluctuations, i.e., by dependence of values or probability distributions of fluctuating properties on Brownian-motional velocity. Such randomness-breaking can spontaneously obtain via interaction between Brownian-motional Doppler effects --- which manifest the required velocity-dependence --- and system geometrical asymmetry. A non random walk is thereby spontaneously superposed on Brownian motion, resulting in a systematic net drift velocity despite thermodynamic equilibrium. The time evolution of this systematic net drift velocity --- and of velocity probability density, force, and power output --- is derived for a velocity-dependent modification of Feynman's ratchet. We show that said spontaneous randomness-breaking, and consequent systematic net drift velocity, imply: bias from the Maxwellian of the system's velocity probability density, the force that tends to accelerate it, and its power output. Maximization, especially of power output, is discussed. Uncompensated decreases in total entropy, challenging the second law of thermodynamics, are thereby implied.
Theory of Atom Optics: Feynman's Path Integral Approach
Institute of Scientific and Technical Information of China (English)
DENG Lü-bi
2006-01-01
The present theory of atom optics is established mainly on the Schr(o)dinger equations or the matrix mechanics equation.The authors present a new theoretical formulation of atom optics: Feynman's path integral theory.Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating),apertures,and standing wave laser field in Earth's gravitational field by using a type of wave function and calculation is simple.For this reason,we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction),double slit,N slit,rectangular aperture,circular aperture,the Mach-Zehndertype interferometer,the interferometer with the Raman beams,the Sagnac effect,the Aharonov-Casher effect,the Kapitza-Dirac diffraction effect,and the Aharonov-Bohm effect.The authors give a wave function of the state of particles on the screen in abovementioned configurations.Our formulas show good agreement with present experimental measurements.
New results for algebraic tensor reduction of Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Fleischer, Jochem [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, Valery [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center
2012-02-15
We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2{epsilon}. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)
Diagonal Slices of 3D Young Diagrams in the Approach of Maya Diagrams
Cai, Li-Qiang; Wang, Li-Fang; Wu, Ke; Yang, Jie
2014-09-01
According to the correspondence between 2D Young diagrams and Maya diagrams and the relation between 2D and 3D Young diagrams, we construct 3D Young diagrams in the approach of Maya diagrams. Moreover, we formulate the generating function of 3D Young diagrams, which is the MacMahon function in terms of Maya diagrams.
Diagrams and Proofs in Analysis
DEFF Research Database (Denmark)
Carter, Jessica M H Grund
2010-01-01
The article discusses the role of diagrams in mathematical reasoning based on a case study in analysis. In the presented example certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures are replaced by reasoning about permutation groups...
Modeling process flow using diagrams
Kemper, B.; de Mast, J.; Mandjes, M.
2010-01-01
In the practice of process improvement, tools such as the flowchart, the value-stream map (VSM), and a variety of ad hoc variants of such diagrams are commonly used. The purpose of this paper is to present a clear, precise, and consistent framework for the use of such flow diagrams in process
Modeling process flow using diagrams
Kemper, B.; de Mast, J.; Mandjes, M.
2010-01-01
In the practice of process improvement, tools such as the flowchart, the value-stream map (VSM), and a variety of ad hoc variants of such diagrams are commonly used. The purpose of this paper is to present a clear, precise, and consistent framework for the use of such flow diagrams in process improv
Genus Ranges of Chord Diagrams.
Burns, Jonathan; Jonoska, Nataša; Saito, Masahico
2015-04-01
A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can be, and those that cannot be, realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.
Institute of Scientific and Technical Information of China (English)
贺拥军; 周绪红; 唐家云
2014-01-01
A tridimensional parking structure with diaphragms was presented by setting diaphragms at some levels of the quadrangular tube-type steel frame .A structural analysis model was established by finite element software SAP2000 .By comparing the static property of the structures with different diaphragm arrangement schemes ,the effects of diaphragms on structural optimum properties , including the lateral displacement and internal force distribution of the middle frame and the deformation of the parking areas and lifting areas , were studied . Meanwhile ,the optimal arrangement scheme of diaphragms was investigated .Results indicate that the behavior of the quadrangular tube-type steel frame tridimensional parking structure is significantly improved for the diaphragms .Besides ,the storey shifts of the middle frame become smaller and more uniformly ,the deformation of the parking areas and lifting areas is effectively restrained ,which is conducive to parking of vehicles and operation of the lifting equipment . Moreover , the sudden change of column internal forces becomes relatively moderate . Synthesizing the cost and structural behaviors ,arranging diaphragms every four storeys is the optimal scheme .%提出在垂直升降型立体车库承重骨架的四边形筒式钢构架结构中设置一定间距的横隔，形成带横隔的立体停车结构，以提高结构的整体性。利用有限元软件 SAP2000建立了结构分析模型，通过对不同横隔设置方案的结构静力性能，即中间框架的侧移和内力分布、停车区间和提升井变形的比较，探讨了横隔对结构性能的影响及横隔设置的最佳方案。结果表明：设置横隔能加强结构整体性，有效保证中间框架与边框架的同步侧移且显著减小中间框架侧移，结构停车区间和提升井的变形得到有效控制，利于车辆停放及设备的运行，同时柱内力突变相对缓和；综合考虑制作成本
Feynman force components: basis for a solution to the covalent vs. ionic dilemma.
Dominikowska, Justyna; Jabłoński, Mirosław; Palusiak, Marcin
2016-09-14
The Hellmann-Feynman theorem, when applied to nuclear coordinates in a molecular system, states that Feynman forces, i.e. forces acting on a nucleus in a molecule, are solely of an electrostatic nature. This theorem is described by Slater as "the most powerful" theorem applicable to molecules. However, its possibilities have hardly been harnessed. This work presents the use of the Hellmann-Feynman theorem in conjunction with the partitioning of the molecular space into atoms in the spirit of the quantum theory of atoms in molecules (QTAIM). Homopolar and heteropolar diatomic molecules of varying polarity are studied in the context of Feynman force components, i.e. the components exerted on each nucleus by the other nucleus and by the electron density distributions of each of the atoms. These results are further related to electronegativity differences used in the differentiation between covalent and ionic bond. The approach based on the directions of Feynman force components gives physical fundamentals for covalent vs. ionic bond distinction without referring to the electronegativity concept.
Farthest-Polygon Voronoi Diagrams
Cheong, Otfried; Glisse, Marc; Gudmundsson, Joachim; Hornus, Samuel; Lazard, Sylvain; Lee, Mira; Na, Hyeon-Suk
2010-01-01
Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log^3 n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k-1 connected components, but if one component is bounded, then it is equal to the entire region.
Dudley, J. M.; Kwan, A. M.
1996-06-01
The subject of quantum electrodynamics (QED) was the subject of QED—The Strange Theory of Light and Matter, the popular book by Richard Feynman which was published by Princeton University Press in 1985. On p. 1, Feynman makes passing reference to the fact that the book is based on a series of general lectures on QED which were, however, first delivered in New Zealand. At Auckland University, these lectures were delivered in 1979, as the Sir Douglas Robb lectures, and videotapes of the lectures are held by the Auckland University Physics Department. We have carried out a detailed examination of these videotapes, and we discuss here the major differences between the original Auckland lectures and the published version. We use selected quotations from the lectures to show that the original lectures provide additional insight into Feynman's character, and have great educational value.
Causal diagrams for physical models
Kinsler, Paul
2015-01-01
I present a scheme of drawing causal diagrams based on physically motivated mathematical models expressed in terms of temporal differential equations. They provide a means of better understanding the processes and causal relationships contained within such systems.
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Probabilistic networks, also known as Bayesian networks and influence diagrams, have become one of the most promising technologies in the area of applied artificial intelligence, offering intuitive, efficient, and reliable methods for diagnosis, prediction, decision making, classification......, troubleshooting, and data mining under uncertainty. Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. Intended...
Wind Diagrams in Medieval Iceland
DEFF Research Database (Denmark)
Kedwards, Dale
2014-01-01
This article presents a study of the sole wind diagram that survives from medieval Iceland, preserved in the encyclopaedic miscellany in Copenhagen's Arnamagnæan Institute with the shelf mark AM 732b 4to (c. 1300-25). It examines the wind diagram and its accompanying text, an excerpt on the winds...... from Isidore of Seville's Etymologies. It also examines the perimeter of winds on two medieval Icelandic world maps, and the visual traditions from which they draw....
Lau, S. S.; Liu, B. X.; Nicolet, M.-A.
1983-05-01
Interactions induced by ion irradiation are generally considered to be non-equilibrium processes, whereas phase diagrams are determined by phase equilibria. These two entities are seemingly unrelated. However, if one assumes that quasi-equilibrium conditions prevail after the prompt events, subsequent reactions are driven toward equilibrium by thermodynamical forces. Under this assumption, ion-induced reactions are related to equilibrium and therefore to phase diagrams. This relationship can be seen in the similarity that exists in thin films between reactions induced by ion irradiation and reactions induced by thermal annealing. In the latter case, phase diagrams have been used to predict the phase sequence of stable compound formation, notably so in cases of silicide formation. Ion-induced mixing not only can lead to stable compound formation, but also to metastable alloy formation. In some metal-metal systems, terminal solubilities can be greatly extended by ion mixing. In other cases, where the two constituents of the system have different crystal structures, extension of terminal solubility from both sides of the phase diagram eventually becomes structurally incompatible and a glassy (amorphous) mixture can form. The composition range where this bifurcation is likely to occur is in the two-phase regions of the phase diagram. These concepts are potentially useful guides in selecting metal pairs that from metallic glasses by ion mixing. In this report, phenomenological correlation between stable (and metastable) phase formation and phase diagram is discussed in terms of recent experimental data.
Change of Scale Formulas for Wiener Integrals Related to Fourier-Feynman Transform and Convolution
Directory of Open Access Journals (Sweden)
Bong Jin Kim
2014-01-01
Full Text Available Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in Banach algebra S on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class F(B and in a generalized Fresnel class FA1,A2 on abstract Wiener space. We express Fourier-Feynman transform and convolution product of functionals in S as limits of Wiener integrals. Moreover we obtain change of scale formulas for Wiener integrals related to Fourier-Feynman transform and convolution product of these functionals.
Projection Operator and Feynman Propagator for a Free MassiVe Particle of Arbitrary Spin
Institute of Scientific and Technical Information of China (English)
HUANG Shi-Zhong; ZHANG Peng-Fei; RUAN Tu-Nan; ZHU Yu-Can; ZHENG Zhi-Peng
2004-01-01
Based on the solution to the Bargmann-Wigner equations, a direct derivation of the projection operator and Feynman propagatorfor a free massive particle of arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin, the general commutation rules and Feynman propagator with additional non-covariant terms for a free massive particle with any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, and 4 are provided.
Feynman graphs, and nerve theorem for compact symmetric multicategories (extended abstract)
Joyal, André
2009-01-01
We describe a category of Feynman graphs and show how it relates to compact symmetric multicategories (coloured modular operads) just as linear orders relate to categories and rooted trees relate to multicategories. More specifically we obtain the following nerve theorem: compact symmetric multicategories can be characterised as presheaves on the category of Feynman graphs subject to a Segal condition. This text is a write-up of the second-named author's QPL6 talk; a more detailed account of this material will appear elsewhere.
FaRe: A Mathematica package for tensor reduction of Feynman integrals
Re Fiorentin, Michele
2016-08-01
In this paper, we present FaRe, a package for Mathematica that implements the decomposition of a generic tensor Feynman integral, with arbitrary loop number, into scalar integrals in higher dimension. In order for FaRe to work, the package FeynCalc is needed, so that the tensor structure of the different contributions is preserved and the obtained scalar integrals are grouped accordingly. FaRe can prove particularly useful when it is preferable to handle Feynman integrals with free Lorentz indices and tensor reduction of high-order integrals is needed. This can then be achieved with several powerful existing tools.
FaRe: a Mathematica package for tensor reduction of Feynman integrals
Fiorentin, Michele Re
2015-01-01
We present FaRe, a package for Mathematica that implements the decomposition of a generic tensor Feynman integral, with arbitrary loop number, into scalar integrals in higher dimension. In order for FaRe to work, the package FeynCalc is needed, so that the tensor structure of the different contributions is preserved and the obtained scalar integrals are grouped accordingly. FaRe can prove particularly useful when it is preferable to handle Feynman integrals with free Lorentz indices and tensor reduction of high-order integrals is needed. This can then be achieved with several powerful existing tools.
Perfect orderings on Bratteli diagrams
Bezuglyi, Sergey; Yassawi, Reem
2012-01-01
Given a Bratteli diagram B, we study the set O(B) of all possible orderings w on a Bratteli diagram B and its subset P(B) consisting of `perfect' orderings that produce Bratteli-Vershik dynamical systems (Vershik maps). We give necessary and sufficient conditions for w to be perfect. On the other hand, a wide class of non-simple Bratteli diagrams that do not admit Vershik maps is explicitly described. In the case of finite rank Bratteli diagrams, we show that the existence of perfect orderings with a prescribed number of extreme paths affects significantly the values of the entries of the incidence matrices and the structure of the diagram B. Endowing the set O(B) with product measure, we prove that there is some j such that almost all orderings on B have j maximal and minimal paths, and that if j is strictly greater than the number of minimal components that B has, then almost all orderings are imperfect.
Improving modeling with layered UML diagrams
DEFF Research Database (Denmark)
Störrle, Harald
2013-01-01
Layered diagrams are diagrams whose elements are organized into sets of layers. Layered diagrams are routinely used in many branches of engineering, except Software Engineering. In this paper, we propose to add layered diagrams to UML modeling tools, and elaborate the concept by exploring usage...
su(2) Lie algebra approach for the Feynman propagator of the one-dimensional harmonic oscillator
Martínez, D.; Avendaño, C. G.
2014-04-01
We evaluate the Feynman propagator for the harmonic oscillator in one dimension. Considering the ladder operators for the Hamiltonian of this system, we construct a set of operators which satisfy the su(2) Lie algebra to obtain Mehler’s formula.
An elementary derivation of the quantum virial theorem from Hellmann-Feynman theorem
İpekoğlu, Y.; Turgut, S.
2016-07-01
A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann-Feynman theorem produces the final statement of the virial theorem.
Derivation of quantum work equalities using a quantum Feynman-Kac formula.
Liu, Fei
2012-07-01
On the basis of a quantum mechanical analog of the famous Feynman-Kac formula, we present a method to derive nonequilibrium work equalities for isolated quantum systems, which include the Jarzynski equality and Bochkov-Kuzovlev equality. Compared with other methods in the literature, our method shows a higher similarity in form to the method deriving the fluctuation relations in the classical systems.
An enzyme-free and DNA-based Feynman gate for logically reversible operation.
Zhou, Chunyang; Wang, Kun; Fan, Daoqing; Wu, Changtong; Liu, Dali; Liu, Yaqing; Wang, Erkang
2015-06-28
A logically reversible Feynman gate was successfully realized under enzyme-free conditions by integrating graphene oxide and DNA for the first time. The gate has a one-to-one mapping function to identify inputs from the corresponding outputs. This type of reversible logic gate may have great potential applications in information processing and biosensing systems.
The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory
Directory of Open Access Journals (Sweden)
Claude Semay
2015-01-01
Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.
Relation between Feynman cycles and off-diagonal long-range order.
Ueltschi, Daniel
2006-10-27
The usual order parameter for Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We discuss its validity with the help of rigorous results and heuristic arguments. The conclusion is that infinite cycles do not always represent the Bose condensate.
Feynman propagator for a free scalar field on a causal set.
Johnston, Steven
2009-10-30
The Feynman propagator for a free bosonic scalar field on the discrete spacetime of a causal set is presented. The formalism includes scalar field operators and a vacuum state which define a scalar quantum field theory on a causal set. This work can be viewed as a novel regularization of quantum field theory based on a Lorentz invariant discretization of spacetime.
On the Presentation of Wave Phenomena of Electrons with the Young-Feynman Experiment
Matteucci, Giorgio
2011-01-01
The Young-Feynman two-hole interferometer is widely used to present electron wave-particle duality and, in particular, the buildup of interference fringes with single electrons. The teaching approach consists of two steps: (i) electrons come through only one hole but diffraction effects are disregarded and (ii) electrons come through both holes…
Shifting and Variational Properties for Fourier-Feynman Transform and Convolution
Directory of Open Access Journals (Sweden)
Byoung Soo Kim
2015-01-01
Full Text Available Shifting, scaling, modulation, and variational properties for Fourier-Feynman transform of functionals in a Banach algebra S are given. Cameron and Storvick's translation theorem can be obtained as a corollary of our result. We also study shifting, scaling, and modulation properties for the convolution product of functionals in S.
Huygens-Feynman-Fresnel principle as the basis of applied optics.
Gitin, Andrey V
2013-11-01
The main relationships of wave optics are derived from a combination of the Huygens-Fresnel principle and the Feynman integral over all paths. The stationary-phase approximation of the wave relations gives the correspondent relations from the point of view of geometrical optics.
Attacking One-loop Multi-leg Feynman Integrals with the Loop-Tree Duality
Chachamis, Grigorios; Draggiotis, Petros; Rodrigo, German
2016-01-01
We discuss briefly the first numerical implementation of the Loop-Tree Duality (LTD) method. We apply the LTD method in order to calculate ultraviolet and infrared finite multi-leg one-loop Feynman integrals. We attack scalar and tensor integrals with up to six legs (hexagons). The LTD method shows an excellent performance independently of the number of external legs.
Einstein-Podolski-Rosen Paradox and Stochastic Wheeler-Feynman Absorber Theory
"今枝,国之助/今枝,真理"; "イマエダ,クニノスケ/イマエダ,マリ"; "Imaeda,Kuninosuke/Imaeda,Mari"
1982-01-01
"The basic idea of the theory developed in a previous paper : the theory of stochastic electrodynamics with classical Wheeler-Feynman absorber theory, the character of the Lorentz invariant zero point radiation and a minimum ""emitter-absorber transaction"" of Cramer extended to the case where the zero point radiation exists, has been studied."
Methods of numerical analysis of 1-dimensional 2-body problem in Wheeler-Feynman electrodynamics
Klimenko, S. V.; Nikitin, I. N.; Urazmetov, W. F.
2000-04-01
Numerical methods for solution of differential equations with deviating arguments describing 1-dimensional ultra-relativistic scattering of 2 identical charged particles in classical electrodynamics with half-retarded/halfadvanced interaction (Wheeler and Feynman, 1949) are developed. A bifurcation of solutions and violation of their reflectional symmetries in the region of velocities v>0.937c are found in numerical analysis.
The Feynman-Wheeler Perfect Absorber Theory in a New Light
Sidharth, B. G.
2010-08-01
The original Feynman-Wheeler perfect absorber theory lead to the Instantaneous Action at a Distance formulation. We observe that this is perfectly meaningful in the light of recent studies pointing to a small but non-zero photon mass. The Quantum Mechanical effects within the Compton scale of such a small mass photon would lead to the above formulation.
Deriving Internal Energy by Virtue of Generalized Feynman-Hellmann Theorem for Mixed States
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; JIANG Zhong-Hua
2005-01-01
We show how to directly use the generalized Feynman-Hellmann theorem, which is suitable for mixed state ensemble average, to derive the internal energy of Hamiltonian systems. A concrete example, which is a two coupled harminic oscillators, is used for elucidating our approach.
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo
2012-01-01
This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo
2012-01-01
This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)
Visualizing spacetimes via embedding diagrams
Hledik, Stanislav; Cipko, Alois
2016-01-01
It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an intuitive insight into the gravitational field rendered into a curved spacetime, and to assess the influence of parameters like electric charge and spin of a black hole, magnetic field or cosmological constant. Optical reference geometry and related inertial forces and their relationship to embedding diagrams are particularly useful for investigation of test particles motion. Embedding diagrams of static and spherically symmetric, or stationary and axially symmetric black-hole and naked-singularity spacetimes thus present a useful concept for intuitive understanding of these spacetimes' nature. We concentrate on general way of embedding into 3-dimensional Euclidean space, and give a set of illustrative examples.
Systematics of one-loop Yang-Mills diagrams from bosonic string amplitudes
Frizzo, A; Russo, R; Frizzo, Alberto; Magnea, Lorenzo; Russo, Rodolfo
2001-01-01
We present a general algorithm to compute off-shell, one-loop multigluon Green functions using bosonic string amplitudes. We identify and parametrize the regions in the space of moduli of one-loop Riemann surfaces that contribute to the field theory limit of string amplitudes. Each of these regions can be precisely associated with a Feynman-like scalar graph with cubic and quartic vertices, whose lines represent the joint propagation of ghosts and gluons. We give a procedure to compute the contribution of each graph to a gluon Green function, for arbitrarily polarized off-shell gluons, reducible and irreducible diagrams, planar and non-planar topologies. Explicit examples are given for up to six gluons.
Aoyama, T; Kinoshita, T; Nio, M
2014-01-01
This paper presents a detailed account of evaluation of the electron anomalous magnetic moment a_e which arises from the gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value of the sum of Set V diagrams evaluated by the Monte-Carlo integration routine VEGAS is 8.726(336)(\\alpha/\\pi)^5, which replaces the very preliminary value reported in 2012. Combining it with other 6318 tenth-order diagrams published previously we obtain 7.795(336)(\\alpha/\\pi)^5 as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to a_e(theory)=1 159 652 181.643 (25)(23)(16)(763) \\times 10^{-12}, where first three uncertainties are from the eighth-order term, tenth-order term, and hadronic and elecroweak terms. The fourth and largest uncertainty is from \\alpha^{-1}=137.035 999 049(90), the fine-structure constant derived from the rubidium recoil measurement. a_e(theory) and a_e(experiment) agree wi...
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...
Electrical elementary diagrams and operators
Energy Technology Data Exchange (ETDEWEB)
Patterson, B.K. [Human Factors Practical Inc., Dipper Harbour, New Brunswick (Canada)]. E-mail: HumanFactors@netscape.ca
2005-07-01
After 40 years of reading and interrupting electrical elementary logic drawings, I have concluded that we need to make a change. We need to write and express our nuclear power plant logic in some other language than relay ladder logic, solid state logic or computer mnemonics. The language should be English, or your native language, and the format should be Descriptive Block Diagrams. (author)
The diagram for phyllotactic series
Directory of Open Access Journals (Sweden)
Joanna Szymanowska-Pułka
2014-01-01
Full Text Available Many authors studying phyllotaxis in various plant species have reported the occurrence of many different numbers of contact parastichy pairs that are members of different Fibonacci-like series. On the basis of these reports a diagram was constructed in which any theoretically possible series was represented by the two first members of a given series.
BIHOURLY DIAGRAMS OF FORBUSH DECREASES
Bihourly diagrams were made of Forbush decreases of cosmic ray intensity as observed at Uppsala from 31 Aug 56 to 31 Dec 59, at Kiruna from Nov 56 to 31 Dec 59, and at Murchison Bay from 26 Aug 57 to 30 Apr 59. (Author)
Phase diagram of Hertzian spheres
Pàmies, J.C.; Cacciuto, A.; Frenkel, D.
2009-01-01
We report the phase diagram of interpenetrating Hertzian spheres. The Hertz potential is purely repulsive, bounded at zero separation, and decreases monotonically as a power law with exponent 5/2, vanishing at the overlapping threshold. This simple functional describes the elastic interaction of wea
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...
Multi-currency Influence Diagrams
DEFF Research Database (Denmark)
Nielsen, Søren Holbech; Nielsen, Thomas Dyhre; Jensen, Finn V.
2007-01-01
When using the influence diagrams framework for solving a decision problem with several different quantitative utilities, the traditional approach has been to convert the utilities into one common currency. This conversion is carried out using a tacit transformation, under the assumption that the...
Multi-currency Influence Diagrams
DEFF Research Database (Denmark)
Nielsen, Søren Holbech; Nielsen, Thomas Dyhre; Jensen, Finn Verner
2004-01-01
that the converted problem is equivalent to the original one. In this paper we present an extension of the Influence Diagram framework, which allows for these decision problems to be modelled in their original form. We present an algorithm that, given a conversion function between the currencies, discovers...
Institute of Scientific and Technical Information of China (English)
王子冠; 沈峰
2015-01-01
Feynman-α方法是中子噪声分析方法的一种,它根据增殖介质中探测器中子计数会偏离泊松分布的原理,计算次临界系统的α本征值,从而得到该系统的次临界度.已有的Feynman-α方程基于点堆单群模型,无法精确描述带有反射层的次临界系统.通过推导基于双区单群次临界系统模型的Feynman-α方程的解析解,能为次临界系统α本征值和次临界度计算提供更精确的方法.本文构造了基于双区单群次临界系统模型的Feynman-α方程,考虑了全部可能的中子反应类型(包括中子吸收、裂变、迁移和被探测),并考虑了1组缓发中子的影响.通过求解此双区单群Feynman-α方程,得到了Feynman-Y表达式的解析解,可用于次临界度的计算.
Hero's journey in bifurcation diagram
Monteiro, L. H. A.; Mustaro, P. N.
2012-06-01
The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films.
Anatomy of geodesic Witten diagrams
Chen, Heng-Yu; Kuo, En-Jui; Kyono, Hideki
2017-05-01
We revisit the so-called "Geodesic Witten Diagrams" (GWDs) [1], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.
Nakamura, Nozomu; Yamasaki, Kazuhito
2016-08-01
We consider the relationship between the magnetic field and the non-elastic displacement field including defects, from the viewpoints of non-commutativity of the positions and non-commutativity of the derivatives. The former non-commutativity is related to the magnetic field by Feynman's proof (1948), and the latter is related to the defect fields by the continuum theory of defects. We introduce the concept of differential geometry to the non-elastic displacement field and derive an extended relation that includes basic equations, such as Gauss's law for magnetism and the conservation law for dislocation density. The relation derived in this paper also extends the first Bianchi identity in linear approximation to include the effect of magnetism. These findings suggest that Feynman's approach with a non-elastic displacement field is useful for understanding the relationship between magnetism and non-elastic mechanics.
The dependence of J/ψ-nucleon inelastic cross section on the Feynman variable
Institute of Scientific and Technical Information of China (English)
DUAN Chun-Gui; LIU Na; MIAO Wen-Dan
2011-01-01
By means of two typical sets of nuclear parton distribution functions,meanwhile taking account of the energy loss of the beam proton and the nuclear absorption of the charmonium states traversing the nuclear matter in the uniform framework of the Glauber model,a leading order phenomenological analysis is given in the color evaporation model of the E866 experimental data on J/Ψ production differential cross section ratios RFe/Be(xF).It is shown that the energy loss effect of beam proton on RFe/Be(xF)is more important than the nuclear effects on parton distribution functions in the high Feynman variable xF region.It is found that the J/Ψ-nucleon inelastic cross section depends on the Feynman variable XF and increases linearly with XF in the region xF > 0.2.
Nakamura, Nozomu; Yamasaki, Kazuhito
2016-12-01
We consider the relationship between the magnetic field and the non-elastic displacement field including defects, from the viewpoints of non-commutativity of the positions and non-commutativity of the derivatives. The former non-commutativity is related to the magnetic field by Feynman's proof (1948), and the latter is related to the defect fields by the continuum theory of defects. We introduce the concept of differential geometry to the non-elastic displacement field and derive an extended relation that includes basic equations, such as Gauss's law for magnetism and the conservation law for dislocation density. The relation derived in this paper also extends the first Bianchi identity in linear approximation to include the effect of magnetism. These findings suggest that Feynman's approach with a non-elastic displacement field is useful for understanding the relationship between magnetism and non-elastic mechanics.
Simon, Martin
2015-01-01
This monograph is concerned with the analysis and numerical solution of a stochastic inverse anomaly detection problem in electrical impedance tomography (EIT). Martin Simon studies the problem of detecting a parameterized anomaly in an isotropic, stationary and ergodic conductivity random field whose realizations are rapidly oscillating. For this purpose, he derives Feynman-Kac formulae to rigorously justify stochastic homogenization in the case of the underlying stochastic boundary value problem. The author combines techniques from the theory of partial differential equations and functional analysis with probabilistic ideas, paving the way to new mathematical theorems which may be fruitfully used in the treatment of the problem at hand. Moreover, the author proposes an efficient numerical method in the framework of Bayesian inversion for the practical solution of the stochastic inverse anomaly detection problem. Contents Feynman-Kac formulae Stochastic homogenization Statistical inverse problems Targe...
Wheeler-Feynman absorber theory, the Einstein-Podolski-Rosen paradox, and stochastic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Imaeda, K. (Dublin Inst. for Advanced Studies (Ireland)); Imaeda, M. (IFUP, Dublin (Ireland))
1982-04-04
The classical Wheeler-Feynman absorber theory with a postulate of Lorentz-invariant zero-point electromagnetic radiation is proposed to explain quantum phenomena in a similar manner to that of stochastic electrodynamics. For this purpose, Cramer's model (Phys. Rev.; D22:362 (1980)) of a 'minimum emitter-absorber transaction' is extended to the case where zero-point radiation exists, in the context of the classical Wheeler-Feynman theory. The Einstein-Podolski-Rosen paradox and the quantum levels of a charged simple harmonic oscillator are derived from the theory. It is shown that the condition for a transaction plays an essential role, such as in the radiative balance of a simple harmonic oscillator.
Improved Parameterization of $K^+$ Production at Low Energy Using Feynman Scaling
Mariani, C; Conrad, J M; Shaevitz, M H
2011-01-01
This paper describes an improved parameterization for proton-beryllium production of secondary $K^{+}$ mesons for experiments with primary proton beams from 8.9 to 24 GeV. The parameterization is based on Feynman scaling in which the invariant cross section is described as a function of $x_{F}$ and $p_{T}$. This method is theoretically motivated and provides a better description of the energy dependence of kaon production at low beam energies than other parameterizations such as the commonly used "Modified Sanford-Wang" model. This Feynman scaling parameterization has been used for the simulation of the neutrino flux from the Booster Neutrino Beam (BNB) at Fermilab and has been shown to agree with the neutrino interaction data from the SciBooNE experiment. This parameterization will also be useful for future neutrino experiments with low primary beam energies, such as those planned for the Project X accelerator.
Hubble's diagram and cosmic expansion
Kirshner, Robert P.
2003-01-01
Edwin Hubble's classic article on the expanding universe appeared in PNAS in 1929 [Hubble, E. P. (1929) Proc. Natl. Acad. Sci. USA 15, 168–173]. The chief result, that a galaxy's distance is proportional to its redshift, is so well known and so deeply embedded into the language of astronomy through the Hubble diagram, the Hubble constant, Hubble's Law, and the Hubble time, that the article itself is rarely referenced. Even though Hubble's distances have a large systematic error, Hubble's velo...
Hubble's diagram and cosmic expansion
Kirshner, Robert P.
2003-01-01
Edwin Hubble's classic article on the expanding universe appeared in PNAS in 1929 [Hubble, E. P. (1929) Proc. Natl. Acad. Sci. USA 15, 168–173]. The chief result, that a galaxy's distance is proportional to its redshift, is so well known and so deeply embedded into the language of astronomy through the Hubble diagram, the Hubble constant, Hubble's Law, and the Hubble time, that the article itself is rarely referenced. Even though Hubble's distances have a large systematic error, Hubble's velo...
Reliability computation from reliability block diagrams
Chelson, P. O.; Eckstein, E. Y.
1975-01-01
Computer program computes system reliability for very general class of reliability block diagrams. Four factors are considered in calculating probability of system success: active block redundancy, standby block redundancy, partial redundancy, and presence of equivalent blocks in the diagram.
Phase diagram of crushed powders
Bodard, Sébastien; Jalbaud, Olivier; Saurel, Richard; Burtschell, Yves; Lapebie, Emmanuel
2016-12-01
Compression of monodisperse powder samples in quasistatic conditions is addressed in a pressure range such that particles fragmentation occurs while the solid remains incompressible (typical pressure range of 1-300 MPa for glass powders). For a granular bed made of particles of given size, the existence of three stages is observed during compression and crush up. First, classical compression occurs and the pressure of the granular bed increases along a characteristic curve as the volume decreases. Then, a critical pressure is reached for which fragmentation begins. During the fragmentation process, the granular pressure stays constant in a given volume range. At the end of this second stage, 20%-50% of initial grains are reduced to finer particles, depending on the initial size. Then the compression undergoes the third stage and the pressure increases along another characteristic curve, in the absence of extra fragmentation. The present paper analyses the analogies between the phase transition in liquid-vapour systems and powder compression with crush-up. Fragmentation diagram for a soda lime glass is determined by experimental means. The analogues of the saturation pressure and latent heat of phase change are determined. Two thermodynamic models are then examined to represent the crush-up diagram. The first one uses piecewise functions while the second one is of van der Waals type. Both equations of state relate granular pressure, solid volume fraction, and initial particle diameter. The piecewise functions approach provides reasonable representations of the phase diagram while the van der Waals one fails.
Scheil-Gulliver Constituent Diagrams
Pelton, Arthur D.; Eriksson, Gunnar; Bale, Christopher W.
2017-03-01
During solidification of alloys, conditions often approach those of Scheil-Gulliver cooling in which it is assumed that solid phases, once precipitated, remain unchanged. That is, they no longer react with the liquid or with each other. In the case of equilibrium solidification, equilibrium phase diagrams provide a valuable means of visualizing the effects of composition changes upon the final microstructure. In the present study, we propose for the first time the concept of Scheil-Gulliver constituent diagrams which play the same role as that in the case of Scheil-Gulliver cooling. It is shown how these diagrams can be calculated and plotted by the currently available thermodynamic database computing systems that combine Gibbs energy minimization software with large databases of optimized thermodynamic properties of solutions and compounds. Examples calculated using the FactSage system are presented for the Al-Li and Al-Mg-Zn systems, and for the Au-Bi-Sb-Pb system and its binary and ternary subsystems.
Efficient implementation of the Hellmann-Feynman theorem in a diffusion Monte Carlo calculation.
Vitiello, S A
2011-02-07
Kinetic and potential energies of systems of (4)He atoms in the solid phase are computed at T = 0. Results at two densities of the liquid phase are presented as well. Calculations are performed by the multiweight extension to the diffusion Monte Carlo method that allows the application of the Hellmann-Feynman theorem in a robust and efficient way. This is a general method that can be applied in other situations of interest as well.
Feynman rules in the Lorentz violating extension of the standard model
Directory of Open Access Journals (Sweden)
A Binandeh
2011-12-01
Full Text Available We consider the Lorentz violating extension of the standard model introduced by D. Colladay and V. A. Kostelecky. In this framework, we obtain all Feynman rules for the electroweak part of the standard model extension (SME, for the first time. Among the new obtained interactions one finds new vertices for the Higgs boson that is interesting in the phenomenology of the Higgs particle.
Inelastic electron holography as a variant of the Feynman thought experiment.
Potapov, P L; Verbeeck, J; Schattschneider, P; Lichte, H; van Dyck, D
2007-08-01
Using a combination of electron holography and energy filtering, interference fringes produced after inelastic interaction of electrons with hydrogen molecules are examined. Surprisingly, the coherence of inelastic scattering increases when moving from the surface of a hydrogen-containing bubble to the vacuum. This phenomenon can be understood in terms of the Feynman two-slit thought experiment with a variable ambiguity of the which-way registration.
Tugai, V V
1996-01-01
A supersymmetric formulation of the classical action of interacting charged and neutral fermions with arbitrary anomalous magnetic moment is considered. This formulation generalizes the known action for scalar charged particles investigated in papers by Fokker, Schwarzschild, Tetrode, Wheeler and Feynman. The superfield formulation of the electrodynamics of the Maxwell supermultiplet, constructed from the world coordinates of charged or neutral fermions is carried out basing on the proposed action.
Tugai, V. V.; Zheltukhin, A. A.
1996-01-01
A supersymmetric formulation of the classical action of interacting charged and neutral fermions with arbitrary anomalous magnetic moment is considered. This formulation generalizes the known action for scalar charged particles investigated in papers by Fokker, Schwarzschild, Tetrode, Wheeler and Feynman. The superfield formulation of the electrodynamics of the Maxwell supermultiplet, constructed from the world coordinates of charged or neutral fermions is carried out basing on the proposed a...
Two-Group Theory of the Feynman-Alpha Method for Reactivity Measurement in ADS
Directory of Open Access Journals (Sweden)
Lénárd Pál
2012-01-01
Full Text Available The theory of the Feynman-alpha method, which is used to determine the subcritical reactivity of systems driven by an external source such as an ADS, is extended to two energy groups with the inclusion of delayed neutrons. This paper presents a full derivation of the variance to mean formula with the inclusion of two energy groups and delayed neutrons. The results are illustrated quantitatively and discussed in physical terms.
General $\\varepsilon$-representation for scalar one-loop Feynman integrals
Bluemlein, Johannes; Riemann, Tord
2015-01-01
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms of higher transcendental functions. The integrals play a role as building blocks in general higher-loop or multi-leg processes. We also perform numerical checks of the calculations using AMBRE/MB and LoopTools/FF.
Nikolov, Nikolay M.
2016-01-01
We propose a new renormalization procedure to all orders in perturbation theory, which is formulated on an extended position space. This allows us to apply methods from massless Quantum Field Theory to models of massive fields. These include the technique of homogeneous and associate homogeneous distributions for the extension problem contained in the renormalization theory on position space. This also makes it possible to generalize the notion of residues of Feynman amplitudes, which charact...
A new look at the Feynman `hodograph' approach to the Kepler first law
Cariñena, Jose F; Santander, M
2016-01-01
Hodographs for the Kepler problem are circles. This fact, known since almost two centuries ago, still provides the simplest path to derive the Kepler first law. Through Feynman `lost lecture', this derivation has now reached to a wider audience. Here we look again at Feynman's approach to this problem as well as at the recently suggested modification by van Haandel and Heckman (vHH), with two aims in view, both of which extend the scope of the approach. First we review the geometric constructions of the Feynman and vHH approaches (that prove the existence of {\\itshape elliptic} orbits without making use of integral calculus or differential equations) and then we extend the geometric approach to cover also the {\\itshape hyperbolic} orbits (corresponding to $E>0$). In the second part we analyse the properties of the director circles of the conics, which are used to simplify the approach and we relate with the properties of the hodographs and with the Laplace-Runge-Lenz vector, the constant of motion specific to...
Directory of Open Access Journals (Sweden)
Nikesh S. Dattani
2012-03-01
Full Text Available One of the most successful methods for calculating reduced density operator dynamics in open quantum systems, that can give numerically exact results, uses Feynman integrals. However, when simulating the dynamics for a given amount of time, the number of time steps that can realistically be used with this method is always limited, therefore one often obtains an approximation of the reduced density operator at a sparse grid of points in time. Instead of relying only on ad hoc interpolation methods (such as splines to estimate the system density operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the density operator dynamics to be captured with as little as two time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating density operator dynamics within a desired accuracy. Since this method does not change the way the Feynman integral itself is calculated, the value of the density operator approximation at the points in time used to discretize the Feynamn integral will be the same whether or not this method is used, but its approximation in between these points in time is considerably improved by this method. A list of ways in which this proposed method can be further improved is presented in the last section of the article.
Feynman-like Rules for Calculating n-Point Correlators of the Primordial Curvature Perturbation
Valenzuela-Toledo, Cesar A; Almeida, J P Beltran
2011-01-01
A diagrammatic approach to calculate n-point correlators of the primordial curvature perturbation \\zeta was developed a few years ago following the spirit of the Feynman rules in Quantum Field Theory. The methodology is very useful and time-saving, as it is for the case of the Feynman rules in the particle physics context, but, unfortunately, is not very well known by the cosmology community. In the present work, we extend such an approach in order to include not only scalar field perturbations as the generators of \\zeta, but also vector field perturbations. The purpose is twofold: first, we would like the diagrammatic approach (which we would call the Feynman-like rules) to become widespread among the cosmology community; second, we intend to give an easy tool to formulate any correlator of \\zeta for those cases that involve vector field perturbations and that, therefore, may generate prolonged stages of anisotropic expansion and/or important levels of statistical anisotropy. Indeed, the usual way of formula...
Operations space diagram for ECRH and ECCD
DEFF Research Database (Denmark)
Bindslev, H.
2004-01-01
A Clemmov-Mullaly-Allis (CMA) type diagram, the ECW-CMA diagram, for representing the operational possibilities of electron cyclotron heating and current drive (ECRH/ECCD) systems for fusion plasmas is presented. In this diagram, with normalized density and normalized magnetic field coordinates...
Diagram, a Learning Environment for Initiation to Object-Oriented Modeling with UML Class Diagrams
Py, Dominique; Auxepaules, Ludovic; Alonso, Mathilde
2013-01-01
This paper presents Diagram, a learning environment for object-oriented modelling (OOM) with UML class diagrams. Diagram an open environment, in which the teacher can add new exercises without constraints on the vocabulary or the size of the diagram. The interface includes methodological help, encourages self-correcting and self-monitoring, and…
Diagram, a Learning Environment for Initiation to Object-Oriented Modeling with UML Class Diagrams
Py, Dominique; Auxepaules, Ludovic; Alonso, Mathilde
2013-01-01
This paper presents Diagram, a learning environment for object-oriented modelling (OOM) with UML class diagrams. Diagram an open environment, in which the teacher can add new exercises without constraints on the vocabulary or the size of the diagram. The interface includes methodological help, encourages self-correcting and self-monitoring, and…
Directory of Open Access Journals (Sweden)
Paulo S. G. Pereira
2002-03-01
Full Text Available Introdução: Este trabalho é um estudo morfológico do desenvolvimento da cartilagem quadrangular humana ao longo da vida. Para tal retiramos cartilagens quadrangulares em bloco com as demais cartilagens do nariz, utilizando a técnica de rinoplastia aberta, em cadáveres autopsiados no Serviço de Patologia do Hospital das Clínicas da Faculdade de Medicina de Ribeirão Preto - USP e no serviço de verificação de óbitos do interior, em Ribeirão Preto. Forma de estudo: Experimental. Métodos: As peças anatômicas foram cortadas em dois pontos dividindo-as em três partes, com relação ao eixo caudo-cefálico correspondendo à borda livre da cartilagem, terço caudal (posição 1, médio (posição 2 e cefálico (posição 3. Tem relação com a placa perpendicular do etmóide e volmer. As amostras foram fixadas em formol a 10% e incluídas em parafina. Foram examinados cortes histológicos de 7 µm de espessura e corados por hematoxilina e eosina (HE e Alcian Blue. Em cada posição, três diferentes locais, em relação ao eixo ântero-posterior do nariz: Terço superior (local 1, terço médio (local 2 e terço inferior (local 3 foram estudados sobre Microscopia Óptica, com métodos fotométricos, histológicos e morfométricos. Resultado: Mostra que o tecido cartilaginoso apresenta maior velocidade de crescimento até cinco anos de idade. A menor velocidade de crescimento ocorre a partir dos oito anos de idade. Não ocorreu diferença de atividade metabólica entre as diversas regiões estudadas. Conclusões: As intervenções cirúrgicas no septo cartilaginoso podem ser realizadas após os cinco anos de idade. A idade inicial mais adequada para as cirurgias do septo nasal ocorreria aos oito anos.Introduction: The present paper is a morphological study of human quadrilateral cartilage including 0 to 66 years old subjects. The quadrilateral cartilage was removed in block with the others nasal cartilages. The open rhinoplasty was the
Origin and use of crystallization phase diagrams.
Rupp, Bernhard
2015-03-01
Crystallization phase diagrams are frequently used to conceptualize the phase relations and also the processes taking place during the crystallization of macromolecules. While a great deal of freedom is given in crystallization phase diagrams owing to a lack of specific knowledge about the actual phase boundaries and phase equilibria, crucial fundamental features of phase diagrams can be derived from thermodynamic first principles. Consequently, there are limits to what can be reasonably displayed in a phase diagram, and imagination may start to conflict with thermodynamic realities. Here, the commonly used `crystallization phase diagrams' are derived from thermodynamic excess properties and their limitations and appropriate use is discussed.
Using Affinity Diagrams to Evaluate Interactive Prototypes
DEFF Research Database (Denmark)
Lucero, Andrés
2015-01-01
Affinity diagramming is a technique used to externalize, make sense of, and organize large amounts of unstructured, far-ranging, and seemingly dissimilar qualitative data. HCI and interaction design practitioners have adopted and used affinity diagrams for different purposes. This paper discusses...... our particular use of affinity diagramming in prototype evaluations. We reflect on a decade’s experience using affinity diagramming across a number of projects, both in industry and academia. Our affinity diagramming process in interaction design has been tailored and consists of four stages: creating...
Diagram Size vs. Layout Flaws: Understanding Quality Factors of UML Diagrams
DEFF Research Database (Denmark)
Störrle, Harald
2016-01-01
, though, is our third goal of extending our analysis aspects of diagram quality. Method: We improve our definition of diagram size and add a (provisional) definition of diagram quality as the number of topographic layout flaws. We apply these metrics on 60 diagrams of the five most commonly used types...... of UML diagram. We carefully analyze the structure of our diagram samples to ensure representativeness. We correlate diagram size and layout quality with modeler performance data obtained in previous experiments. The data set is the largest of its kind (n-156). Results: We replicate earlier findings......, and extend them to two new diagram types. We provide an improved definition of diagram size, and provide a definition of topographic layout quality, which is one more step towards a comprehensive definition of diagram quality as such. Both metrics are shown to be objectively applicable. We quantify...
Grid diagrams and Khovanov homology
DEFF Research Database (Denmark)
Droz, Jean-Marie; Wagner, Emmanuel
2009-01-01
We explain how to compute the Jones polynomial of a link from one of its grid diagrams and we observe a connection between Bigelow’s homological definition of the Jones polynomial and Kauffman’s definition of the Jones polynomial. Consequently, we prove that the Maslov grading on the Seidel......–Smith symplectic link invariant coincides with the difference between the homological grading on Khovanov homology and the Jones grading on Khovanov homology. We give some evidence for the truth of the Seidel–Smith conjecture....
Phase Diagrams of Nuclear Pasta
Caplan, Matthew; Horowitz, Chuck; Berry, Don; da Silva Schneider, Andre
2016-03-01
In the inner crust of neutrons stars, where matter is near the saturation density, protons and neutrons arrange themselves into complex structures called nuclear pasta. Early theoretical work predicted a simple graduated hierarchy of pasta phases, consisting of spheres, cylinders, slabs, and uniform matter with voids. Previous work has simulated these phases with a simple classical model and has shown that the formation of these structures is dependent on the temperature, density, and proton fraction. However, previous work only studied a limited range of these parameters due to computational limitations. Thanks to recent advances in computing it is now possible to survey the structure of nuclear pasta for a larger range of parameters. By simulating nuclear pasta with constant temperature and proton fraction in an expanding simulation volume we are able to study the phase transitions in nuclear pasta, and thus produce a set of phase diagrams. We report on these phase diagrams as well as newly identified phases of nuclear pasta and discuss their implications for neutron star observables.
Asteroseismology Across the HR Diagram
Thompson, M. J.; Cunha, M. S.; Monteiro, M. J. P. F. G.
2003-05-01
Ground-based observations have detected solar-like oscillations on Sun-like stars, and diagnostics similar to those used in helioseismology are now being used to test and constrain the physics and evolutionary state of these stars. Multi-mode oscillations are being observed in an abundance of other stars, including slowly pulsating B stars (SPB stars), delta-Scuti stars, Ap stars and the pulsating white dwarfs. New classes of pulsators continue to be discovered across the Herzsprung-Russell diagram. Yet the chances still to be faced to make asteroseismology across the HR diagram a reality are formidable. Observation, data analysis and theory all pose hard problems to be overcome. This book, reflecting the goal of the meeting, aims to facilitate a cross-fertilisation of ideas and approaches between fields covering different pulsators and with different areas of expertise. The book successfully covers most known types of pulsators, reflecting a highly productive and far reaching interchange of ideas which we believe is conveyed by the papers and posters published, making it a reference for researchers and postgraduate students working on stellar structure and evolution. Link: http://www.wkap.nl/prod/b/1-4020-1173-3
关于广义Feynman-Kac半群的一个注记%A note of generalized Feynman-Kac semigroups
Institute of Scientific and Technical Information of China (English)
马丽; 韩新方
2007-01-01
设(Xt)t＞0是Lévy过程,(ε,D(ε))为其联系的狄氏型;对任意的u,∈Dε),设Nut为u(xt)-u(xO)的Fukushima分解中的零能量连续可加泛函.本论文主要研究了广义FeynmanKac半群Ttf(χ)=Eχ[eNutf(Xt)],得到当u的能量测度μ《u》属于Hardy类且Hardy类系数大于0小于1/2时,(Tt)t≥0是强连续半群,并且得到了其对应的二次型表达式.
Feynman's thesis: A new approach to quantum theory
Energy Technology Data Exchange (ETDEWEB)
Das, Ashok [Department of Physics and Astronomy, University of Rochester (United States)
2007-01-07
It is not usual for someone to write a book on someone else's Ph.D. thesis, but then Feynman was not a usual physicist. He was without doubt one of the most original physicists of the twentieth century, who has strongly influenced the developments in quantum field theory through his many ingenious contributions. Path integral approach to quantum theories is one such contribution which pervades almost all areas of physics. What is astonishing is that he developed this idea as a graduate student for his Ph.D. thesis which has been printed, for the first time, in the present book along with two other related articles. The early developments in quantum theory, by Heisenberg and Schroedinger, were based on the Hamiltonian formulation, where one starts with the Hamiltonian description of a classical system and then promotes the classical observables to noncommuting quantum operators. However, Dirac had already stressed in an article in 1932 (this article is also reproduced in the present book) that the Lagrangian is more fundamental than the Hamiltonian, at least from the point of view of relativistic invariance and he wondered how the Lagrangian may enter into the quantum description. He had developed this idea through his 'transformation matrix' theory and had even hinted on how the action of the classical theory may enter such a description. However, although the brief paper by Dirac contained the basic essential ideas, it did not fully develop the idea of a Lagrangian description in detail in the functional language. Feynman, on the other hand, was interested in the electromagnetic interactions of the electron from a completely different point of view rooted in a theory involving action-at-a-distance. His theory (along with John Wheeler) did not have a Hamiltonian description and, in order to quantize such a theory, he needed an alternative formulation of quantum mechanics. When the article by Dirac was brought to his attention, he immediately realized
Continuation of point clouds via persistence diagrams
Gameiro, Marcio; Hiraoka, Yasuaki; Obayashi, Ippei
2016-11-01
In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton-Raphson continuation method in this setting. Given an original point cloud P, its persistence diagram D, and a target persistence diagram D‧, we gradually move from D to D‧, by successively computing intermediate point clouds until we finally find a point cloud P‧ having D‧ as its persistence diagram. Our method can be applied to a wide variety of situations in topological data analysis where it is necessary to solve an inverse problem, from persistence diagrams to point cloud data.
Mathematical review on source-type diagrams
Aso, Naofumi; Ohta, Kazuaki; Ide, Satoshi
2016-03-01
A source-type diagram is a visualization tool used to display earthquake sources, including double-couples, compensated linear vector dipoles, and isotropic deformation. Together with recent observations of non-double-couple events in a variety of tectonic settings, it is important to be able to recognize the source type intuitively from a representative diagram. Since previous works have proposed diagrams created using a range of projections, we review these diagrams in the framework of the moment tensor eigenvalue space. For further applications, we also provide complete formulas for conversion between moment tensor representation and the coordinate system of each diagram style. Using both a global catalog and synthetic data, we discuss differences between types of diagrams and the relative effectiveness of each.
Retrospect and Prospect of the Influence Diagram
Institute of Scientific and Technical Information of China (English)
LiuYanqiong; ShenYongping; ChenYingwu
2005-01-01
The evaluation algorithm and the application of the influence diagram were surveyed, which argues that to construct an explicit,compact and objective influence diagram is of the most importance. There are two suggested ways for realization of the influence diagram: introducing the achievements of the modern psychology, cognitive science, behavior science, and so on to represent and solve uncertainty to build a well-constructed influence diagram; based on the observed data to build an influence diagram. Also, the limitations of the influence diagram were analyzed, such as that it cannot deal with asynunetric problems efficiently, cannot picture dynamic problems,cannot model the problems with a limitless horizon, and ther is no highly efficient algorithm. And some potential methods to overcome these limitations were pointed out.
Rajagopal, K
1999-01-01
The QCD vacuum in which we live, which has the familiar hadrons as its excitations, is but one phase of QCD, and far from the simplest one at that. One way to better understand this phase and the nonperturbative dynamics of QCD more generally is to study other phases and the transitions between phases. We are engaged in a voyage of exploration, mapping the QCD phase diagram as a function of temperature T and baryon number chemical potential mu . Because of asymptotic freedom, the high temperature and high baryon density phases of QCD are more simply and more appropriately described in terms of quarks and gluons as degrees of freedom, rather than hadrons. The chiral symmetry breaking condensate which characterizes the vacuum phase melts away. At high densities, quarks form Cooper pairs and new condensates develop. The formation of such superconducting phases requires only weak attractive interactions; these phases may nevertheless break chiral symmetry and have excitations which are indistinguishable from thos...
Herrmann, Enrico
2016-01-01
We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only $\\dlog$-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for $\\N=8$ supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum, poles at infinity are present and loop amplitudes show special behavior on certain collinear cuts. We demonstrate on 1-loop and 2-loop examples that the behavior on collinear cuts is a highly non-trivial property which requires cancellations between all terms contributing to the amplitude.
Energy Technology Data Exchange (ETDEWEB)
Herrmann, Enrico [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Trnka, Jaroslav [Center for Quantum Mathematics and Physics (QMAP),Department of Physics, University of California,Davis, CA 95616 (United States)
2016-11-22
We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only dlog-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for N=8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinity are present, in complete agreement with the conjecture presented in http://dx.doi.org/10.1007/JHEP06(2015)202.
Solving Limited Memory Influence Diagrams
Mauá, Denis Deratani; Zaffalon, Marco
2011-01-01
We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and $10^{64}$ solutions. We show that the problem is NP-hard even if the underlying graph structure of the problem has small treewidth and the variables take on a bounded number of states, but that a fully polynomial time approximation scheme exists for these cases. Moreover, we show that the bound on the number of states is a necessary condition for any efficient approximation scheme.
Phase diagram of ammonium nitrate
Dunuwille, M.; Yoo, C. S.
2014-05-01
Ammonium Nitrate (AN) has often subjected to uses in improvised explosive devices, due to its wide availability as a fertilizer and its capability of becoming explosive with slight additions of organic and inorganic compounds. Yet, the origin of enhanced energetic properties of impure AN (or AN mixtures) is neither chemically unique nor well understood -resulting in rather catastrophic disasters in the past1 and thereby a significant burden on safety in using ammonium nitrates even today. To remedy this situation, we have carried out an extensive study to investigate the phase stability of AN at high pressure and temperature, using diamond anvil cells and micro-Raman spectroscopy. The present results confirm the recently proposed phase IV-to-IV' transition above 17 GPa2 and provide new constraints for the melting and phase diagram of AN to 40 GPa and 400 °C.
Stereo 3D spatial phase diagrams
Energy Technology Data Exchange (ETDEWEB)
Kang, Jinwu, E-mail: kangjw@tsinghua.edu.cn; Liu, Baicheng, E-mail: liubc@tsinghua.edu.cn
2016-07-15
Phase diagrams serve as the fundamental guidance in materials science and engineering. Binary P-T-X (pressure–temperature–composition) and multi-component phase diagrams are of complex spatial geometry, which brings difficulty for understanding. The authors constructed 3D stereo binary P-T-X, typical ternary and some quaternary phase diagrams. A phase diagram construction algorithm based on the calculated phase reaction data in PandaT was developed. And the 3D stereo phase diagram of Al-Cu-Mg ternary system is presented. These phase diagrams can be illustrated by wireframe, surface, solid or their mixture, isotherms and isopleths can be generated. All of these can be displayed by the three typical display ways: electronic shutter, polarization and anaglyph (for example red-cyan glasses). Especially, they can be printed out with 3D stereo effect on paper, and watched by the aid of anaglyph glasses, which makes 3D stereo book of phase diagrams come to reality. Compared with the traditional illustration way, the front of phase diagrams protrude from the screen and the back stretches far behind of the screen under 3D stereo display, the spatial structure can be clearly and immediately perceived. These 3D stereo phase diagrams are useful in teaching and research. - Highlights: • Stereo 3D phase diagram database was constructed, including binary P-T-X, ternary, some quaternary and real ternary systems. • The phase diagrams can be watched by active shutter or polarized or anaglyph glasses. • The print phase diagrams retains 3D stereo effect which can be achieved by the aid of anaglyph glasses.
Process Flow Diagrams for Training and Operations
Venter, Jacobus
This paper focuses on the use of process flow diagrams for training first responders who execute search and seizure warrants at electronic crime scenes. A generic process flow framework is presented, and the design goals and layout characteristics of process flow diagrams are discussed. An evaluation of the process flow diagrams used in training courses indicates that they are beneficial to first responders performing searches and seizures, and they speed up investigations, including those conducted by experienced personnel.
Nikolov, Nikolay M.
2016-11-01
We propose a new renormalization procedure to all orders in perturbation theory, which is formulated on an extended position space. This allows us to apply methods from massless Quantum Field Theory to models of massive fields. These include the technique of homogeneous and associate homogeneous distributions for the extension problem contained in the renormalization theory on position space. This also makes it possible to generalize the notion of residues of Feynman amplitudes, which characterize the presence of additional scales due to renormalization, to the massive case.
Properties of the Feynman-alpha method applied to accelerator-driven subcritical systems.
Taczanowski, S; Domanska, G; Kopec, M; Janczyszyn, J
2005-01-01
A Monte Carlo study of the Feynman-method with a simple code simulating the multiplication chain, confined to pertinent time-dependent phenomena has been done. The significance of its key parameters (detector efficiency and dead time, k-source and spallation neutrons multiplicities, required number of fissions etc.) has been discussed. It has been demonstrated that this method can be insensitive to properties of the zones surrounding the core, whereas is strongly affected by the detector dead time. In turn, the influence of harmonics in the neutron field and of the dispersion of spallation neutrons has proven much less pronounced.
Directory of Open Access Journals (Sweden)
Marcos Moshinsky
2007-11-01
Full Text Available A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function is presented, and the propagator can be obtained later with an inverse Laplace transform. The method is illustrated through simple one dimensional examples and for time independent potentials, though it can be generalized to the derivation of more complicated propagators.
Singla, Pradeep
2012-01-01
This paper present the research work directed towards the design of reversible programmable logic array using very high speed integrated circuit hardware description language (VHDL). Reversible logic circuits have significant importance in bioinformatics, optical information processing, CMOS design etc. In this paper the authors propose the design of new RPLA using Feynman & MUX gate.VHDL based codes of reversible gates with simulating results are shown .This proposed RPLA may be further used to design any reversible logic function or Boolean function (Adder, subtractor etc.) which dissipate very low or ideally no heat.
How I got to work with Feynman on the covariant quark model
Ravndal, Finn
2014-01-01
In the period 1968 - 1974 I was a graduate student and then a postdoc at Caltech and was involved with the developments of the quark and parton models. Most of this time I worked in close contact with Richard Feynman and thus was present from the parton model was proposed until QCD was formulated. A personal account is presented how the collaboration took place and how the various stages of this development looked like from the inside until QCD was established as a theory for strong interactions with the partons being quarks and gluons.
Stability of Feynman-Kac formulae with path-dependent potentials
Chopin, Nicolas; Rubenthaler, Sylvain
2009-01-01
Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state trajectory. An important example is the mixture Kalman filter, but other models and algorithms of practical interest fall in this category. We study the asymptotic stability of such particle algorithms as time goes to infinity. As a corollary, practical conditions for the stability of the mixture Kalman filter, and a mixture GARCH filter, are derived. Finally, we show that our results can also lead to weaker conditions for the stability of standard particle algorithms, such that the potential function depends on the last state only.
Baur, Benedict; Conrad, Florian; Grothaus, Martin
2010-01-01
We prove two assumptions made in an article by Ya.A. Butko, M. Grothaus, O.G. Smolyanov concerning the existence of a strongly continuous operator semigroup solving a Cauchy-Dirichlet problem for an elliptic differential operator in a bounded domain and the existence of a smooth contractive embedding of a core of the generator of the semigroup into the space $C_c^{2,\\alpha}(\\R^n)$. Based on these assumptions a Feynman formula for the solution of the Cauchy-Dirichlet problem is constructed in ...
Energy Technology Data Exchange (ETDEWEB)
Nikolov, Nikolay M., E-mail: mitov@inrne.bas.bg
2016-11-15
We propose a new renormalization procedure to all orders in perturbation theory, which is formulated on an extended position space. This allows us to apply methods from massless Quantum Field Theory to models of massive fields. These include the technique of homogeneous and associate homogeneous distributions for the extension problem contained in the renormalization theory on position space. This also makes it possible to generalize the notion of residues of Feynman amplitudes, which characterize the presence of additional scales due to renormalization, to the massive case.
Directory of Open Access Journals (Sweden)
Nikolay M. Nikolov
2016-11-01
Full Text Available We propose a new renormalization procedure to all orders in perturbation theory, which is formulated on an extended position space. This allows us to apply methods from massless Quantum Field Theory to models of massive fields. These include the technique of homogeneous and associate homogeneous distributions for the extension problem contained in the renormalization theory on position space. This also makes it possible to generalize the notion of residues of Feynman amplitudes, which characterize the presence of additional scales due to renormalization, to the massive case.
Quantum leap from Dirac and Feynman, across the universe, to human body and mind
Ivancevic, Vladimir G
2008-01-01
This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body - all from the perspective of quantum mechanics and quantum field theory.This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosm
Feynman integrals as Hida distributions: the case of non-perturbative potentials
Grothaus, Martin; Vogel, Anna
2008-01-01
Feynman integrands are constructed as Hida distributions. For our approach we first have to construct solutions to a corresponding Schroedinger equation with time-dependent potential. This is done by a generalization of the Doss approach to time-dependent potentials. This involves an expectation w.r.t. a complex scaled Brownian motion. As examples polynomial potentials of degree $4n+2, n\\in\\mathbb N,$ and singular potentials of the form $\\frac{1}{|x|^n}, n\\in\\mathbb N$ and $\\frac{1}{x^n}, n\\in\\mathbb N,$ are worked out.
The spectroscopic Hertzsprung-Russell diagram
Langer, N
2014-01-01
The Hertzsprung-Russell diagram is an essential diagnostic diagram for stellar structure and evolution, which has now been in use for more than 100 years. Our spectroscopic Hertzsprung-Russell (sHR) diagram shows the inverse of the flux-mean gravity versus the effective temperature. Observed stars whose spectra have been quantitatively analyzed can be entered in this diagram without the knowledge of the stellar distance or absolute brightness. Observed stars can be as conveniently compared to stellar evolution calculations in the sHR diagram as in the Hertzsprung-Russell diagram. However, at the same time, our ordinate is proportional to the stellar mass-to-luminosity ratio, which can thus be directly determined. For intermediate- and low-mass star evolution at constant mass, we show that the shape of an evolutionary track in the sHR diagram is identical to that in the Hertzsprung-Russell diagram. We also demonstrate that for hot stars, their stellar Eddington factor can be directly read off the sHR diagram. ...
Hofstadter Butterfly Diagram in Noncommutative Space
Takahashi, H; Takahashi, Hidenori; Yamanaka, Masanori
2006-01-01
We study an energy spectrum of electron moving under the constant magnetic field in two dimensional noncommutative space. It take place with the gauge invariant way. The Hofstadter butterfly diagram of the noncommutative space is calculated in terms of the lattice model which is derived by the Bopp's shift for space and by the Peierls substitution for external magnetic field. We also find the fractal structure in new diagram. Although the global features of the new diagram are similar to the diagram of the commutative space, the detail structure is different from it.
Stage line diagram: An age-conditional reference diagram for tracking development
Buuren, S. van; Ooms, J.C.L.
2009-01-01
This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and
Stage line diagram: an age-conditional reference diagram for tracking development.
Van Buuren, S.; Ooms, J.C.L.
2009-01-01
This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and
Aoyama, T; Hayakawa, M; Kinoshita, T; Nio, M; Watanabe, N
2010-01-01
This paper reports the result of our evaluation of the tenth-order QED correction to the lepton g-2 from Feynman diagrams which have sixth-order light-by-light-scattering subdiagrams, none of whose vertices couples to the external magnetic field. The gauge-invariant set of these diagrams, called Set II(e), consists of 180 vertex diagrams. In the case of the electron g-2 (a_e) where the light-by-light subdiagram consists of the electron loop, the contribution to a_e is found to be $-1.344 9 (10) (\\alpha /\\pi)^5$. The contribution of the muon loop to a_e is $-0.000 465 (4) (\\alpha /\\pi)^5$. The contribution of the tau-lepton loop is about two orders of magnitudes smaller than that of the muon loop and hence negligible. The sum of all these contributions to a_e is $-1.345 (1) (\\alpha/\\pi)^5$. We have also evaluated the contribution of Set II(e) to the muon g-2 (a_\\mu). The contribution to a_\\mu from the electron loop is $3.265 (12) (\\alpha /\\pi)^5$, while the contribution of the tau-lepton loop is $-0.038 06 (13...
Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops
Aoyama, Tatsumi; Hayakawa, Masashi; Kinoshita, Toichiro; Nio, Makiko
2015-02-01
This paper presents a detailed account of the evaluation of the electron anomalous magnetic moment ae which arises from a gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value of the sum of Set V diagrams evaluated by the Monte Carlo integration routine VEGAS is 8.726 (336 )(α /π )5 , which replaces the very preliminary value reported in 2012. Combining it with 6318 previously published tenth-order diagrams, we obtain 7.795 (336 )(α /π )5 as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to ae(theory)=1 159 652 181.643 (25 )(23 )(16 )(763 )×1 0-12 , where the first three uncertainties are from the eighth-order, tenth-order, and hadronic and elecroweak terms. The fourth and largest uncertainty is from α-1=137.035 999 049 (90 ) , the fine-structure constant derived from the rubidium recoil measurement. Thus, ae(experiment)-ae(theory)=-0.91 (0.82 )×1 0-12 . Assuming the validity of the standard model, we obtain the fine-structure constant α-1(ae)=137.035 999 1570 (29 )(27 )(18 )(331 ) , where uncertainties are from the eighth-order, tenth-order, and hadronic and electroweak terms, and the measurement of ae. This is the most precise value of α available at present and provides a stringent constraint on possible theories beyond the standard model.
A note on Feynmanʼs calculation of reflection amplitudes for radiation striking a glass surface
Reali, Giancarlo
2014-07-01
In this paper we present a detailed calculation of reflection amplitudes for s- and p-polarized radiation striking a glass surface, closely following the derivation found in the Feynman Lectures on Physics, vol I. The basic idea underlying Feynman's exposition is the extinction theorem, which is used here in a very unique, Feynmanesque way. The calculation is carried out both for the case of radiation coming from the air and from the glass. We also show that the same reasonings are useful to discuss the internal Brewster's law.
The Feynman-Dyson Propagators for Neutral Particles (Local or Non-local?)
Dvoeglazov, Valeriy V
2016-01-01
An analog of the S=1/2 Feynman-Dyson propagator is presented in the framework of the S=1 Weinberg's theory. The basis for this construction is the concept of the Weinberg field as a system of four field functions differing by parity and by dual transformations. Next, we analyze the recent controversy in the definitions of the Feynman-Dyson propagator for the field operator containing the S=1/2 self/anti-self charge conjugate states in the papers by D. Ahluwalia et al. and by W. Rodrigues Jr. et al. The solution of this mathematical controversy is obvious. It is related to the necessary doubling of the Fock Space (as in the Barut and Ziino works), thus extending the corresponding Clifford Algebra. However, the logical interrelations of different mathematical foundations with the physical interpretations are not so obvious (Physics should choose only one correct formalism - it is not clear, why two correct mathematical formalisms (which are based on the same postulates) lead to different physical results?)
A white noise approach to the Feynman integrand for electrons in random media
Grothaus, M.; Riemann, F.; Suryawan, H. P.
2014-01-01
Using the Feynman path integral representation of quantum mechanics it is possible to derive a model of an electron in a random system containing dense and weakly coupled scatterers [see F. Edwards and Y. B. Gulyaev, "The density of states of a highly impure semiconductor," Proc. Phys. Soc. 83, 495-496 (1964)]. The main goal of this paper is to give a mathematically rigorous realization of the corresponding Feynman integrand in dimension one based on the theory of white noise analysis. We refine and apply a Wick formula for the product of a square-integrable function with Donsker's delta functions and use a method of complex scaling. As an essential part of the proof we also establish the existence of the exponential of the self-intersection local times of a one-dimensional Brownian bridge. As a result we obtain a neat formula for the propagator with identical start and end point. Thus, we obtain a well-defined mathematical object which is used to calculate the density of states [see, e.g., F. Edwards and Y. B. Gulyaev, "The density of states of a highly impure semiconductor," Proc. Phys. Soc. 83, 495-496 (1964)].
Calculation of electric dipole hypershieldings at the nuclei in the Hellmann-Feynman approximation.
Soncini, Alessandro; Lazzeretti, Paolo; Bakken, Vebjørn; Helgaker, Trygve
2004-02-15
The third-rank electric hypershieldings at the nuclei of four small molecules have been evaluated at the Hartree-Fock level of theory in the Hellmann-Feynman approximation. The nuclear electric hypershieldings are closely related to molecular vibrational absorption intensities and a generalization of the atomic polar tensors (expanded in powers of the electric field strength) is proposed to rationalize these intensities. It is shown that the sum rules for rototranslational invariance and the constraints imposed by the virial theorem provide useful criteria for basis-set completeness and for near Hartree-Fock quality of nuclear shieldings and hypershieldings evaluated in the Hellmann-Feynman approximation. Twelve basis sets of different size and quality have been employed for the water molecule in an extended numerical test on the practicality of the proposed scheme. The best results are obtained with the R12 and R12+ basis sets, designed for the calculation of electronic energies by the explicitly correlated R12 method. The R12 basis set is subsequently used to investigate three other molecules, CO, N2, and NH3, verifying that the R12 basis consistently performs very well.
Developing a Framework for Analyzing Definitions: A study of The Feynman Lectures
Wong, Chee Leong; Chu, Hye-Eun; Yap, Kueh Chin
2014-10-01
One important purpose of a definition is to explain the meaning of a word. Any problems associated with a definition may impede students' learning. However, research studies on the definitional problems from the perspective of physics education are limited. Physics educators may not be aware of the nature and extent of definitional problems. As an example, The Feynman Lectures of Physics suggest that there are at least four problems of definition: precision, circularity, context and completeness in knowledge. Feynman had the tendency of mentioning the words 'define' and 'definition' and discussing the problems of definition: they can be insightful, or challenge the conventional, preconceived notions of many physical concepts. One benefit of this study is that a framework can be developed to improve statements of definitions. This framework may guide educators or students to analyze the knowledge that is embedded in a definition. In the future, the learning of definition need not be content-oriented, but problem-based instead, with the help of definitional problems. Therefore, the use of these problems of definition in lessons can be an interesting area for future physics education research. Furthermore, we should be cognizant of inadequacies or inaccuracies in definition that may result in alternative conceptions.
Feynman Rules in the Type III Natural Flavour-Conserving Two-Higgs Doublet Model
Lin, C; Yang, Y W; Lin, Chilong; Lee, Chien-er; Yang, Yeou-Wei
1994-01-01
We consider a two Higgs-doublet model with $S_3$ symmetry, which implies a $\\pi \\over 2$ rather than 0 relative phase between the vacuum expectation values $$ and $$. The corresponding Feynman rules are derived accordingly and the transformation of the Higgs fields from the weak to the mass eigenstates includes not only an angle rotation but also a phase transformation. In this model, both doublets couple to the same type of fermions and the flavour-changing neutral currents are naturally suppressed. We also demonstrate that the Type III natural flavour-conserving model is valid at tree-level even when an explicit $S_3$ symmetry breaking perturbation is introduced to get a reasonable CKM matrix. In the special case $\\beta = \\alpha$, as the ratio $\\tan\\beta = {v_2 \\over v_1}$ runs from 0 to $\\infty$, the dominant Yukawa coupling will change from the first two generations to the third generation. In the Feynman rules, we also find that the charged Higgs currents are explicitly left-right asymmetric. The ratios ...
Lubrication modes and the IRG transition diagram
Schipper, D.J.; Gee, de A.W.J.
1995-01-01
The relationship between a Lubrication Mode Diagram (LMD) for concentrated contacts (LCC's) and the IRG transition diagram has been studied. In addition, scuffing results, obtained by the IRG (International Research Group) have been analysed, as well as the results of scuffing tests performed by dif
Comprehending process diagrams in biology education
Kragten, M.
2015-01-01
Students in secondary Science education seem to have difficulties with comprehending diagrams. Process diagrams are an important type of representation in Biology for explaining processes like protein synthesis, compound cycles, etc. In this thesis, we aimed at getting deeper insight into students’
Ferroelectric phase diagram of PVDF:PMMA
Li, M.; Stingelin, N.; Michels, J.J.; Spijkman, M.-J.; Asadi, K.; Feldman, K.; Blom, P.W.M.; Leeuw, D.M. de
2012-01-01
We have investigated the ferroelectric phase diagram of poly(vinylidene fluoride) (PVDF) and poly(methyl methacrylate) (PMMA). The binary nonequilibrium temperature composition diagram was determined and melting of α- and β-phase PVDF was identified. Ferroelectric β-PVDF:PMMA blend films were made b
Ferroelectric Phase Diagram of PVDF : PMMA
Li, Mengyuan; Stingelin, Natalie; Michels, Jasper J.; Spijkman, Mark-Jan; Asadi, Kamal; Feldman, Kirill; Blom, Paul W. M.; de Leeuw, Dago M.
2012-01-01
We have investigated the ferroelectric phase diagram of poly(vinylidene fluoride) (PVDF) and poly(methyl methacrylate) (PMMA). The binary nonequilibrium temperature composition diagram was determined and melting of alpha- and beta-phase PVDF was identified. Ferroelectric beta-PVDF:PMMA blend films w
Automatically extracting class diagrams from spreadsheets
Hermans, F.; Pinzger, M.; Van Deursen, A.
2010-01-01
The use of spreadsheets to capture information is widespread in industry. Spreadsheets can thus be a wealthy source of domain information. We propose to automatically extract this information and transform it into class diagrams. The resulting class diagram can be used by software engineers to under
Structural Controllability and Observability in Influence Diagrams
Chan, Brian Y.; Shachter, Ross D.
2013-01-01
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and structural observability theorems are developed and algorithms are formulated. Controllability and observability are fundamental concepts in dynamic systems (Luenberger 1979). Controllability corresponds to the ability to control a system while observability a...
Automatic fitting procedure for the fundamental diagram
Knoop, V.L.; Daamen, W.
2014-01-01
The fundamental diagram of a road, including free flow capacity and queue discharge rate, is very important for traffic engineering purposes. In the real word, most traffic measurements come from stationary loop detectors. This paper proposes a method to fit Wu’s fundamental diagram to loop detector
Resummation of Cactus Diagrams in Lattice QCD
Panagopoulos, H
1998-01-01
We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, this expansion yields results remarkably close to corresponding nonperturbative estimates.
Persistence Diagrams and the Heat Equation Homotopy
Fasy, Brittany Terese
2010-01-01
Persistence homology is a tool used to measure topological features that are present in data sets and functions. Persistence pairs births and deaths of these features as we iterate through the sublevel sets of the data or function of interest. I am concerned with using persistence to characterize the difference between two functions f, g : M -> R, where M is a topological space. Furthermore, I formulate a homotopy from g to f by applying the heat equation to the difference function g-f. By stacking the persistence diagrams associated with this homotopy, we create a vineyard of curves that connect the points in the diagram for f with the points in the diagram for g. I look at the diagrams where M is a square, a sphere, a torus, and a Klein bottle. Looking at these four topologies, we notice trends (and differences) as the persistence diagrams change with respect to time.
Free-Body Diagrams: Necessary or Sufficient?
Rosengrant, David; Van Heuvelen, Alan; Etkina, Eugenia
2005-09-01
The Rutgers PAER group is working to help students develop various scientific abilities. One of the abilities is to create, understand and learn to use for qualitative reasoning and problem solving different representations of physical processes such as pictorial representations, motion diagrams, free-body diagrams, and energy bar charts. Physics education literature indicates that using multiple representations is beneficial for student understanding of physics ideas and for problem solving. We developed a special approach to construct and utilize free-body diagrams for representing physical phenomena and for problem solving. We will examine whether students draw free-body diagrams in solving problems when they know they will not receive credit for it; the consistency of their use in different conceptual areas; and if students who use free-body diagrams while solving problems in different areas of physics are more successful then those who do not.
Phase diagram of elastic spheres.
Athanasopoulou, L; Ziherl, P
2017-02-15
Experiments show that polymeric nanoparticles often self-assemble into several non-close-packed lattices in addition to the face-centered cubic lattice. Here, we explore theoretically the possibility that the observed phase sequences may be associated with the softness of the particles, which are modeled as elastic spheres interacting upon contact. The spheres are described by two finite-deformation theories of elasticity, the modified Saint-Venant-Kirchhoff model and the neo-Hookean model. We determine the range of indentations where the repulsion between the spheres is pairwise additive and agrees with the Hertz theory. By computing the elastic energies of nine trial crystal lattices at densities far beyond the Hertzian range, we construct the phase diagram and find the face- and body-centered cubic lattices as well as the A15 lattice and the simple hexagonal lattice, with the last two being stable at large densities where the spheres are completely faceted. These results are qualitatively consistent with observations, suggesting that deformability may indeed be viewed as a generic property that determines the phase behavior in nanocolloidal suspensions.
Faceting diagram for sticky steps
Directory of Open Access Journals (Sweden)
Noriko Akutsu
2016-03-01
Full Text Available Faceting diagrams for the step-faceting zone, the step droplet zone, and the Gruber-Mullins-Pokrovsky-Talapov (GMPT zone for a crystal surface are obtained by using the density matrix renormalization group method to calculate the surface tension. The model based on these calculations is the restricted solid-on-solid (RSOS model with a point-contact-type step-step attraction (p-RSOS model on a square lattice. The point-contact-type step-step attraction represents the energy gain obtained by forming a bonding state with orbital overlap at the meeting point of the neighboring steps. In the step-faceting zone, disconnectedness in the surface tension leads to the formation of a faceted macrostep on a vicinal surface at equilibrium. The disconnectedness in the surface tension also causes the first-order shape transition for the equilibrium shape of a crystal droplet. The lower zone boundary line (ZBL, which separates the step-faceting zone and the step droplet zone, is obtained by the condition γ 1 = lim n → ∞ γ n / n , where γn is the step tension of the n-th merged step. The upper ZBL, which separates the GMPT zone and the step droplet zone, is obtained by the condition Aq,eff = 0 and Bq,eff = 0, where Aq,eff and Bq,eff represent the coefficients for the | q → | 2 term and the | q → | 3 term, respectively, in the | q → | -expanded form of the surface free energy f eff ( q → . Here, q → is the surface gradient relative to the (111 surface. The reason why the vicinal surface inclined in the 〈101〉 direction does not exhibit step-faceting is explained in terms of the one-dimensional spinless quasi-impenetrable attractive bosons at absolute zero.
Fanaro, Maria de los Angeles; Arlego, Marcelo; Otero, Maria Rita
2012-01-01
This work comprises an investigation about basic Quantum Mechanics (QM) teaching in the high school. The organization of the concepts does not follow a historical line. The Path Integrals method of Feynman has been adopted as a Reference Conceptual Structure that is an alternative to the canonical formalism. We have designed a didactic sequence…
Prykarpatski, A. K.; Bogolubov, N. N.
2017-01-01
A quantum fermionic massless charged particle self-intercating with its own self-generated bosonic electromagnetic field is reanalyzed in the framework of the Fock many-temporal and Feynman proper time approaches. The self-interaction phenomenon structure is discussed within the renormalized quantum Fock space. The quantum electromagnetic charged particle mass origin is suggested.
One of the many visiting theoreticians, R P Feynman, who gave lectures at CERN during the year
1970-01-01
Visiting CERN in January was R P Feynman, who has recently been working on strong interaction theory. On 8 January, he packed the lecture theatre, as usual, when he gave a talk on inelastic hadron collisions and is here caught in a typically graphic pose.
Onorato, P.
2011-01-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of…
Chauhan, Chanderkanta; Bedi, Amna; Kumar, Santosh
2017-02-01
In this ultra fast computing era power optimization is a major technological challenge that requires new computing paradigms. Conservative and reversible logic opens up the possibility of ultralow power computing. In this paper, basic reversible logic gate (double Feynman gate) using the lithium-niobate based Mach-Zehnder interferometer is proposed. The results are verified using beam propagation method and MATLAB simulations.
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Breviz: Visualizing Spreadsheets using Dataflow Diagrams
Hermans, Felienne; van Deursen, Arie
2011-01-01
Spreadsheets are used extensively in industry, often for business critical purposes. In previous work we have analyzed the information needs of spreadsheet professionals and addressed their need for support with the transition of a spreadsheet to a colleague with the generation of data flow diagrams. In this paper we describe the application of these data flow diagrams for the purpose of understanding a spreadsheet with three example cases. We furthermore suggest an additional application of the data flow diagrams: the assessment of the quality of the spreadsheet's design.
Modeling Workflow Using UML Activity Diagram
Institute of Scientific and Technical Information of China (English)
Wei Yinxing(韦银星); Zhang Shensheng
2004-01-01
An enterprise can improve its adaptability in the changing market by means of workflow technologies. In the build time, the main function of Workflow Management System (WFMS) is to model business process. Workflow model is an abstract representation of the real-world business process. The Unified Modeling Language (UML) activity diagram is an important visual process modeling language proposed by the Object Management Group (OMG). The novelty of this paper is representing workflow model by means of UML activity diagram. A translation from UML activity diagram to π-calculus is established. Using π-calculus, the deadlock property of workflow is analyzed.
Between Analogue and Digital Diagrams
Directory of Open Access Journals (Sweden)
Zoltan Bun
2012-10-01
Full Text Available This essay is about the interstitial. About how the diagram, as a method of design, has lead fromthe analogue deconstruction of the eighties to the digital processes of the turn of the millennium.Specifically, the main topic of the text is the interpretation and the critique of folding (as a diagramin the beginning of the nineties. It is necessary then to unfold its relationship with immediatelypreceding and following architectural trends, that is to say we have to look both backwards andforwards by about a decade. The question is the context of folding, the exchange of the analogueworld for the digital. To understand the process it is easier to investigate from the fields of artand culture, rather than from the intentionally perplicated1 thoughts of Gilles Deleuze. Both fieldsare relevant here because they can similarly be used as the yardstick against which the era itselfit measured. The cultural scene of the eighties and nineties, including performing arts, movies,literature and philosophy, is a wide milieu of architecture. Architecture responds parallel to itsera; it reacts to it, and changes with it and within it. Architecture is a medium, it has always beena medium, yet the relations are transformed. That’s not to say that technical progress, for exampleusing CAD-software and CNC-s, has led to the digital thinking of certain movements ofarchitecture, (it is at most an indirect tool. But the ‘up-to-dateness’ of the discipline, however,a kind of non-servile reading of an ‘applied culture’ or ‘used philosophy’2 could be the key.(We might recall here, parenthetically, the fortunes of the artistic in contemporary mass society.The proliferation of museums, the magnification of the figure of the artist, the existence of amassive consumption of printed and televised artistic images, the widespread appetite for informationabout the arts, all reflect, of course, an increasingly leisured society, but also relateprecisely to the fact
Transforming differential equations of multi-loop Feynman integrals into canonical form
Meyer, Christoph
2016-01-01
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics.
McClean, Jarrod R; Parkhill, John A; Aspuru-Guzik, Alán
2013-10-08
We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the time-embedded variational principle presented. Sample calculations are presented, applying the idea to a hydrogen molecule and the spin degrees of freedom of a model inorganic compound, demonstrating the parallel speedup of our method as well as its flexibility in applying ground-state methodologies. Finally, we take advantage of the unique perspective of this variational principle to examine the error of basis approximations in quantum dynamics.
Gaussian white noise analysis and its application to Feynman path integral
Suryawan, Herry Pribawanto
2016-02-01
In applied science, Gaussian white noise (the time derivative of Brownian motion) is often chosen as a mathematical idealization of phenomena involving sudden and extremely large fluctuations. It is also possible to define and study Gaussian white noise in a mathematically rigorous framework. In this survey paper we review the Gaussian white noise as an object in an infinite dimensional topological vector space. A brief construction of Gaussian white noise space and Gaussian white noise distributions will be presented. Gaussian white noise analysis provides a framework which offers various generalization of concept known from finite dimensional analysis to the infinite dimensional case, among them are differential operators, Fourier transform, and distribution theory. We will also present some recent developments and results on the application of Gaussian white noise theory to Feynman's path integral approach for quantum mechanics.
On the maximal cut of Feynman integrals and the solution of their differential equations
Primo, Amedeo
2016-01-01
The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try to solve them as a Laurent series in $\\epsilon = (4-d)/2$, where $d$ are the space-time dimensions. The differential equations are, in general, coupled and can be solved using Euler's variation of constants, provided that a set of homogeneous solutions is known. Given an arbitrary differential equation of order higher than one, there exist no general method for finding its homogeneous solutions. In this paper we show that the maximal cut of the integrals under consideration provides one set of homogeneous solutions, simplifying substantially the solution of the differential equations.
Generation of basis sets with high degree of fulfillment of the Hellmann-Feynman theorem.
Rico, J Fernández; López, R; Ema, I; Ramírez, G
2007-03-01
A direct relationship is established between the degree of fulfillment of the Hellman-Feynman (electrostatic) theorem, measured as the difference between energy derivatives and electrostatic forces, and the stability of the basis set, measured from the indices that characterize the distance of the space generated by the basis functions to the space of their derivatives with respect to the nuclear coordinates. On the basis of this relationship, a criterion for obtaining basis sets of moderate size with a high degree of fulfillment of the theorem is proposed. As an illustrative application, previously reported Slater basis sets are extended by using this criterion. The resulting augmented basis sets are tested on several molecules finding that the differences between energy gradient and electrostatic forces are reduced by at least one order of magnitude.
Directory of Open Access Journals (Sweden)
Nikolai N. Bogolubov
2015-04-01
Full Text Available We review new electrodynamics models of interacting charged point particles and related fundamental physical aspects, motivated by the classical A.M. Ampère magnetic and H. Lorentz force laws electromagnetic field expressions. Based on the Feynman proper time paradigm and a recently devised vacuum field theory approach to the Lagrangian and Hamiltonian, the formulations of alternative classical electrodynamics models are analyzed in detail and their Dirac type quantization is suggested. Problems closely related to the radiation reaction force and electron mass inertia are analyzed. The validity of the Abraham-Lorentz electromagnetic electron mass origin hypothesis is argued. The related electromagnetic Dirac–Fock–Podolsky problem and symplectic properties of the Maxwell and Yang–Mills type dynamical systems are analyzed. The crucial importance of the remaining reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized.
The Feynman trajectories: determining the path of a protein using fixed-endpoint assays.
Ketteler, Robin
2010-03-01
Richard Feynman postulated in 1948 that the path of an electron can be best described by the sum or functional integral of all possible trajectories rather than by the notion of a single, unique trajectory. As a consequence, the position of an electron does not harbor any information about the paths that contributed to this position. This observation constitutes a classical endpoint observation. The endpoint assay is the desired type of experiment for high-throughput screening applications, mainly because of limitations in data acquisition and handling. Quite contrary to electrons, it is possible to extract information about the path of a protein using endpoint assays, and these types of applications are reviewed in this article.
Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything
Tipler, Frank J
2005-01-01
I argue that the (extended) Standard Model (SM) of particle physics and the renormalizable Feynman-Weinberg theory of quantum gravity comprise a theory of everything. I show that imposing the appropriate cosmological boundary conditions make the theory finite. The infinities that are normally renormalized away and the series divergence infinities are both eliminated by the same mechanism. Furthermore, this theory can resolve the horizon, flatness, and isotropy problems of cosmology. Joint mathematical consistency naturally yields a scale-free, Gaussian, adiabatic perturbation spectrum, and more matter than antimatter. I show that mathematical consistency of the theory requires the universe to begin at an initial singularity with a pure $SU(2)_L$ gauge field. I show that quantum mechanics requires this field to have a Planckian spectrum whatever its temperature. If this field has managed to survive thermalization to the present day, then it would be the CMBR. If so, then we would have a natural explanation for...
On the maximal cut of Feynman integrals and the solution of their differential equations
Directory of Open Access Journals (Sweden)
Amedeo Primo
2017-03-01
Full Text Available The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try to solve them as a Laurent series in ϵ=(4−d/2, where d are the space–time dimensions. The differential equations are, in general, coupled and can be solved using Euler's variation of constants, provided that a set of homogeneous solutions is known. Given an arbitrary differential equation of order higher than one, there exists no general method for finding its homogeneous solutions. In this paper we show that the maximal cut of the integrals under consideration provides one set of homogeneous solutions, simplifying substantially the solution of the differential equations.
A Novel Design of Half Subtractor using Reversible Feynman Gate in Quantum Dot cellular Automata
Directory of Open Access Journals (Sweden)
Rubina Akter
2014-12-01
Full Text Available Quantum Dot cellular Automata (QCA is an emerging, promising alternative to CMOS technology that performs its task by encoding binary information on electronic charge configuration of a cell. All circuit based on QCA has an advantages of high speed, high parallel processing, high integrityand low power consumption. Reversible logic gates are the leading part in Quantum Dot cellular Automata. Reversible logic gates have an extensive feature that does not lose information. In this paper, we present a novel architecture of half subtractor gate design by reversible Feynman gate. This circuit is designedbased on QCA logic gates such as QCA majority voter gate, majority AND gate, majority OR gate and inverter gate. This circuit will provide an effective working efficiency on computational units of the digital circuit system.
Feynman's clock, a new variational principle, and quantum time-orbitals
McClean, Jarrod R; Aspuru-Guzik, Alán
2013-01-01
We introduce a new discrete-time variational principle inspired by the quantum clock originally proposed by Feynman, and use it to write down quantum evolution as a ground state eigenvalue problem. This allows one to apply ground state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. We draw an explicit connection between previously known time-dependent variational principles and the new time embedded variational principle presented. Sample calculations are presented applying the idea to the electronic degrees of freedom in a Hydrogen molecule and the spin degrees of freedom of a model inorganic compound. We employ the configuration-interaction approximation on a basis in which time is a variable. Finally, we take advantage of the unique perspective of the new variational principle to examine the error of basis approximations in quantum dynamics.
O (θ ) Feynman rules for quadrilinear gauge boson couplings in the noncommutative standard model
Sajadi, Seyed Shams; Boroun, G. R.
2017-02-01
We examine the electroweak gauge sector of the noncommutative standard model and, in particular, obtain the O (θ ) Feynman rules for all quadrilinear gauge boson couplings. Surprisingly, an electroweak-chromodynamics mixing appears in the gauge sector of the noncommutative standard model, where the photon as well as the neutral weak boson is coupled directly to three gluons. The phenomenological perspectives of the model in W-W+→Z Z scattering are studied and it is shown that there is a characteristic oscillatory behavior in azimuthal distribution of scattering cross sections that can be interpreted as a direct signal of the noncommutative standard model. Assuming the integrated luminosity 100 fb-1, the number of W-W+→Z Z subprocesses are estimated for some values of noncommutative scale ΛNC at different center of mass energies and the results are compared with predictions of the standard model.
Dual representation for the generating functional of the Feynman path-integral
Matone, Marco
2016-09-01
The generating functional for scalar theories admits a representation which is dual with respect to the one introduced by Schwinger, interchanging the role of the free and interacting terms. It maps ∫ V (δJ) and JΔJ to δϕc Δδϕc and ∫ V (ϕc), respectively, with ϕc = ∫ JΔ and Δ the Feynman propagator. Comparing the Schwinger representation with its dual version one gets a little known relation that we prove to be a particular case of a more general operatorial relation. We then derive a new representation of the generating functional T [ϕc ] = W [ J ] expressed in terms of covariant derivatives acting on 1
Wu, Wei; Ferrero, Michel; Georges, Antoine; Kozik, Evgeny
2017-07-01
We introduce a method for summing Feynman's perturbation series based on diagrammatic Monte Carlo that significantly improves its convergence properties. This allows us to investigate in a controllable manner the pseudogap regime of the Hubbard model and to study the nodal/antinodal dichotomy at low doping and intermediate coupling. Marked differences from the weak-coupling scenario are manifest, such as a higher degree of incoherence at the antinodes than at the "hot spots". Our results show that the pseudogap and reduction of quasiparticle coherence at the antinode is due to antiferromagnetic spin correlations centered around the commensurate (π ,π ) wave vector. In contrast, the dominant source of scattering at the node is associated with incommensurate momentum transfer. Umklapp scattering is found to play a key role in the nodal/antinodal dichotomy.
Oriti, D
2004-01-01
We discuss the notion of causality in Quantum Gravity in the context of sum-over-histories approaches, in the absence therefore of any background time parameter. In the spin foam formulation of Quantum Gravity, we identify the appropriate causal structure in the orientation of the spin foam 2-complex and the data that characterize it; we construct a generalised version of spin foam models introducing an extra variable with the interpretation of proper time and show that different ranges of integration for this proper time give two separate classes of spin foam models: one corresponds to the spin foam models currently studied, that are independent of the underlying orientation/causal structure and are therefore interpreted as a-causal transition amplitudes; the second corresponds to a general definition of causal or orientation dependent spin foam models, interpreted as causal transition amplitudes or as the Quantum Gravity analogue of the Feynman propagator of field theory, implying a notion of ''timeless ord...
Quantization of second-order Lagrangians: The Fokker-Wheeler-Feynman model of electrodynamics
Moore, R. A.; Scott, T. C.
1992-10-01
The consequences of quantizing the Fokker-Wheeler-Feynman model of electrodynamics, treating the Lagrangian via its acceleration-dependent (1/c) power-series representation, is examined using recently validated methods. An exact treatment of this acceleration dependence yields, under certain circumstances, high-energy resonant modes. In the past, such modes have been assumed unphysical and have been removed by perturbative or order-reduction techniques. However, these modes appear to be of physical significance. This conclusion follows because this completely ab initio calculation, with no adjustable parameters, has a number of successes. It provides a description for resonances observed in the electron-positron emission from heavy-ion collisions, in particular, and in diproton collisions and, possibly, in other collision experiments as well.
Baur, Benedict; Grothaus, Martin
2010-01-01
We prove two assumptions made in an article by Ya.A. Butko, M. Grothaus, O.G. Smolyanov concerning the existence of a strongly continuous operator semigroup solving a Cauchy-Dirichlet problem for an elliptic differential operator in a bounded domain and the existence of a smooth contractive embedding of a core of the generator of the semigroup into the space $C_c^{2,\\alpha}(\\R^n)$. Based on these assumptions a Feynman formula for the solution of the Cauchy-Dirichlet problem is constructed in the article mentioned above. In this article we show that the assumptions are fulfilled for domains with $C^{4,\\alpha}$-smooth boundary and coefficients in $C^{2,\\alpha}$.
Relation among C-curve characterization diagrams
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane can, therefore, be partitioned into regions labelled according to the characterization of the curve when the fourth point is in each region. This partitioned plane is called a "characterization diagram". By moving one of the control points but fixing the rest, one can induce different characterization diagrams. In this paper, we investigate the relation among all different characterization diagrams of cubic C-curves based on the singularity conditions proposed by Yang and Wang (2004). We conclude that, no matter what the C-curve type is or which control point varies, the characterization diagrams can be obtained by cutting a common 3D characterization space with a corresponding plane.
Revised Diagnostic Diagrams for Planetary Nebulae
Riesgo, H
2006-01-01
Diagnostic diagrams of electron density - excitation for a sample of 613 planetary nebulae are presented. The present extensive sample allows the definition of new statistical limits for the distribution of planetary nebulae in the log [Ha/[SII
A Smart Thermal Block Diagram Tool
Tsuyuki, Glenn; Miyake, Robert; Dodge, Kyle
2008-01-01
The presentation describes a Smart Thermal Block Diagram Tool. It is used by JPL's Team X in studying missions during the Pre-Phase A. It helps generate cost and mass estimates using proprietary data bases.
Phase diagram to design passive nanostructures
Lee, Jeng Yi
2015-01-01
A phase diagram, defined by the amplitude square and phase of scattering coefficients for absorption cross-section in each individual channel, is introduced as a universal map on the electromagnetic properties for passive scatterers. General physical bounds are naturally revealed based on the intrinsic power conservation in a passive scattering system, entailing power competitions among scattering, absorption, and extinction. Exotic scattering and absorption phenomena, from resonant scattering, invisible cloaking, coherent perfect absorber, and subwavelength superscattering can all be illustrated in this phase diagram. With electrically small core-shell scatterers as an example, we demonstrate a systematic method to design field-controllable structures based on the allowed trajectories in the phase diagram. The proposed phase diagram not only provides a simple tool to design optical devices but also promotes a deep understanding on Mie's scattering theory.