The Experts below are selected from a list of 120 Experts worldwide ranked by ideXlab platform
Matteo Polettini - One of the best experts on this subject based on the ideXlab platform.
-
nonequilibrium thermodynamics as a gauge theory
EPL, 2012Co-Authors: Matteo PolettiniAbstract:We assume that Markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the Transformation Law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally detailed balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic Transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not.
Naoto Yokoi - One of the best experts on this subject based on the ideXlab platform.
-
non abelian duality from vortex moduli a dual model of color confinement
Nuclear Physics, 2007Co-Authors: Minoru Eto, Luca Ferretti, Kenichi Konishi, Giacomo Marmorini, Muneto Nitta, Keisuke Ohashi, Walter Vinci, Naoto YokoiAbstract:It is argued that the dual Transformation of non-Abelian monopoles occurring in a system with gauge symmetry breaking G -> H is to be defined by setting the low-energy H system in Higgs phase, so that the dual system is in confinement phase. The Transformation Law of the monopoles follows from that of monopole-vortex mixed configurations in the system (with a large hierarchy of energy scales, v_1 >> v_2) G -> H -> 0, under an unbroken, exact color-flavor diagonal symmetry H_{C+F} \sim {\tilde H}. The Transformation property among the regular monopoles characterized by \pi_2(G/H), follows from that among the non-Abelian vortices with flux quantized according to \pi_1(H), via the isomorphism \pi_1(G) \sim \pi_1(H) / \pi_2(G/H). Our idea is tested against the concrete models -- softly-broken {\cal N}=2 supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v_1 >> v_2 >> \Lambda) of these models are consistent with those inferred from the fully quantum-mechanical low-energy effective action of the systems (at v_1, v_2 \sim \Lambda).
Meyer Christoph - One of the best experts on this subject based on the ideXlab platform.
-
Algorithmic Transformation of multi-loop Feynman integrals to a canonical basis
2018Co-Authors: Meyer ChristophAbstract:The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven to be a powerful tool for the computation of Feynman integrals. It has been observed that the differential equation of Feynman integrals can in many instances be transformed into a so-called canonical form, which significantly simplifies its integration in terms of iterated integrals. The main result of this thesis is an algorithm to compute rational Transformations of differential equations of Feynman integrals into a canonical form. Apart from requiring the existence of such a rational Transformation, the algorithm needs no further assumptions about the differential equation. In particular, it is applicable to problems depending on multiple kinematic variables and also allows for a rational dependence on the dimensional regulator. First, the Transformation Law is expanded in the dimensional regulator to derive differential equations for the coefficients of the Transformation. Using an ansatz in terms of rational functions, these differential equations are then solved to determine the Transformation. This thesis also presents an implementation of the algorithm in the Mathematica package CANONICA, which is the first publicly available program to compute Transformations to a canonical form for differential equations depending on multiple variables. The main functionality and its usage are illustrated with some simple examples. Furthermore, the package is applied to state-of-the-art integral topologies appearing in recent multi-loop calculations. These topologies depend on up to three variables and include previously unknown topologies contributing to higher-order corrections to the cross section of single top-quark production at the LHC.Comment: Ph.D. thesi
-
Algorithmic Transformation of multi-loop Feynman integrals to a canonical basis
Humboldt-Universität zu Berlin, 2018Co-Authors: Meyer ChristophAbstract:Die Auswertung von Mehrschleifen-Feynman-Integralen ist eine der größten Herausforderungen bei der Berechnung präziser theoretischer Vorhersagen für die am LHC gemessenen Wirkungsquerschnitte. In den vergangenen Jahren hat sich die Nutzung von Differentialgleichungen bei der Berechnung von Feynman-Integralen als sehr erfolgreich erwiesen. Es wurde dabei beobachtet, dass die von den Feynman-Integralen erfüllte Differentialgleichung oftmals in eine sogenannte kanonische Form transformiert werden kann, welche die Integration der Differentialgleichung mittels iterierter Integrale wesentlich vereinfacht. Das zentrale Ergebnis der vorliegenden Arbeit ist ein Algorithmus zur Berechnung rationaler Transformationen von Differentialgleichungen von Feynman-Integralen in eine kanonische Form. Neben der Existenz einer solchen rationalen Transformation stellt der Algorithmus keinerlei weitere Bedingungen an die Differentialgleichung. Insbesondere ist der Algorithmus auf Mehrskalenprobleme anwendbar und erlaubt eine rationale Abhängigkeit der Differentialgleichung vom dimensionalen Regulator. Bei der Anwendung des Algorithmus wird zunächst das Transformationsgesetz im dimensionalen Regulator entwickelt, um Differentialgleichungen für die Koeffizienten in der Entwicklung der Transformation herzuleiten. Diese Differentialgleichungen werden dann mit einem rationalen Ansatz für die gesuchte Transformation gelöst. Es wird zudem eine Implementation des Algorithmus in dem Mathematica Paket CANONICA vorgestellt, welches das erste veröffentlichte Programm dieser Art ist, das auf Mehrskalenprobleme anwendbar ist. CANONICAs Potential für moderne Mehrschleifenrechnungen wird anhand mehrerer nicht trivialer Mehrschleifen-Integraltopologien demonstriert. Die gezeigten Topologien hängen von bis zu drei Variablen ab und umfassen auch vormals ungelöste Topologien, die zu Korrekturen höherer Ordnung zum Wirkungsquerschnitt der Produktion einzelner Top-Quarks am LHC beitragen.The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven to be a powerful tool for the computation of Feynman integrals. It has been observed that the differential equation of Feynman integrals can in many instances be transformed into a so-called canonical form, which significantly simplifies its integration in terms of iterated integrals. The main result of this thesis is an algorithm to compute rational Transformations of differential equations of Feynman integrals into a canonical form. Apart from requiring the existence of such a rational Transformation, the algorithm needs no further assumptions about the differential equation. In particular, it is applicable to problems depending on multiple kinematic variables and also allows for a rational dependence on the dimensional regulator. First, the Transformation Law is expanded in the dimensional regulator to derive differential equations for the coefficients of the Transformation. Using an ansatz in terms of rational functions, these differential equations are then solved to determine the Transformation. This thesis also presents an implementation of the algorithm in the Mathematica package CANONICA, which is the first publicly available program to compute Transformations to a canonical form for differential equations depending on multiple variables. The main functionality and its usage are illustrated with some simple examples. Furthermore, the package is applied to state-of-the-art integral topologies appearing in recent multi-loop calculations. These topologies depend on up to three variables and include previously unknown topologies contributing to higher-order corrections to the cross section of single top-quark production at the LHC
Minoru Eto - One of the best experts on this subject based on the ideXlab platform.
-
non abelian duality from vortex moduli a dual model of color confinement
Nuclear Physics, 2007Co-Authors: Minoru Eto, Luca Ferretti, Kenichi Konishi, Giacomo Marmorini, Muneto Nitta, Keisuke Ohashi, Walter Vinci, Naoto YokoiAbstract:It is argued that the dual Transformation of non-Abelian monopoles occurring in a system with gauge symmetry breaking G -> H is to be defined by setting the low-energy H system in Higgs phase, so that the dual system is in confinement phase. The Transformation Law of the monopoles follows from that of monopole-vortex mixed configurations in the system (with a large hierarchy of energy scales, v_1 >> v_2) G -> H -> 0, under an unbroken, exact color-flavor diagonal symmetry H_{C+F} \sim {\tilde H}. The Transformation property among the regular monopoles characterized by \pi_2(G/H), follows from that among the non-Abelian vortices with flux quantized according to \pi_1(H), via the isomorphism \pi_1(G) \sim \pi_1(H) / \pi_2(G/H). Our idea is tested against the concrete models -- softly-broken {\cal N}=2 supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v_1 >> v_2 >> \Lambda) of these models are consistent with those inferred from the fully quantum-mechanical low-energy effective action of the systems (at v_1, v_2 \sim \Lambda).
Christoph K Meyer - One of the best experts on this subject based on the ideXlab platform.
-
algorithmic Transformation of multi loop master integrals to a canonical basis with canonica
Computer Physics Communications, 2018Co-Authors: Christoph K MeyerAbstract:Abstract The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA , which implements a recently developed algorithm to automatize the Transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant Transformations. Program summary Program Title: CANONICA Program Files doi: http://dx.doi.org/10.17632/fmwnmmhn77.1 Licensing provisions: GNU General Public License version 3 Programming language: Wolfram Mathematica, version 10 or higher Nature of problem: Computation of a rational basis Transformation of master integrals leading to a canonical form of the corresponding differential equation. Solution method: The Transformation Law is expanded in the dimensional regulator. The resulting differential equations for the expansion coefficients of the Transformation are solved with a rational ansatz.
