scholarly journals Connected Chord Diagrams and Bridgeless Maps

10.37236/7400 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Julien Courtiel ◽  
Karen Yeats ◽  
Noam Zeilberger
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lambda Calculus ◽  
The Other ◽  
Combinatorial Proof ◽  
Quantum Field ◽  
Technical Parameter ◽  
Simple Application ◽  
Chord Diagrams ◽  
Combinatorial Maps

We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on the other hand. We describe a bijection between these two classes, which naturally extends to indecomposable diagrams and general rooted maps. As an application, this bijection provides a simplifying framework for some technical quantum field theory work realized by some of the authors. Most notably, an important but technical parameter naturally translates to vertices at the level of maps. We also give a combinatorial proof to a formula which previously resulted from a technical recurrence, and with similar ideas we prove a conjecture of Hihn. Independently, we revisit an equation due to Arquès and Béraud for the generating function counting rooted maps with respect to edges and vertices, giving a new bijective interpretation of this equation directly on indecomposable chord diagrams, which moreover can be specialized to connected diagrams and refined to incorporate the number of crossings. Finally, we explain how these results have a simple application to the combinatorics of lambda calculus, verifying the conjecture that a certain natural family of lambda terms is equinumerous with bridgeless maps.

THE CLASSICAL HARMONIC OSCILLATOR ON GALOIS AND P-ADIC FIELDS

1989 ◽  
Vol 04 (09) ◽  
pp. 2211-2233 ◽  
Author(s):  
YANNICK MEURICE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Difference Equation ◽  
Harmonic Oscillator ◽  
Continuum Limit ◽  
The Other ◽  
Quantum Field ◽  
Real Numbers ◽  
Technical Tool ◽  
Classical Motion

Starting from a difference equation corresponding to the harmonic oscillator, we discuss various properties of the classical motion (cycles, conserved quantity, boundedness, continuum limit) when the dynamical variables take their values on Galois or p-adic fields. We show that these properties can be applied as a technical tool to calculate the motion on the real numbers. On the other hand, we also give an example where the motions over Galois and p-adic fields have a direct physical interpretation. Some perspectives for quantum field theory and strings are briefly discussed.

scholarly journals GRAVITATIONAL RENORMALIZATION OF QUANTUM FIELD THEORY

2012 ◽  
Vol 27 (32) ◽  
pp. 1250186 ◽  
Author(s):  
ROBERTO CASADIO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Feynman Graph ◽  
The Other ◽  
Quantum Field ◽  
High Momentum ◽  
Feynman Propagator ◽  
Virtual Particle ◽  
Virtual Particles

We propose to include gravity in quantum field theory nonperturbatively, by modifying the propagators so that each virtual particle in a Feynman graph move in the space–time determined by the four-momenta of the other particles in the same graph. By making additional working assumptions, we are able to put this idea at work in a simplified context, and obtain a modified Feynman propagator for the massless neutral scalar field. Our expression shows a suppression at high momentum, strong enough to entail finite results, to all loop orders, for processes involving at least two virtual particles.

scholarly journals NEW DUAL RELATIONS BETWEEN QUANTUM FIELD THEORY AND STRING REGIMES IN CURVED BACKGROUNDS

2003 ◽  
Vol 18 (36) ◽  
pp. 2537-2544 ◽  
Author(s):  
M. RAMON MEDRANO ◽  
N. G. SANCHEZ
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Characteristic Length ◽  
A Priori ◽  
The Other ◽  
Back Reaction ◽  
Quantum Field ◽  
De Sitter ◽  
Quantum Matter ◽  
Dual Transform

A ℛ "dual" transform is introduced which relates Quantum Field Theory and String regimes, both in a curved background with D-non-compact dimensions. This operation maps the characteristic length of one regime into the other (and, as a consequence, mass domains as well). The ℛ-transform is not an assumed or a priori imposed symmetry but is revealed by the QFT and String dynamics in curved backgrounds. The Hawking–Gibbons temperature and the string maximal or critical temperature are ℛ-mapped one into the other. If back reaction of quantum matter is included, Quantum Field Theory and String phases appear, and ℛ-relations between them manifest as well. These ℛ-transformations are explicitly shown in two relevant examples: Black Hole and de Sitter spacetimes.

scholarly journals COMMENT ON FERMION PROPAGATOR IN REAL-TIME QUANTUM-FIELD THEORY AT FINITE TEMPERATURE AND DENSITY

2002 ◽  
Vol 17 (05) ◽  
pp. 303-308 ◽  
Author(s):  
A. NIÉGAWA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Green Function ◽  
Finite Temperature ◽  
Standard Form ◽  
Quark Propagator ◽  
The Other ◽  
Quantum Field ◽  
Fermion Propagator ◽  
Time Quantum

Two forms are available for the fermion propagator at finite temperature and density. It is shown that, when one deals with a diquark-condensation-operator inserted Green function in hot and dense QCD, the standard form of the quark propagator does not work. On the other hand, another form of the quark propagator does work.

scholarly journals COMBINATORIAL HOPF ALGEBRAS IN QUANTUM FIELD THEORY I

2005 ◽  
Vol 17 (08) ◽  
pp. 881-976 ◽  
Author(s):  
HÉCTOR FIGUEROA ◽  
JOSÉ M. GRACIA-BONDÍA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hopf Algebra ◽  
Hopf Algebras ◽  
Combinatorial Proof ◽  
Quantum Field ◽  
Simple Derivation ◽  
Combinatorial Hopf Algebras ◽  
Incidence Algebras ◽  
Algebra Theory

This paper stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Sec. 1.1 is the introduction, and contains an elementary invitation to the subject as well. The rest of Sec. 1 is devoted to the basics of Hopf algebra theory and examples in ascending level of complexity. Section 2 turns around the all-important Faà di Bruno Hopf algebra. Section 2.1 contains a first, direct approach to it. Section 2.2 gives applications of the Faà di Bruno algebra to quantum field theory and Lagrange reversion. Section 2.3 rederives the related Connes–Moscovici algebras. In Sec. 3, we turn to the Connes–Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Sec. 3.1, we describe the first. Then in Sec. 3.2, we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Sec. 3.3, general incidence algebras are introduced, and the Faà di Bruno bialgebras are described as incidence bialgebras. In Sec. 3.4, deeper lore on Rota's incidence algebras allows us to reinterpret Connes–Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained. The structure results for commutative Hopf algebras are found in Sec. 4. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota–Baxter map in renormalization.

FINITE-SIZE CORRECTIONS TO DYONIC GIANT MAGNONS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2239-2240
Author(s):  
YASUYUKI HATSUDA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Relativistic Quantum ◽  
Finite Size ◽  
The Other ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Finite Size Corrections

We compute finite-size corrections to dyonic giant magnons in two ways1. One is by using classical string solutions corresponding to finite-size dyonic giant magnons called "helical strings". The other is by applying the Lüscher formula known in relativistic quantum field theory to the case in which incoming particles are boundstates. We find these two methods lead the same result.

scholarly journals Nonlocal quantum field theory without acausality and nonunitarity at quantum level: Is SUSY the key?

2015 ◽  
Vol 30 (15) ◽  
pp. 1550103 ◽  
Author(s):  
Andrea Addazi ◽  
Giampiero Esposito
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
The Other ◽  
Tree Level ◽  
Quantum Field ◽  
Quantum Level ◽  
Fermionic Sector ◽  
Nonlocal Quantum ◽  
The One

The realization of a nonlocal quantum field theory without losing unitarity, gauge invariance and causality is investigated. It is commonly retained that such a formulation is possible at tree level, but at quantum level acausality is expected to reappear at one loop. We suggest that the problem of acausality is, in a broad sense, similar to the one about anomalies in quantum field theory. By virtue of this analogy, we suggest that acausal diagrams resulting from the fermionic sector and the bosonic one might cancel each other, with a suitable content of fields and suitable symmetries. As a simple example, we show how supersymmetry can alleviate this problem in a simple and elegant way, i.e. by leading to exact cancellations of harmful diagrams, to all orders of perturbation theory. An infinite number of divergent diagrams cancel each other by virtue of the nonrenormalization theorem of supersymmetry. However, supersymmetry is not enough to protect a theory from all acausal divergences. For instance, acausal contributions to supersymmetric corrections to D-terms are not protected by supersymmetry. On the other hand, we show in detail how supersymmetry also helps in dealing with D-terms: divergences are not canceled but they become softer than in the nonsupersymmetric case. The supergraphs' formalism turns out to be a powerful tool to reduce the complexity of perturbative calculations.

TRANSITIVITY OF LOCALITY AND DUALITY IN QUANTUM FIELD THEORY

1994 ◽  
Vol 06 (04) ◽  
pp. 597-619 ◽  
Author(s):  
H. J. BORCHERS ◽  
JAKOB YNGVASON
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Von Neumann Algebras ◽  
The Other ◽  
Quantum Field ◽  
Bounded Operators ◽  
Unbounded Operators ◽  
Von Neumann ◽  
Lorentz Covariance ◽  
Wightman Fields

Duality conditions for Wightman fields are formulated in terms of the Tomita conjugations S associated with algebras of unbounded operators. It is shown that two fields which are relatively local to an irreducible field fulfilling a condition of this type are relatively local to each other. Moreover, a local net of von Neumann algebras associated with such a field satisfies (essential) duality. These results do not rely on Lorentz covariance but follow from the observation that two algebras of (un)bounded operators with the same Tomita conjugation have the same (un)bounded weak commutant if one algebra is contained in the other.

scholarly journals OPE for XXX

2018 ◽  
Vol 30 (06) ◽  
pp. 1840006 ◽  
Author(s):  
Philippe Di Francesco ◽  
Fedor Smirnov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Experimental Data ◽  
Correlation Functions ◽  
Spin Chain ◽  
Operator Product Expansion ◽  
The Other ◽  
Operator Product ◽  
Quantum Field ◽  
Xxx Model

We explain a new method for finding the correlation functions for the XXX model which is based on the concepts of Operator Product Expansion of Quantum Field Theory on one hand and of fermionic bases for the XXX spin chain on the other. With this method, we are able to perform computations for up to 11 lattice sites. We show that these “experimental” data allow to guess exact formulae for the OPE coefficients. In memory of Ludwig Dmitrievich Faddeev

Sign in / Sign up

Export Citation Format

Share Document