scholarly journals Differential Dyson–Schwinger equations for quantum chromodynamics

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Marco Frasca
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Chromodynamics ◽  
Background Field ◽  
Low Energy ◽  
Quantum Field ◽  
Approximate Form ◽  
Energy Behavior ◽  
Hooft Limit ◽  
Dynamical Breaking

Abstract Using a technique devised by Bender, Milton and Savage, we derive the Dyson–Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The ’t Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.

scholarly journals Gauge and infrared properties of hadronic structure of nucleon in neutron beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

2019 ◽  
Vol 34 (02) ◽  
pp. 1950010 ◽  
Author(s):  
A. N. Ivanov ◽  
R. Höllwieser ◽  
N. I. Troitskaya ◽  
M. Wellenzohn ◽  
Ya. A. Berdnikov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Electron Energy ◽  
Low Energy ◽  
Radiative Corrections ◽  
Quantum Field ◽  
Neutron Lifetime ◽  
Gauge Invariant ◽  
Hadronic Structure ◽  
Lepton Current

Within the standard [Formula: see text] theory of weak interactions, Quantum Electrodynamics (QED) and the linear [Formula: see text]-model [Formula: see text] of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron [Formula: see text]-decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order [Formula: see text], induced by hadronic structure of the nucleon, to the rate of the neutron [Formula: see text]-decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin’s analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative [Formula: see text]-decay and neutron [Formula: see text]-decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective [Formula: see text] vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and [Formula: see text], which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the [Formula: see text], where the effective [Formula: see text] vertex of hadron–lepton current–current interactions is caused by the [Formula: see text]-electroweak-boson exchange.

scholarly journals Classical simulation of quantum fields I

2006 ◽  
Vol 84 (10) ◽  
pp. 861-877 ◽  
Author(s):  
T Hirayama ◽  
B Holdom
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Zero Point ◽  
Background Field ◽  
Field Configuration ◽  
Classical Electrodynamics ◽  
Quantum Field ◽  
Point Energy ◽  
Classical Simulation ◽  
Feynman Rules

We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical electrodynamics by Wheeler–Feynman and the theory of stochastic electrodynamics of Boyer. The nonperturbative effects of interactions in these theories can be very efficiently studied on the lattice. In [Formula: see text] theory in 1 + 1 dimensions, we find results, in particular, for mass renormalization and the critical coupling for symmetry breaking that are in agreement with their quantum counterparts. We then study the perturbative expansion of the n-point Green's functions and find a loop expansion very similar to that of quantum field theory. When compared to the usual Feynman rules, we find some differences associated with particular combinations of internal lines going on-shell simultaneously. PACS Nos.: 03.70.+k, 03.50.–z, 11.15.Tk

scholarly journals Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Global Symmetries ◽  
Low Energy ◽  
Field Theories ◽  
Continuum Models ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Lattice Systems ◽  
Continuum Field

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

scholarly journals QCD on the Lattice

2020 ◽  
pp. 137-262
Author(s):  
Hartmut Wittig
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Ab Initio ◽  
Quantum Chromodynamics ◽  
Lattice Qcd ◽  
Strong Interaction ◽  
Quantum Field ◽  
Low Energies ◽  
Lattice Approach ◽  
Established Technique

AbstractSince Wilson’s seminal papers of the mid-1970s, the lattice approach to Quantum Chromodynamics has become increasingly important for the study of the strong interaction at low energies, and has now turned into a mature and established technique. In spite of the fact that the lattice formulation of Quantum Field Theory has been applied to virtually all fundamental interactions, it is appropriate to discuss this topic in a chapter devoted to QCD, since by far the largest part of activity is focused on the strong interaction. Lattice QCD is, in fact, the only known method which allows ab initio investigations of hadronic properties, starting from the QCD Lagrangian formulated in terms of quarks and gluons.

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