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Register a new userThe Schwinger Model in Point Form
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We attempt to solve the Schwinger model, i.e. massless QED in 1+1 dimensions, by quantizing it on a space-time hyperboloid x_mu x^mu =tau^2. The Fock-space representation of the 2-momentum operator is derived and its algebraic structure is analyzed. We briefly outline a solution strategy.
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We present a calculation of the electromagnetic form factors of the $rho^+$ meson. Our formalism is based on the point-form of relativistic quantum mechanics. Electron-$rho$-meson scattering is formulated as a coupled-channel problem for a Bakamjian-Thomas mass operator, such that the dynamics of the exchanged photon is taken explicitly into account. The $rho$-meson current is extracted from on-shell matrix elements of the optical potential of the scattering process. As a consequence of the violation of cluster separability in the Bakamjian-Thomas framework, our current includes additional, unphysical contributions, which can be separated from the physical ones uniquely. Our results for the form factors are in good agreement with other approaches.
We present a review of the description of hadron properties along an invariant mass operator in the point form of Poincare-invariant relativistic dynamics. The quark-quark interaction is furnished by a linear confinement, consistent with the QCD string tension, and a hyperfine interaction derived from Goldstone-boson exchange. The main advantage of the point-form approach is the possibility of calculating manifestly covariant observables, since the generators of Lorentz transformations remain interaction-free. We discuss the static properties of the mass-operator eigenstates, such as the invariant mass spectra of light- and heavy-flavor baryons, the characteristics of the eigenstates in terms of their spin, flavor, and spatial dependences as well as their classification into spin-flavor multiplets. Regarding dynamical observables we address the electroweak structures of the nucleon and hyperon ground states, including their electric radii, magnetic moments as well as axial charges, and in addition a recently derived microscopic description of the $pi NN$ as well as $pi NDelta$ interaction vertices. Except for hadronic resonance decays, which are not addressed here due to space limitations, all of these observables are obtained in good agreement with existing phenomenology. Relativistic (boost) effects are generally sizable. We conclude that low-energy hadrons can be well described by an effective theory with a finite number of degrees of freedom, as long as the symmetries of low-energy quantum chromodynamics (spontaneously broken chiral symmetry) as well as special relativity (Poincare invariance) are properly taken into account. The latter requirement is particularly well and efficiently met in the point-form approach.
We discuss electromagnetic currents in the point-form formulation of relativistic quantum mechanics. The construction is along a spectator model and implies that only one quark is explicitly coupled to the photon, but nevertheless many-body contributions are present in the current operator. Such effects are unavoidable in relativistic constructions and resulting ambiguities are notably reduced by imposing charge normalization and time-reversal invariance. The residual theoretical indetermination introduces small but sizeable changes in the nucleon form-factors, particularly at higher Q-squared values, with the data generally centered in the middle of the theoretical band.
We study the dynamics of the massive Schwinger model on a lattice using exact diagonalization. When periodic boundary conditions are imposed, analytic arguments indicate that a non-zero electric flux in the initial state can unwind and decrease to a minimum value equal to minus its initial value, due to the effects of a pair of charges that repeatedly traverse the spatial circle. Our numerical results support the existence of this flux unwinding phenomenon, both for initial states containing a charged pair inserted by hand, and when the charges are produced by Schwinger pair production. We also study boundary conditions where charges are confined to an interval and flux unwinding cannot occur, and the massless limit, where our results agree with the predictions of the bosonized description of the Schwinger model.
A synopsis exemplifying the employment of Dyson-Schwinger equations in the calculation and explanation of hadron electromagnetic form factors and related phenomena. In particular the contribution: presents the pion form factor computed simultaneously at spacelike and timelike momenta; reports aspects of the evolution of the nucleon and Delta masses with current-quark mass and the correlation of their mass difference with that between scalar and axial-vector diquarks; describes an estimate of the s-quark content of a dressed u-quark and its impact on the nucleons strangeness magnetic moment; and comments upon the domain within which a pseudoscalar meson cloud can materially contribute to hadron form factors.
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