arXiv subjects
Publications and source records attributed to B. Blankleider.
In a recent paper by A. Das and X. Zhou [Phys. Rev. D 68, 065017 (2003)] it is claimed that explicit evaluation of the thermal photon self-energy in the Schwinger model gives off-shell thermal Green functions that are different in light-front and conventional quantizations. We show that the claimed difference originates from an erroneous simplification of the fermion propagator used in the light-front calculation.
Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a non-linear function of energy. Such derivations cannot be used, for example, in the context of relativistic quantum field theory. Here we solve this problem by providing a new, general formulation of perturbation theory for calculating the changes in the energy spectrum and wave function of bound states and resonances induced by perturbations to the Hamiltonian. Although our derivation is valid for energy-dependent potentials and is not restricted to inverse free Green functions that are linear in the energy, the expressions obtained for the energy and wave function corrections are compact, practical, and maximally similar to the ones of quantum mechanics. For the case of relativistic quantum field theory, our approach provides a direct covariant way of obtaining corrections to bound and resonance state masses, as well as to wave functions that are not in the centre of mass frame.
The problem of constructing gauge invariant currents in terms of light-cone bound-state wave functions is solved by utilising the gauging of equations method. In particular, it is shown how to construct perturbative expansions of the electromagnetic current in the light-cone formalism, such that current conservation is satisfied at each order of the perturbation theory.
The doublet channel neutron-deuteron scattering amplitude is calculated in leading order effective field theory (EFT). It is shown that this amplitude does not depend on a constant contact interaction three-body force. Satisfactory agreement with available data is obtained when only two-body forces are included.
The use of leading order effective field theory (EFT) to describe neutron-deuteron scattering leads to integral equations that have unusual behaviour: when only two-body interactions are included, the scattering amplitude does not approach a limit when the cutoff used to solve the equations is removed. It has recently been shown that this cutoff dependence can be eliminated by the careful inclusion of a three-body force. In this paper we show that the cutoff dependence is just a reflection of the fact that the aforementioned integral equations admit an infinite number of solutions amongst which only one corresponds to the physical scattering amplitude. We show how to numerically extract the physical scattering amplitude from the general solution and in this way explicitly demonstrate that the amplitude for a particle scattering off a two-body bound state, in leading order EFT, is in fact determined entirely by two-body forces.
Traditional few-body descriptions of pion production use integral equations to sum the strong interactions nonperturbatively. Although much physics is thereby included, there has not been a practical way of incorporating the constraints of chiral symmetry into such approaches. Thus the traditional few-body descriptions fail to reflect the underlying theory of strong interactions, QCD, which is largely chirally symmetric. In addition, the lack of chiral symmetry in the few-body approaches means that their predictions of pion production are in principle not consistent with the partial conservation of axial current (PCAC), a fact that has especially large consequences at low energies. We discuss how the recent introduction of the ``gauging of equations method'' can be used to include PCAC into traditional few-body descriptions and thereby solve this long standing problem
Authors of Phys. Rev. C 60, 062201 (1999) presented a calculation of the electromagnetic form factors of the nucleon using a diquark ansatz in the relativistic three-quark Faddeev equations. In this Comment it is pointed out that the calculations of these form factors stem from a three-quark bound state current that contains overcounted contributions. The corrected expression for the three-quark bound state current is derived.
We show how to derive the complete set of electromagnetic corrections to the Nambu-Jona-Lasinio (NJL) model of the nucleon. Our results enable an accurate estimate of the electromagnetic contribution to the neutron-proton mass difference within this model. At the same time, our procedure demonstrates the way to calculate the complete set of meson corrections to the NJL model that maintains chiral symmetry.
We present a general method for incorporating an external electromagnetic field into descriptions of few-body systems whose strong interactions are described by integral equations. In particular, we address the case where the integral equations are those of quantum field theory and effectively sum up an infinite number of Feynman diagrams. The method involves the idea of gauging the integral equations themselves, and results in electromagnetic amplitudes where an external photon is effectively coupled to every part of every strong interaction diagram in the model. Current conservation is therefore implemented in the way prescribed by quantum field theory. We apply our gauging procedure to the four-dimensional integral equations describing a system of three distinguishable relativistic particles. In this way we obtain the expressions needed to calculate all possible electromagnetic processes of the three-body system. An interesting aspect of our results is the natural appearance of a subtraction term needed to avoid the overcounting of diagrams.
The gauging of equations method, introduced in the preceding paper, is applied to the four-dimensional integral equations describing the strong interactions of three identical relativistic particles. In this way we obtain gauge invariant expressions for all possible electromagnetic transition currents of the identical three-particle system. In the three-nucleon system with no isospin violation, for example, our expressions describe the electromagnetic form factors of ^3H, pd->pd gamma, gamma ^3He-> pd, gamma ^3He-> ppn, etc. A feature of our approach is that gauge invariance is achieved through the coupling of the photon to all possible places in the (nonperturbative) strong interaction model. Moreover, once the proper identical particle symmetry is incorporated into the integral eqations describing the strong interactions, the gauging procedure automatically provides electromagnetic transition currents with the proper symmetry. In this way the gauging of equations method results in a unified description of strong and electromagnetic interaction of strongly interacting systems.
We present a unified description of the relativistic piNN and gamma-piNN systems where the strong interactions are described non-perturbatively by four-dimensional integral equations. A feature of our approach is that the photon is coupled in all possible ways to the strong interaction contributions. Thus the hadronic processes NN -> NN, NN -> pid, pid -> pid, etc. and corresponding electromagnetic processes NN -> gamma-NN, gamma-d -> NN, gamma-d -> pid, ed -> ed, ed -> e'pid, etc., are described simultaneously within the one model of strong interactions. Our formulation obeys two and three-body unitarity, and as photons are coupled everywhere in the strong interaction model, gauge invariance is implemented in the way prescribed by quantum field theory. Our formulation is also free from the overcounting and undercounting problems plaguing four-dimensional descriptions of piNN-like systems. The unified description is achieved through the use of the recently introduced gauging of equations method.
We show how to obtain a complete set of electromagnetic corrections to a given nonperturbative model of strong interactions based on integral equations. The gauge invariance of these corrections is a consequence of their completeness.
We present a unified description of the relativistic piNN and gamma-piNN systems where the strong interactions are described non-perturbatively by four-dimensional integral equations. Our formulation obeys two and three-body unitarity and is strictly gauge invariant with photons coupled to all possible places in the strong interaction model. At the same time our formulation is free from the overcounting problems plaguing four-dimensional descriptions of piNN and gamma-piNN systems. The accurate nature of our description is achieved through the use of the recently introduced gauging of equations method.
We present a general method for incorporating the electromagnetic interaction into descriptions of hadronic processes based on four-dimensional scattering integral equations. The method involves the idea of gauging the scattering equations themselves, and results in electromagnetic amplitudes where an external photon is effectively coupled to every part of every strong interaction diagram in the model. Current conservation is therefore implemented in the theoretically correct fashion. To illustrate our gauging procedure we apply it to the three-nucleon problem whose strong interactions are described by standard three-body integral equations. In this way we obtain the expressions needed to calculate all possible electromagnetic processes of the three-nucleon system: the electromagnetic form factors of the three-body bound state, pd->pd gamma, gamma 3He-> pd, gamma 3He-> ppn, etc. As the photon is coupled everywhere in the strong interaction model, a unified description of the NNN-gamma NNN system is obtained. An interesting aspect of our results is the natural appearance of a subtraction term needed to avoid the overcounting of diagrams.
We show how to attach an external photon to a system of three strongly interacting nucleons described by three-body scattering equations. Our method involves the idea of gauging the scattering equations themselves, and results in electromagnetic amplitudes where the external photon is effectively coupled to every part of every strong interaction diagram in the model. Current conservation is therefore implemented in the theoretically correct fashion. In this way we obtain the expressions needed to calculate all possible electromagnetic processes of the three-nucleon system including the electromagnetic form factors of the three-body bound state, pd -> pd gamma, gamma He3 -> pd, gamma He3 -> ppn, etc. As the photon is coupled everywhere in the strong interaction model, a unified description of the NNN-gamma NNN system is obtained. An interesting aspect of our results is the natural appearance of subtraction terms needed to avoid the overcounting of diagrams. We have also applied the gauging of equations method to the four-dimensional description of the piNN system which, because of the possibility of pion absorption, has overcounting problems all of its own, and is therefore much more complicated than the NNN case discussed here. Despite these complications, the gauging procedure itself is very simple and leads easily to a unified description of the piNN-gamma piNN system.
We show how to derive relativistic, unitary, gauge invariant, and charge conserving three-dimensional scattering equations for a system of hadrons interacting with an electromagnetic field. In the method proposed, the spectator equations describing the strong interactions of the hadrons are gauged using our recently introduced gauging of equations method. A key ingredient in our model is the on-mass-shell particle propagator. We discuss how to gauge this on-mass-shell propagator so that both the Ward-Takahashi and Ward identities are satisfied. We then demonstrate our gauging procedure by deriving the gauge-invariant three-dimensional expression for the deuteron photodisintegration amplitude within the spectator approach.
We derive relativistic three-dimensional integral equations describing the interaction of the three-nucleon system with an external electromagnetic field. Our equations are unitary, gauge invariant, and they conserve charge. This has been achieved by applying the recently introduced gauging of equations method to the three-nucleon spectator equations where spectator nucleons are always on mass shell. As a result, the external photon is attached to all possible places in the strong interaction model, so that current and charge conservation are implemented in the theoretically correct fashion. Explicit expressions are given for the three-nucleon bound state electromagnetic current, as well as the transition currents for the scattering processes γHe3 -> NNN, Nd -> γNd, and γHe3 -> Nd. As a result, a unified covariant three-dimensional description of the NNN-γNNN system is achieved.
We summarise the recent theoretical progress in few-body descriptions of the piNN system. Previous descriptions, both three- and four-dimensional, are shown to possess serious theoretical inconsistencies. We illustrate how three-dimensional approaches suffer from renormalisation problems, and how four-dimensional descriptions contain both overcounting and undercounting of diagrams. We then show how such theoretical problems have been recently overcome, leading to new practical few-body equations for the piNN system.