arXiv subjects

R. Rosenfelder

Publications and source records attributed to R. Rosenfelder.

33 records · Page 2Linked to original sources

arXiv2000

What Can We Learn from QED at Large Couplings?

In order to understand QCD at the energies relevant to hadronic physics one requires analytical methods for dealing with relativistic gauge field theories at large couplings. Strongly coupled quenched QED provides an ideal laboratory for the development of such techniques, in particular as many calculations suggest that - like QCD - this theory has a phase with broken chiral symmetry. In this talk we report on a nonperturbative variational calculation of the electron propagator within quenched QED and compare results to those obtained in other approaches. We find surprising differences among these results.

hep-th↗

arXiv2000

Non-Perturbative Mass Renormalization in Quenched QED from the Worldline Variational Approach

Following Feynman's successful treatment of the polaron problem we apply the same variational principle to quenched QED in the worldline formulation. New features arise from the description of fermions by Grassmann trajectories, the supersymmetry between bosonic and fermionic variables and the much more singular structure of a renormalizable gauge theory like QED in 3+1 dimensions. We take as trial action a general retarded quadratic action both for the bosonic and fermionic degrees of freedom and derive the variational equations for the corresponding retardation functions. We find a simple analytic, non-perturbative, solution for the anomalous mass dimension gamma_m(alpha) in the MS scheme. For small couplings we compare our result with recent four-loop perturbative calculations while at large couplings we find that gamma_m(alpha) becomes proportional to (alpha)^(1/2). The anomalous mass dimension shows no obvious sign of the chiral symmetry breaking observed in calculations based on the use of Dyson-Schwinger equations, however we find that a perturbative expansion of gamma_m(alpha) diverges for alpha > 0.7934. Finally, we investigate the behaviour of gamma_m(alpha) at large orders in perturbation theory.

hep-th↗

arXiv1999

Coulomb Corrections to Elastic Electron-Proton Scattering and the Proton Charge Radius

Recent values of the proton charge radius derived from the Lamb shift in electronic hydrogen tend to be larger than those from electron scattering. Therefore low-momentum-transfer scattering data from different groups and laboratories have been reanalyzed with Coulomb and recoil corrections included. This was done by calculating at each scattering angle and scattering energy the corresponding correction obtained from a partial wave program which includes recoil approximately. Corrections due to magnetic scattering were also made before the rms-radius was determined by a fit which allows free normalization for each experiment. It is shown that an analysis of electron scattering data including Coulomb corrections lowers the $χ^2$ of the fit and increases the proton radius by about (0.008 - 0.013) fm depending on the fit strategy. A value of r_p = 0.880 (15) fm is obtained which is in good agreement with the one extracted from Lamb shift measurements.

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arXiv1999

Comment on the paper: ``Feynman-Schwinger representation approach to nonperturbative physics'' by C. Savkli et al. [Phys. Rev. C 60, 055210 (1999), hep-ph/9906211]

We point out that the scalar Wick-Cutkosky model (with $χ^2 ϕ$ interaction) used in this study has been known for a long time to be unstable. However, the numerical results presented in this paper do not show any sign of this instability which casts some doubt on their reliability. We compare with the worldline variational approach.

hep-ph↗

arXiv1999

Proton Polarization Shifts in Electronic and Muonic Hydrogen

The contribution of virtual excitations to the energy levels of electronic and muonic hydrogen is investigated combining a model-independent approach for the main part with quark model predictions for the remaining corrections. Precise values for the polarization shifts are obtained in the long-wavelength dipole approximation by numerically integrating over measured total photoabsorption cross sections. These unretarded results are considerably reduced by including retardation effects in an approximate way since the average momentum transfer (together with the mean excitation energy) turns out to be larger than usually assumed. Transverse and seagull contributions are estimated in a simple harmonic oscillator quark model and found to be non-negligible. Possible uncertainties and improvements of the final results are discussed.

hep-ph↗

arXiv1999

Worldline path integral for the massive Dirac propagator : A four-dimensional approach

We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically without the usual five-dimensional extension and shown to be equivalent due to the supersymmetry of the action. They correspond to a projection on the mass of the particle either continuously or at the end of the time evolution. It is shown that the supersymmetry transformations are generated by shifting and scaling the supertimes and the invariant difference of two supertimes is given for the general case. A nonrelativistic reduction of the relativistic propagator leads to a three-dimensional path integral with the usual Pauli Hamiltonian. By integrating out the photons we obtain the effective action for quenched QED and use it to derive the gauge-transformation properties of the general Green function of the theory.

hep-th↗

arXiv1998

The Feynman Variational Principle in the Worldline Representation of Field Theory

Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in terms of particle trajectories (worldlines) instead of field operators. The Green functions of the theory are then approximated variationally on the pole of the external particles by using a retarded quadratic trial action. Application to a scalar theory gives non-perturbative, covariant results for vertex functions and scattering processes. Recent progress in dealing with the spin degrees of freedom in fermionic systems, in particular Quantum Electrodynamics, is discussed. We evaluate the averages needed in the Feynman variational principle for a general quadratic trial action and study the structure of the dressed fermion propagator.

hep-th↗

arXiv1997

Scaling in SU(3) theory with a MCRG improved lattice action

We test various improved gauge actions which are made of linear combinations of Wilson loops. We observe the restoration of rotational symmetry in the static interquark potential already on coarse lattices as small as 6^3x12. Furthermore, we study scaling and asymptotic scaling of the string tension with a MCRG-improved action on 12^3x24 lattices. Preliminary results show that scaling sets in at a ~ 0.3 fm.

hep-lat↗

arXiv1997

Variational treatment of quenched QED using the worldline technique

There has been growing interest in studying the behaviour of QED in its strong coupling limit. The reason for this is not only that it serves as a simple prototype gauge theory for testing nonperturbative calculational techniques which one then goes on to apply to QCD, but also because the theory exhibits interesting behaviour in its own right. In particular, it now appears to be quite well established that QED breaks chiral symmetry dynamically as long as the coupling is sufficiently large. In this contribution we describe the progress made in applying the polaron variational approach to quenched QED within the context of the worldline formulation of field theory. Although it is too early for quantitative results, qualitatively the approach seems promising: The method is formulated covariantly in Minkowski space-time, the Ward-Takahashi identities are satisfied, the connection between the bare- and pole-masses of the electron is gauge independent, the known exact result for the infrared dependence of the on-shell renormalized propagator is reproduced and corrections to the variational approximation can be calculated systematically.

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arXiv1997

Variational Field Theoretic Approach to Relativistic Scattering

Nonperturbative polaron variational methods are applied, within the so-called particle or worldline representation of relativistic field theory, to study scattering in the context of the scalar Wick - Cutkosky model. Important features of the variational calculation are that it is a controlled approximation scheme valid for arbitrary coupling strengths, the Green functions have all the cuts and poles expected for the exact result at any order in perturbation theory and that the variational parameters are simultaneously sensitive to the infrared as well as the ultraviolet behaviour of the theory. We generalize the previously used quadratic trial action by allowing more freedom for off-shell propagation without a change in the on-shell variational equations and evaluate the scattering amplitude at first order in the variational scheme. Particular attention is paid to the $s$-channel scattering near threshold because here non-perturbative effects can be large. We check the unitarity of a our numerical calculation and find it greatly improved compared to perturbation theory and to the zeroth order variational results.

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arXiv1995

First Order Variational Calculation of Form Factor in a Scalar Nucleon--Meson Theory

We investigate a relativistic quantum field theory in the particle representation using a non-perturbative variational technique. The theory is that of two massive scalar particles, `nucleons' and `mesons', interacting via a Yukawa coupling. We calculate the general Euclidean Green function involving two external nucleons and an arbitrary number of external mesons in the quenched approximation for the nucleons. The non-perturbative renormalization and truncation is done in a consistent manner and results in the same variational functional independent of the number of external mesons. We check that the calculation agrees with one-loop perturbation theory for small couplings. As an illustration the special case of meson absorption on the nucleon is considered in detail. We derive the radius of the dressed particle and numerically investigate the vertex function after analytic continuation to Minkowski space.

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arXiv1995

Variational Calculation of Relativistic Meson-Nucleon Scattering In Zeroth Order

We extend the polaron variational treatment previously developed for the propagator to the case where one nucleon and $n$ external mesons are present. Using the particle representation of the scalar Wick-Cutkosky model this is done in lowest order of an expansion of the exact action around a retarded quadratic trial action. In particular, we evaluate the form factor for scattering of mesons from the scalar nucleon and determine the radius of the dressed particle. After analytic continuation to Minkowski space we study elastic meson-nucleon scattering both analytically and numerically near threshold and show that it is essential to incorporate the correct behaviour of the retardation function at large proper times. Only if this is done the optical theorem is approximately fulfilled over a range of energies and coupling constants.

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arXiv1995

Polaron Variational Methods In The Particle Representation Of Field Theory : II. Numerical Results For The Propagator

For the scalar Wick-Cutkosky model in the particle representation we perform a similar variational calculation for the 2-point function as was done by Feynman for the polaron problem. We employ a quadratic nonlocal trial action with a retardation function for which several ansätze are used. The variational parameters are determined by minimizing the variational function and in the most general case the nonlinear variational equations are solved numerically. We obtain the residue at the pole, study analytically and numerically the instability of the model at larger coupling constants and calculate the width of the dressed particle.

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arXiv1995

Polaron Variational Methods In The Particle Representation Of Field Theory : I. General Formalism

We apply nonperturbative variational techniques to a relativistic scalar field theory in which heavy bosons (``nucleons'') interact with light scalar mesons via a Yukawa coupling. Integrating out the meson field and neglecting the nucleon vacuum polarization one obtains an effective action in terms of the heavy particle coordinates which is nonlocal in the proper time. As in Feynman's polaron approach we approximate this action by a retarded quadratic action whose parameters are to be determined variationally on the pole of the two-point function. Several ansätze for the retardation function are studied and for the most general case we derive a system of coupled variational equations. An approximate analytic solution displays the instability of the system for coupling constants beyond a critical value.

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arXiv1993

Nuclear Polarization Corrections for the S--Levels of Electronic and Muonic Deuterium

We calculate the second-order corrections to the atomic energy level shifts in ordinary and muonic deuterium due to virtual excitations of the deuteron which are important for ongoing and planned precise experiments in these systems. For light atoms a method can be used in which the shift is expressed as integrals over the longitudinal and transverse inelastic structure functions of the nucleus. We employ the structure functions arising from separable NN potentials of the Yamaguchi and Tabakin form which can be evaluated analytically. Special emphasis is put on gauge invariance which requires a consistent inclusion of interaction currents and seagull terms. The effect of the D-wave component of the deuteron is investigated for the leading longitudinal contribution. We also estimate the shift for pionic deuterium.

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