Special Research Centre for the Subatomic Structure of Matter
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The central mission of the Centre is to carry out research activities in the forefront of the fields of theoretical nuclear and particle physics with special emphasis on the strong interactions and their importance in determining the nature of matter.
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University of Adelaide,
SA 5005, Australia
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Browsing Special Research Centre for the Subatomic Structure of Matter by Author "Alexandrou, C."
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Item Open Access Nonperturbative mass renormalization in quenched QED from the worldline variational approach(American Physical Soc, 2000) Alexandrou, C.; Rosenfelder, R.; Schreiber, A.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 such as QED in 3+1 dimensions. We take as a 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 γm(α) in the MS scheme. For small couplings we compare our result with recent four-loop perturbative calculations while at large couplings we find that γm(α) becomes proportional to √α. 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 γm(α) diverges for α>0.7934. Finally, we investigate the behavior of γm(α) at large orders in perturbation theory.Item Metadata only Variational field theoretic approach to relativistic meson-nucleon scattering(ELSEVIER SCIENCE BV, 1998) Alexandrou, C.; Rosenfelder, R.; Schreiber, A.Non-perturbative polaron variational methods are applied, within the so-called particle or world-line 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. © 1998 Elsevier Science B.V.Item Metadata only Variational treatment of quenched QED using the worldline technique(Elsevier BV, 1998) Schreiber, A.; Alexandrou, C.; Rosenfelder, R.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.Item Open Access Worldline path integral for the massive Dirac propagator: A four-dimensional approach(American Physical Society, 1999) Alexandrou, C.; Rosenfelder, R.; Schreiber, A.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.