"Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions

We develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a constant background electromagnetic field, and use these to show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general constant background field. This explains why the square of a one-loop term appears in the renormalized two-loop Heisenberg-Euler effective action. No integrals need be evaluated, and the explicit form of the background field propagators is not needed. This dramatically simplifies the computation of the renormalized two-loop effective action for scalar QED, and generalizes a previous result obtained for self-dual background fields.Comment: 13 pages; uses axodraw.st

Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED, part 1: Two-loop

We continue an effort to obtain information on the QED perturbation series at high loop orders, and particularly on the issue of large cancellations inside gauge invariant classes of graphs, using the example of the l - loop N - photon amplitudes in the limit of large photons numbers and low photon energies. As was previously shown, high-order information on these amplitudes can be obtained from a nonperturbative formula, due to Affleck et al., for the imaginary part of the QED effective lagrangian in a constant field. The procedure uses Borel analysis and leads, under some plausible assumptions, to a number of nontrivial predictions already at the three-loop level. Their direct verification would require a calculation of this `Euler-Heisenberg lagrangian' at three-loops, which seems presently out of reach. Motivated by previous work by Dunne and Krasnansky on Euler-Heisenberg lagrangians in various dimensions, in the present work we initiate a new line of attack on this problem by deriving and proving the analogous predictions in the simpler setting of 1+1 dimensional QED. In the first part of this series, we obtain a generalization of the formula of Affleck et al. to this case, and show that, for both Scalar and Spinor QED, it correctly predicts the leading asymptotic behaviour of the weak field expansion coefficients of the two loop Euler-Heisenberg lagrangians.Comment: 28 pages, 1 figures, final published version (minor modifications, refs. added

Probing the interplay between factors determining reaction rates on silica gel using termolecular systems

This article was published in the journal, Photochemical and Photobiological Sciences [© Royal Society of Chemistry and Owner Societies]. The definitive version is available at: http://dx.doi.org/10.1039/c2pp25171jIn this study we have compared energy and electron transfer reactions in termolecular systems using a nanosecond diffuse reflectance laser flash photolysis technique. We have previously investigated these processes on silica gel surfaces for bimolecular systems and electron transfer in termolecular systems. The latter systems involved electron transfer between three arene molecules with azulene acting as a molecular shuttle. In this study we present an alternative electron transfer system using trans β-carotene as an electron donor in order to effectively immobilise all species except the shuttle, providing the first unambiguous evidence for radical ion mobility. In the energy transfer system we use naphthalene, a structural isomer of azulene, as the shuttle, facilitating energy transfer from a selectively excited benzophenone sensitiser to 9-cyanoanthracene. Bimolecular rate constants for all of these processes have been measured and new insights into the factors determining the rates of these reactions on silica gel have been obtained

Quantum gauge field theory

Canonical quantization of a gauge theory in the spatial axial gauge produces an anisotropic Hamiltonian and matter particles surrounded by physically unrealistic asymmetric electric or chromoelectric fields. In the first part of my dissertation I show how to restore rotational symmetry for a nonabelian theory with a gauge fixing condition Aa3 = 0. I also discuss similarities between recovering isotropy in the spatial axial gauge and finding gauge invariant quantities in the Weyl gauge in both abelian and nonabelian field theories. ^ In the second part I further develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a background electromagnetic field. I show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general background field, which is a generalization of previously obtained results. For a constant background the fully renormalized effective action is found. No integrals need to be evaluated, and the explicit form of the background field propagators is not needed. This dramatically simplifies the computation of the renormalized two-loop effective action for scalar QED. I also show that when the constant background field satisfies F 2 = –f21, which in four dimensions coincides with the condition for self-duality, or definite helicity, the two-loop effective action can be reduced to simple one-loop quantities, using just algebraic manipulations, in arbitrary even dimensions. This result relies on new recursion relations between two-loop and one-loop diagrams, with background field propagators. It also yields an explicit form of the renormalized two-loop effective action in a general constant background field in two dimensions. Further I show how these diagrammatical rules can be applied to calculation of the three-loop effective action.