Multiphoton amplitudes and generalized Landau-Khalatnikov-Fradkin transformation in scalar QED

We apply the worldline formalism to amplitudes in scalar quantum electrodynamics (QED) involving open scalar lines, with an emphasis on their non-perturbative gauge dependence. At the tree-level, we study the scalar propagator interacting with any number of photons in configuration space as well as in momentum space. At one-loop we rederive, in an efficient way, the off-shell vertex in an arbitrary dimension and any covariant gauge. Generalizing the Landau-Khalatnikov-Fradkin transformation (LKFT) for the non-perturbative propagator, we find simple non-perturbative transformation rules for arbitrary x-space amplitudes under a change of the covariant gauge parameter in terms of conformal cross ratios.Comment: 21 pages, 8 figure

Reducible contributions to quantum electrodynamics in external fields

36 pages, 9 figuresWe consider one-particle reducible (1PR) contributions to QED and scalar QED processes in external fields, at one loop and two loops. We investigate three cases in detail: constant crossed fields, constant magnetic fields, and plane waves. We find that 1PR tadpole contributions in plane waves and constant crossed fields are non-zero, but contribute only divergences to be renormalised away. In constant magnetic fields, on the other hand, tadpole contributions give physical corrections to processes at one loop and beyond. Our calculations are exact in the external fields and we give weak field expansions in the magnetic case

Local Neumann semitransparent layers: Resummation, pair production, and duality

We consider local semitransparent Neumann boundary conditions for a quantum scalar field as imposed by a quadratic coupling to a source localized on a flat codimension-one surface. Upon a proper regularization to give meaning to the interaction, we interpret the effective action as a theory in a first-quantized phase space. We compute the relevant heat kernel to all order in a homogeneous background and quadratic order in perturbations, giving a closed expression for the corresponding effective action in D=4. In the dynamical case, we analyze the pair production caused by a harmonic perturbation and a Sauter pulse. Notably, we prove the existence of a strong/weak duality that links this Neumann field theory to the analog Dirichlet one.Fil: Ahmadiniaz, N.. Helmholtz-Zentrum Dresden-Rossendorf; AlemaniaFil: Franchino Viñas, Sebastián Alberto. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Manzo, Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Mazzitelli, Francisco Diego. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin

Compton-like scattering of a scalar particle with N photons and one graviton

Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude, where all the photons and the graviton are directly attached to the scalar line, then derive a \u201ctree replacement\u201d rule to construct the reducible parts of the amplitude which involve irreducible pure N-photon two-scalar amplitudes where one photon line emits the graviton. We test our construction by verifying the on-shell gauge and diffeomorphism Ward identities, at arbitrary N

Photon-graviton amplitudes

We report on an ongoing study of the one-loop photon-graviton amplitudes, using both effective action and worldline techniques. The emphasis is on Kawai-Lewellen-Tye-like relations

Worldline master formulas for the dressed electron propagator. Part 2. On-shell amplitudes

In the first part of this series, we employed the second-order formalism and the \u201csymbol\u201d map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the \u201cN-photon kernel,\u201d where this kernel appears also in \u201csubleading\u201d terms involving only N 12 1 of the N photons. In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications. We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for \u201call +\u201d photon helicities in the massless case, and find a novel relation between the scalar and spinor spin-averaged cross sections in the massive case. Testing the formalism on the standard linear Compton scattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out