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Christian Schubert

Publications and source records attributed to Christian Schubert.

At least 109 records · Page 6Linked to original sources
arXiv2004

Multiloop Information from the QED Effective Lagrangian

We obtain information on the QED photon amplitudes at high orders in perturbation theory starting from known results on the QED effective Lagrangian in a constant electric field. A closed-form all-order result for the weak field limit of the imaginary part of this Lagrangian has been given years ago by Affleck, Alvarez and Manton (for scalar QED) and by Lebedev and Ritus (for spinor QED). We discuss the evidence for its correctness, and conjecture an analogous formula for the case of a self-dual field. From this extension we then obtain, using Borel analysis, the leading asymptotic growth for large N of the maximally helicity violating component of the L - loop N - photon amplitude in the low energy limit. The result leads us to conjecture that the perturbation series converges for the on-shell renormalized QED N - photon amplitudes in the quenched approximation.

hep-th↗
arXiv2003

Self-duality, Helicity and Higher-loop Euler-Heisenberg Effective Actions

The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop. This simplicity is due to the inter-relationship between self-duality, helicity and supersymmetry. Applications include two-loop helicity amplitudes, beta-functions and nonperturbative effects. The two-loop Euler-Heisenberg effective Lagrangian for QED in a self-dual background field is naturally expressed in terms of one-loop quantities. This mirrors similar behavior recently found in two-loop amplitudes in N=4 SUSY Yang-Mills theory.

hep-th↗
arXiv2002

Two-Loop Self-Dual QED

We present explicit closed-form expressions for the two-loop Euler-Heisenberg Lagrangians in a constant self-dual field, for both spinor and scalar QED. The simplicity of these representations allows us to examine in detail the asymptotic properties of these Lagrangians, and to construct their imaginary part using Borel dispersion relations. In particular, for this self-dual case we obtain the explicit form of the Lebedev-Ritus functions appearing in the Schwinger representation of the imaginary part at two loops. Using the connection between self-duality and helicity, we also obtain explicit formulas for the low energy limits of the `all + helicity' N photon amplitudes, in scalar and spinor QED at one and two loops.

hep-ph↗
arXiv2002

Zero modes, beta functions and IR/UV interplay in higher-loop QED

We analyze the relation between the short-distance behavior of quantum field theory and the strong-field limit of the background field formalism, for QED effective Lagrangians in self-dual backgrounds, at both one and two loop. The self-duality of the background leads to zero modes in the case of spinor QED, and these zero modes must be taken into account before comparing the perturbative beta function coefficients and the coefficients of the strong-field limit of the effective Lagrangian. At one-loop this is familiar from instanton physics, but we find that at two-loop the role of the zero modes, and the interplay between IR and UV effects in the renormalization, is quite different. Our analysis is motivated in part by the remarkable simplicity of the two-loop QED effective Lagrangians for a self-dual constant background, and we also present here a new independent derivation of these two-loop results.

hep-th↗
arXiv2002

A Quantum Field Theoretical Representation of Euler-Zagier Sums

We establish a novel representation of arbitrary Euler-Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve Bernoulli polynomials and Clausen functions to arbitrary orders. The Feynman integrals of this model can be decomposed in terms of an algebra of elementary vertex integrals whose structure we investigate. We derive a large class of relations between multiple zeta values, of arbitrary lengths and weights, using only a certain set of graphical manipulations on Feynman diagrams. Further uses and possible generalizations of the model are pointed out.

math.QA↗
arXiv2002

Two-loop self-dual Euler-Heisenberg Lagrangians (II): Imaginary part and Borel analysis

We analyze the structure of the imaginary part of the two-loop Euler-Heisenberg QED effective Lagrangian for a constant self-dual background. The novel feature of the two-loop result, compared to one-loop, is that the prefactor of each exponential (instanton) term in the imaginary part has itself an asymptotic expansion. We also perform a high-precision test of Borel summation techniques applied to the weak-field expansion, and find that the Borel dispersion relations reproduce the full prefactor of the leading imaginary contribution.

hep-th↗
arXiv2002

Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes

We show that, for both scalar and spinor QED, the two-loop Euler-Heisenberg effective Lagrangian for a constant Euclidean self-dual background has an extremely simple closed-form expression in terms of the digamma function. Moreover, the scalar and spinor QED effective Lagrangians are very similar to one another. These results are dramatic simplifications compared to the results for other backgrounds. We apply them to a calculation of the low energy limits of the two-loop massive N-photon `all +' helicity amplitudes. The simplicity of our results can be related to the connection between self-duality, helicity and supersymmetry.

hep-th↗
arXiv2001

Closed-form two-loop Euler-Heisenberg Lagrangian in a self-dual background

We show that the two-loop Euler-Heisenberg effective Lagrangian for scalar QED in a constant Euclidean self-dual background has a simple explicit closed form expression in terms of the digamma function. This result leads to a simple analysis of the weak- and strong-field expansions, the two-loop scalar QED beta function, and the analytic continuation properties of the effective Lagrangian and its imaginary part.

hep-th↗
arXiv2001

Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part III

The string-inspired technique is used for a first calculation of the one-loop axialvector vacuum polarisation in a general constant electromagnetic field. A compact result is reached for the difference between this tensor and the corresponding vector vacuum polarisation. This result is confirmed by a Feynman diagram calculation. Its physical relevance is briefly discussed.

hep-ph↗
arXiv2001

Perturbative Quantum Field Theory in the String-Inspired Formalism

We review the status and present range of applications of the ``string-inspired'' approach to perturbative quantum field theory. This formalism offers the possibility of computing effective actions and S-matrix elements in a way which is similar in spirit to string perturbation theory, and bypasses much of the apparatus of standard second-quantized field theory. Its development was initiated by Bern and Kosower, originally with the aim of simplifying the calculation of scattering amplitudes in quantum chromodynamics and quantum gravity. We give a short account of the original derivation of the Bern-Kosower rules from string theory. Strassler's alternative approach in terms of first-quantized particle path integrals is then used to generalize the formalism to more general field theories, and, in the abelian case, also to higher loop orders. A considerable number of sample calculations are presented in detail, with an emphasis on quantum electrodynamics.

hep-th↗
arXiv2000

Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part I

The string-inspired technique is used for the calculation of vacuum polarisation tensors in constant electromagnetic fields. In the first part of this series, we give a detailed exposition of the method for the case of the QED one-loop N-photon amplitude in a general constant electromagnetic background field. The two-point cases are calculated explicitly, leading to compact representations for the constant field vacuum polarisation tensors for both scalar and spinor QED.

hep-ph↗
arXiv2000

Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT

We show that, although the correlator of four stress-tensor multiplets in N=4 SYM is known to have radiative corrections, certain linear combinations of its components are protected from perturbative renormalisation and remain at their free-field values. This result is valid for weak as well as for strong coupling and for any gauge group. Our argument uses Intriligator's insertion formula, and includes a proof that the possible contact term contributions cannot change the form of the amplitudes. Combining this new non-renormalisation theorem with Maldacena's conjecture allows us to make a prediction for the structure of the corresponding correlator in AdS supergravity. This is verified by first considerably simplifying the strong coupling expression obtained by recent supergravity calculations, and then showing that it does indeed exhibit the expected structure.

hep-th↗
arXiv2000

QED in the Worldline Formalism

A survey is given of applications of the ``string-inspired'' worldline formalism to the computation of amplitudes and effective actions in QED.

hep-ph↗
arXiv2000

Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part II

In the second part of this series we apply the ``string-inspired'' technique to the calculation of one-loop amplitudes involving both vectors and axialvectors, as well as a general constant electromagnetic background field. The vector-axialvector two-point function in a constant field is calculated explicitly.

hep-ph↗
arXiv1999

Two-Loop Euler-Heisenberg QED Pair-Production Rate

We study the divergence of large-order perturbation theory in the worldline expression for the two-loop Euler-Heisenberg QED effective Lagrangian in a constant magnetic field. The leading rate of divergence is identical, up to an overall factor, to that of the one-loop case. From this we deduce, using Borel summation techniques, that the leading behaviour of the imaginary part of the two-loop effective Lagrangian for a constant E field, giving the pair-production rate, is proportional to the one-loop result. This also serves as a test of the mass renormalization, and confirms the earlier analysis by Ritus.

hep-th↗
arXiv1999

Axial Vector Amplitudes, Second Order Fermions, and Standard Model Photon -- Neutrino Processes

We present an extension of the string-inspired technique suitable to the calculation of amplitudes and effective Lagrangians involving both vector and axial vector gauge fields. The technique is easily adaptable to problems involving constant external fields. We demonstrate the advantages of the formalism by a calculation of the one-loop vector-axialvector amplitude in a general constant electromagnetic field. The relevance of this calculation for photon-neutrino processes is commented upon. We also clarify the properties of the formalism with respect to the chiral symmetry, and its connection to second order fermions.

hep-ph↗
arXiv1999

A New Approach to Axial Vector Model Calculations II

We further develop the new approach, proposed in part I (hep-th/9807072), to computing the heat kernel associated with a Fermion coupled to vector and axial vector fields. We first use the path integral representation obtained for the heat kernel trace in a vector-axialvector background to derive a Bern-Kosower type master formula for the one-loop amplitude with $M$ vectors and $N$ axialvectors, valid in any even spacetime dimension. For the massless case we then generalize this approach to the full off-diagonal heat kernel. In the D=4 case the SO(4) structure of the theory can be broken down to $SU(2) \times SU(2)$ by use of the 't Hooft symbols. Various techniques for explicitly evaluating the spin part of the path integral are developed and compared. We also extend the method to external fermions, and to the inclusion of isospin. On the field theory side, we obtain an extension of the second order formalism for fermion QED to an abelian vector-axialvector theory.

hep-th↗