Gauge-Invariant Differential Renormalization: Abelian Case

A new version of differential renormalization is presented. It is based on pulling out certain differential operators and introducing a logarithmic dependence into diagrams. It can be defined either in coordinate or momentum space, the latter being more flexible for treating tadpoles and diagrams where insertion of counterterms generates tadpoles. Within this version, gauge invariance is automatically preserved to all orders in Abelian case. Since differential renormalization is a strictly four-dimensional renormalization scheme it looks preferable for application in each situation when dimensional renormalization meets difficulties, especially, in theories with chiral and super symmetries. The calculation of the ABJ triangle anomaly is given as an example to demonstrate simplicity of calculations within the presented version of differential renormalization.Comment: 15 pages, late

Affine Jacobians of Spectral Curves and Integrable Models

We explicitly construct the algebraic model of affine Jacobian of a generic algebraic curve of high genus and use it to compute the Euler characteristic of the Jacobian and investigate its structure.Comment: 30 pages; acknoledgements adde

On quantization of affine Jacobi varieties of spectral curves

A quantum integrable model related to $U_q(\hat{sl}(N))$ is considered. A reduced model is introduced which allows interpretation in terms of quantized affine Jacobi variety. Closed commutation relations for observables of reduced model are found.Comment: To be published in "Como Proceedings"; 10 pages, 1 figur

Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model

Within the covariant formulation of light-front dynamics, we calculate the state vector of a fermion coupled to identical scalar bosons (the Yukawa model). The state vector is decomposed in Fock sectors and we consider the first three ones: a single fermion, a fermion coupled to one boson, and a fermion coupled to two bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, and these contributions are calculated with no approximations. The divergences of the amplitudes are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we developed. This renormalization scheme is a necessary condition in order to avoid uncancelled divergences when Fock space is truncated. As an example, we present preliminary numerical results for the anomalous magnetic moment of a fermion in the Yukawa model.Comment: 7 pages, 7 figures. Contribution to the proceedings of the Workshop: Light-Cone 2008, "Relativistic Nuclear and Particle Physics", Mulhouse, France, July 7-11, 2008. To be published in the online journal "Proceedings of Science" - Po

Small-threshold behaviour of two-loop self-energy diagrams: two-particle thresholds

The behaviour of two-loop two-point diagrams at non-zero thresholds corresponding to two-particle cuts is analyzed. The masses involved in a cut and the external momentum are assumed to be small as compared to some of the other masses of the diagram. By employing general formulae of asymptotic expansions of Feynman diagrams in momenta and masses, we construct an algorithm to derive analytic approximations to the diagrams. In such a way, we calculate several first coefficients of the expansion. Since no conditions on relative values of the small masses and the external momentum are imposed, the threshold irregularities are described analytically. Numerical examples, using diagrams occurring in the Standard Model, illustrate the convergence of the expansion below the first large threshold.Comment: 28 pages (including 23 pages of text in latex and 5 pages with 6 figures in a separate postcript file

Connecting lattice and relativistic models via conformal field theory

We consider the quantum group invariant XXZ-model. In infrared limit it describes Conformal Field Theory with modified energy-momentum tensor. The correlation functions are related to solutions of level -4 of qKZ equations. We describe these solutions relating them to level 0 solutions. We further consider general matrix elements (form factors) containing local operators and asymptotic states. We explain that the formulae for solutions of qKZ equations suggest a decomposition of these matrix elements with respect to states of corresponding Conformal Field Theory .Comment: 22 pages, 1 figur

Nonperturbative renormalization in light-front dynamics and applications

We present a general framework to calculate the properties of relativistic compound systems from the knowledge of an elementary Hamiltonian. Our framework provides a well-controlled nonperturbative calculational scheme which can be systematically improved. The state vector of a physical system is calculated in light-front dynamics. From the general properties of this form of dynamics, the state vector can be further decomposed in well-defined Fock components. In order to control the convergence of this expansion, we advocate the use of the covariant formulation of light-front dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane \omega \cd x=0 defined by a light-like four-vector $\omega$. This enables us to control any violation of rotational invariance due to the truncation of the Fock expansion. We then present a general nonperturbative renormalization scheme in order to avoid field-theoretical divergences which may remain uncancelled due to this truncation. This general framework has been applied to a large variety of models. As a starting point, we consider QED for the two-body Fock space truncation and calculate the anomalous magnetic moment of the electron. We show that it coincides, in this approximation, with the well-known Schwinger term. Then we investigate the properties of a purely scalar system in the three-body approximation, where we highlight the role of antiparticle degrees of freedom. As a non-trivial example of our framework, we calculate the structure of a physical fermion in the Yukawa model, for the three-body Fock space truncation (but still without antifermion contributions). We finally show why our approach is also well-suited to describe effective field theories like chiral perturbation theory in the baryonic sector.Comment: 17 pages, 19 figures "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ECT*, October 19-23 200

Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model

We present a coherent and operational strategy to calculate, in a nonperturbative way, physical observables in light-front dynamics. This strategy is based on the decomposition of the state vector of any compound system in Fock components, and on the covariant formulation of light-front dynamics, together with the so-called Fock sector dependent renormalization scheme. We apply our approach to the calculation of the electromagnetic form factors of a fermion in the Yukawa model, in the nontrivial three-body Fock space truncation, for rather large values of the coupling constant. We find that, once the renormalization conditions are properly taken into account, the form factors do not depend on the regularization scale, when the latter is much larger than the physical masses. We then extend the Fock space by including antifermion degrees of freedom.Comment: 22 pages, 16 figure