Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup

For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if and only if the weight semigroup of G/H satisfies some simple condition.Comment: v2: title and abstract changed; v3: 16 pages, minor correction

Difficulties of an Infrared Extension of Differential Renormalization

We investigate the possibility of generalizing differential renormalization of D.Z.Freedman, K.Johnson and J.I.Latorre in an invariant fashion to theories with infrared divergencies via an infrared $\tilde{R}$ operation. Two-dimensional $\sigma$ models and the four-dimensional $\phi^4$ theory diagrams with exceptional momenta are used as examples, while dimensional renormalization serves as a test scheme for comparison. We write the basic differential identities of the method simultaneously in co-ordinate and momentum space, introducing two scales which remove ultraviolet and infrared singularities. The consistent set of Fourier-transformation formulae is derived. However, the values for tadpole-type Feynman integrals in higher orders of perturbation theory prove to be ambiguous, depending on the order of evaluation of the subgraphs. In two dimensions, even earlier than this ambiguity manifests itself, renormalization-group calculations based on infrared extension of differential renormalization lead to incorrect results. We conclude that the extended differential renormalization procedure does not perform the infrared $\tilde{R}$ operation in a self-consistent way, as the original recipe does the ultraviolet $R$ operation.Comment: (minor changes have been made to make clear that no infrared problems occur in the original ultraviolet procedure of [1]; subsection 2.1 has been added to outline the ideas a simple example), 26 pages, LaTeX, JINR preprint E2-92-538, Dubna (Dec.1992

Towards Automatic Analytic Evaluation of Diagrams with Masses

A method to calculate two-loop self-energy diagrams of the Standard Model is demonstrated. A direct physical application is the calculation of the two-loop electroweak contribution to the anomalous magnetic moment of the muon ${{1/2}(g-2)}_{\mu}$. Presently, we confine ourselves to a ``toy'' model with only $\mu$, $\gamma$ and a heavy neutral scalar particle (Higgs). The algorithm is implemented as a FORM-based program package. For generating and automatically evaluating any number of two-loop self-energy diagrams, a special C-program has been written. This program creates the initial FORM-expression for every diagram generated by QGRAF, executes the corresponding subroutines and sums up the final results.Comment: LaTeX, 20 pages, 7 eps-figures included; extended version of talk given at AIHEN96, Lausanne, 1-6 Sept. 1996; detailed description of C-program is given; accepted for publication in Comp.Phys.Com

Generating mass and topological terms to the antisymmetric tensor matter field by Higgs mechanism

The interaction between the complex antisymmetric tensor matter field and a scalar field is constructed. We analyze the Higgs mechanism and show the generation of mass and topological terms by spontaneous symmetry breaking.Comment: Accepted for publication in Phys. Lett.

A Bethe Ansatz Study of Free Energy and Excitation Spectrum for Even Spin Fateev Zamolodchikov Model

A Bethe Ansatz study of a self dual Z_N spin model is undertaken for even spin system. One has to solve a coupled system of Bethe Ansatz Equations (BAE) involving zeroes of two families of transfer matrices. A numerical study on finite size lattices is done for identification of elementary excitations over the Ferromagnetic and Antiferromagnetic ground states. The free energies for both Ferromagnetic and Antiferromagnetic ground states and dispersion relation for elementary excitations are found.Comment: 25 pages, 4 figure

Transcendental numbers and the topology of three-loop bubbles

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.Comment: 4 pages in REVTeX, 1 PostScript figure included, submitted to Phys. Rev. Let

Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order

We compute the relation between the pole quark mass and the minimally subtracted quark mass in the framework of QCD applying dimensional reduction as a regularization scheme. Special emphasis is put on the evanescent couplings and the renormalization of the epsilon-scalar mass. As a by-product we obtain the three-loop on-shell renormalization constants Zm(OS) and Z2(OS) in dimensional regularization and thus provide the first independent check of the analytical results computed several years ago.Comment: 22 page