Massive 3-loop Feynman diagrams reducible to SC * primitives of algebras of the sixth root of unity Abstract In each of the 10 cases with propagators of unit or zero mass, the finite part of the scalar 3-loop tetrahedral vacuum diagram is reduced to 4-letter words in the 7-letter alphabet of the 1-forms Ω := dz/z and ω p := dz/(λ −p − z), where λ is the sixth root of unity. Three diagrams yield...

We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncommutative Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which is studied her...

We determine the neutralino and chargino masses in the MSSM at one-loop. We perform a Feynman diagram calculation in the on-shell renormalization scheme, including quark/squark and lepton/slepton loops. We find generically the corrections are of order 6%. For a 20 GeV neutralino the corrections can be larger than 20%. The corrections change the region of μ, M2, tan β parameter space which is ru...

We consider radiative corrections to the decay rate Γ(H → ZZ) of the heavy CP-even Higgs boson of the minimal supersymmetric model to two Z bosons. We perform a one loop Feynman diagram calculation in the on-mass-shell renormalization scheme, and include the third generation of quarks and squarks. The tree level rate is suppressed by a mixing angle factor and decreases as 1/MH for large MH . Th...

We propose that Kreimer’s method of Feynman diagram renormalization via a Hopf algebra of rooted trees can be fruitfully employed in the analysis of block spin renormalization or coarse graining of inhomogeneous statistical systems. Examples of such systems include spin foam formulations of non-perturbative quantum gravity as well as lattice gauge and spin systems on irregular lattices and/or w...

A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar φ⊕φ theory, is presented. The representation is obtained starting from an Initial Parameters Matrix (IPM ), which relates the scalar products between internal and external momenta, and which appears explicitly when this paramet...

Massive Feynman integrals containing more than one loop momentum are hard to evaluate. Fortunately, the understanding of the critical behavior of the field theory requires only knowledge of the divergent counterterms. In the last chapter we have seen that their calculation reduces to the calculation of logarithmically divergent diagrams without tadpole parts for Z g and Z m 2 and of quadratical...

Massive Feynman integrals containing more than one loop momentum are hard to evaluate. Fortunately, the understanding of the critical behavior of the field theory requires only knowledge of the divergent counterterms. In the last chapter we have seen that their calculation reduces to the calculation of logarithmically divergent diagrams without tadpole parts for Z g and Z m 2 and of quadratical...

If entrepreneurs are liquidity constrained and not able to borrow to operate on an e¢ cient scale, economic theory predicts that entrepreneurs with more personal wealth should do better than those with less wealth. We test this hypothesis using a novel dataset covering a large panel of start-ups from Norway. Consistent with liquidity constraints, we …nd a positive relationship between founder p...

Various modern nucleon-nucleon (NN) potentials yield a very accurate fit to the nucleon-nucleon scattering phase shifts. The differences between these interactions in describing properties of nuclear matter are investigated. Various contributions to the total energy are evaluated employing the Hellmann-Feynman theorem. Special attention is paid to the two-nucleon correlation functions derived f...