Efficient Algorithm for Perturbative Calculation of Multiloop Feynman Integrals

We present an efficient algorithm for calculating multiloop Feynman integrals perturbatively.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/29

Solution of Coulomb Path Integral in Momentum Space

The path integral for a point particle in a Coulomb potential is solved in momentum space. The solution permits us to give for the first time a negative answer to an old question of quantum mechanics in curved spaces raised in 1957 by DeWitt, whether the Hamiltonian of a particle in a curved space contains an additional term proportional to the curvature scalar $R$. We show that this would cause experimentally wrong level spacings in the hydrogen atom. Our solution also gives a first experimental confirmation of the correctness of the measure of integration in path integrals in curved space implied by a recently discovered nonholonomic mapping principle.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re/27

Perturbative Calculation of Multi-Loop Feynman Diagrams. New Type of Expansions for Critical Exponents

We show that the calculation of L-loop Feynman integrals in D dimensions can be reduced to a series of matrix multiplications in D times L dimensions. This gives rise to a new type of expansions for the critical exponents in three dimensions in which all coefficients can be calculated exactly.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/29

Strong Enhancement of High Voltage Electronic Transport in Chiral Electrical Nanotube Superlattices

We consider metallic carbon nanotubes with an overlying unidirectional electrical chiral (wavevector out of the radial direction, where the axial direction is included) superlattice potential. We show that for superlattices with a wavevector close to the axial direction, the electron velocity assumes the same value as for nanotubes without superlattice. Due to an increased number of phonons with different momenta but lower electron-phonon scattering probabilities, we obtain a large enhancement of the high-voltage conductance and current sustainability in comparison with the nanotube without superlattice.Comment: 5 pages, 3 figures, published versio