4,746 research outputs found
New strings for old Veneziano amplitudes II. Group-theoretic treatment
In this part of our four parts work (e.g see Part I, hep-th/0410242) we use
the theory of polynomial invariants of finite pseudo-reflection groups in order
to reconstruct both the Veneziano and Veneziano-like (tachyon-free) amplitudes
and the generating function reproducing these amplitudes. We demonstrate that
such generating function can be recovered with help of the finite dimensional
exactly solvable N=2 supersymmetric quantum mechanical model known earlier from
works by Witten, Stone and others. Using the Lefschetz isomorphisms theorem we
replace traditional supersymmetric calculations by the group-theoretic thus
solving the Veneziano model exactly using standard methods of representation
theory. Mathematical correctness of our arguments relies on important theorems
by Shepard and Todd, Serre and Solomon proven respectively in early fifties and
sixties and documented in the monograph by Bourbaki. Based on these theorems we
explain why the developed formalism leaves all known results of conformal field
theories unchanged. We also explain why these theorems impose stringent
requirements connecting analytical properties of scattering amplitudes with
symmetries of space-time in which such amplitudes act.Comment: 57 pages J.Geom.Phys.(in press, available on line
Ab initio Green's function formalism for band structures
Using the Green's function formalism, an ab initio theory for band structures
of crystals is derived starting from the Hartree-Fock approximation. It is
based on the algebraic diagrammatic construction scheme for the self-energy
which is formulated for crystal orbitals (CO-ADC). In this approach, the poles
of the Green's function are determined by solving a suitable Hermitian
eigenvalue problem. The method is not only applicable to the outer valence and
conduction bands, it is also stable for inner valence bands where strong
electron correlations are effective. The key to the proposed scheme is to
evaluate the self-energy in terms of Wannier orbitals before transforming it to
a crystal momentum representation. Exploiting the fact that electron
correlations are mainly local, one can truncate the lattice summations by an
appropriate configuration selection scheme. This yields a flat configuration
space; i.e., its size scales only linearly with the number of atoms per unit
cell for large systems and, under certain conditions, the computational effort
to determine band structures also scales linearly. As a first application of
the new formalism, a lithium fluoride crystal has been chosen. A minimal basis
set description is studied, and a satisfactory agreement with previous
theoretical and experimental results for the fundamental band gap and the width
of the F 2p valence band complex is obtained.Comment: 20 pages, 3 figures, 1 table, RevTeX4, new section on lithium
fluorid
Thermodynamics for Trajectories of a Mass Point
On the basis of information theory, a new formalism of classical
non-relativistic mechanics of a mass point is proposed. The particle
trajectories of a general dynamical system defined on an (1+n)-dimensional
smooth manifold are treated geometrically as dynamical variables. Statistical
mechanics of particle trajectories are constructed in a classical manner.
Thermodynamic variables are introduced through a partition function based on a
canonical ensemble of trajectories. Within this theoretical framework,
classical mechanics can be interpreted as an equilibrium state of statistical
mechanics. The relationships between classical and quantum mechanics are
discussed from this statistical mechanical viewpoint. The maximum entropy
principle is shown to provide a unified view of both classical and quantum
mechanics.Comment: 22 pages, 1 figur
Schnelle Löser für partielle Differentialgleichungen
The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch(Leipzig), Gabriel Wittum (Heidelberg) was held May 22nd - May 28th, 2005. This meeting was well attended by 47 participants with broad geographic representation from 9 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds
Instanton picture of the spin tunneling in the Lipkin model
A consistent theory of the ground state energy and its splitting due to the
process of tunneling for the Lipkin model is presented. For the functional
integral in terms of the spin coherent states for the partition function of the
model we accurately calculate the trivial and the instanton saddle point
contributions. We show that such calculation has to be perfomed very accurately
taking into account the discrete nature of the functional integral. Such
accurate consideration leads to finite corrections to a naive continous
consideration. We present comparison with numerical calculation of the ground
state energy and the tunneling splitting and with the results obtained by the
quasiclassical method and get excellent agreement.Comment: REVTEX, 32 pages, 3 figure
- …