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The first part of this paper deals with the problem of expressing a given boost as the product of an operator which leaves the momentum of a given particle, massive or massless, invariant and a helicity conserving operator. This is done by multiplying boosts and rotations only. In this way more...
Euler–Kirchhoff filaments are solutions of the static Kirchhoff equations for elastic rods with circular cross sections. These equations are known to be formally equivalent to the Euler equations for spinning tops. This equivalence is used to provide a classification of the different shapes a...
We prove a conjecture of Zuber on the signature of intersection forms associated with affine algebras of type A, which is based on connections between N = 2 N = 2 integrable models in two dimensions and certain class of graphs. © 1999 American Institute of Physics.
We discuss Bloch and Wannier functions related to oscillator eigenfunctions. In particular, we construct complete sets of mutually orthogonal Bloch and Wannier functions. We show that they can be expressed in several ways in terms of theta functions and their derivatives. We also analyze their...
For the hydrogenlike atom, with central potential − Z / r , − Z / r , partial differential equations exist for the Slater sum Z ( r , β ) Z ( r , β ) β = ( k B T ) −1 β = ( k B T ) − 1 and for its s -wave ( l = 0) ( l = 0 ) component Z 0 ( r , β ). Z 0 ( r , β ) . It is shown that Z...
© 1999 American Institute of Physics.
Adapting ideas of Daubechies and Klauder J. Math. Phys. 26 , 2239 (1985) we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin coherent vectors parametrized by complex numbers to relate the coherent representation of...
Within the mathematical framework of Quillen, one interprets the Higgs field as part of the superconnection D on a superbundle. We propose to take as superbundle the exterior algebra ∧ V ∧ V obtained from a Hermitian vector bundle V V of rank n with structure group U( n ) U ( n ) and study...
A reinforced random walk on the d -dimensional lattice is considered. It is shown that this walk is equivalent to an iterated function system (IFS). Criteria for the existence of limit cycles are given. Numerical results and conjectures about the quantitative behavior of the walk are stated. ©...
The expectation values of Wilson loop products for the pure Euclidean Yang–Mills theory on × R × R given by Ashtekar et al. in the article “ SU( N ) SU ( N ) Quantum Yang–Mills Theory in Two Dimensions: A Complete Solution” J. Math. Phys. 38 , 5453 (1997) are determined directly for all...
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