9,550 research outputs found
Heat-kernel approach for scattering
An approach for solving scattering problems, based on two quantum field
theory methods, the heat kernel method and the scattering spectral method, is
constructed. This approach converts a method of calculating heat kernels into a
method of solving scattering problems. This allows us to establish a method of
scattering problems from a method of heat kernels. As an application, we
construct an approach for solving scattering problems based on the covariant
perturbation theory of heat-kernel expansions. In order to apply the
heat-kernel method to scattering problems, we first calculate the off-diagonal
heat-kernel expansion in the frame of the covariant perturbation theory.
Moreover, as an alternative application of the relation between heat kernels
and partial-wave phase shifts presented in this paper, we give an example of
how to calculate a global heat kernel from a known scattering phase shift
Scattering theory without large-distance asymptotics
In conventional scattering theory, to obtain an explicit result, one imposes
a precondition that the distance between target and observer is infinite. With
the help of this precondition, one can asymptotically replace the Hankel
function and the Bessel function with the sine functions so that one can
achieve an explicit result. Nevertheless, after such a treatment, the
information of the distance between target and observer is inevitably lost. In
this paper, we show that such a precondition is not necessary: without losing
any information of distance, one can still obtain an explicit result of a
scattering rigorously. In other words, we give an rigorous explicit scattering
result which contains the information of distance between target and observer.
We show that at a finite distance, a modification factor --- the Bessel
polynomial --- appears in the scattering amplitude, and, consequently, the
cross section depends on the distance, the outgoing wave-front surface is no
longer a sphere, and, besides the phase shift, there is an additional phase
(the argument of the Bessel polynomial) appears in the scattering wave
function
A 1+5-dimensional gravitational-wave solution: curvature singularity and spacetime singularity
We solve a -dimensional cylindrical gravitational-wave solution of the
Einstein equation, in which there are two curvature singularities. Then we show
that one of the curvature singularities can be removed by an extension of the
spacetime. The result exemplifies that the curvature singularity is not always
a spacetime singularity; in other words, the curvature singularity cannot serve
as a criterion for spacetime singularities
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