https://doi.org/10.1140/epjc/s10052-015-3512-8
Regular Article - Theoretical Physics
Heat-kernel approach for scattering
1
Department of Physics, Tianjin University, Tianjin, 300072, People’s Republic of China
2
LiuHui Center for Applied Mathematics, Nankai University and Tianjin University, Tianjin, 300072, People’s Republic of China
* e-mail: daiwusheng@tju.edu.cn
Received:
31
March
2015
Accepted:
8
June
2015
Published online:
27
June
2015
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 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.
© The Author(s), 2015
