https://doi.org/10.1140/epjc/s10052-012-2021-2
Regular Article - Theoretical Physics
Relation between heat kernel method and scattering spectral method
1
Department of Physics, Tianjin University, Tianjin, 300072, P.R. China
2
LiuHui Center for Applied Mathematics, Nankai University & Tianjin University, Tianjin, 300072, P.R. China
* e-mail: xiemi@tju.edu.cn
Received:
31
January
2012
Revised:
28
March
2012
Published online:
31
May
2012
In the present paper, we establish the connection between the heat kernel method and the scattering spectral method in quantum field theory. First, we provide the relation between the heat kernel and the scattering phase shift. Then as applications, we derive a large-time approximation of the heat kernel through the low-energy approximation of the phase shift, and we also derive a high-energy expansion of the phase shift expressed with heat kernel coefficients. Finally, we compare the renormalization schemes in the heat kernel method with that in the scattering spectral method. Concretely, we calculate the first- and second-order contributions to the vacuum energy by heat-kernel and Feynman-diagram methods, respectively, and show the coincidence of the results. Especially, in the heat-kernel framework, we perform both dimensional and zeta-function regularization to calculate the vacuum energy, and the result shows that dimensional renormalization procedure works well in the heat kernel method.
© Springer-Verlag / Società Italiana di Fisica, 2012
