Relation between heat kernel method and scattering spectral method

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 k...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2012-05, Vol.72 (5), p.1-13, Article 2021
Main Authors: Pang, Hai, Dai, Wu-Sheng, Xie, Mi
Format: Article
Language:English
Subjects:
Approximation
Astronomy
Astrophysics and Cosmology
Elementary Particles
Exact sciences and technology
Field theory
Hadrons
Heavy Ions
Kernels
Mathematical analysis
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Phase shift
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum theory
Regular Article - Theoretical Physics
Regularization
Scattering
Spectra
Spectral methods
String Theory
The physics of elementary particles and fields
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Summary: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.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-012-2021-2