English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Transport equation approach to calculations of Hadamard Green functions and non-coincident DeWitt coefficients

MPS-Authors
/persons/resource/persons2711

Wardell,  Barry
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)

0906.0005
(Preprint), 2MB

PRD84_104039.pdf
(Any fulltext), 3MB

Supplementary Material (public)
There is no public supplementary material available
Citation

Ottewill, A. C., & Wardell, B. (2011). Transport equation approach to calculations of Hadamard Green functions and non-coincident DeWitt coefficients. Physical Review D, 84(10): 104039. doi:10.1103/PhysRevD.84.104039.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-013B-6
Abstract
Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental bi-tensors, including derivatives of the world-function, \sigma(x,x'), the square root of the Van Vleck determinant, \Delta^{1/2}(x,x'), and the tail-term, V(x,x'), appearing in the Hadamard form of the Green function. These bi-tensors are central to a broad range of problems from radiation reaction to quantum field theory in curved spacetime and quantum gravity. Their transport equations may be used either in a semi-recursive approach to determining their covariant Taylor series expansions, or as the basis of numerical calculations. To illustrate the power of the semi-recursive approach, we present an implementation in \textsl{Mathematica} which computes very high order covariant series expansions of these objects. Using this code, a moderate laptop can, for example, calculate the coincidence limit a_7(x,x) and V(x,x') to order (\sigma^a)^{20} in a matter of minutes. Results may be output in either a compact notation or in xTensor form. In a second application of the approach, we present a scheme for numerically integrating the transport equations as a system of coupled ordinary differential equations. As an example application of the scheme, we integrate along null geodesics to solve for V(x,x') in Nariai and Schwarzschild spacetimes.