Welcome to my page on using the techniques usually associated with perturbative (quantum) field theory -- see here and here -- to calculate general relativistic corrections to the Newtonian gravitational lagrangian for point masses.
Update Dec 2011: I have written the Mathematica package TensoriaCalc to compute geometric tensors - Riemann, Ricci, Christoffel symbols, etc. - within a Riemannian geometry framework. This is closely related to a parallel effort of mine to write a package that can manipulate abstract tensors in physicists' index notation. (I already have a beta version of TensoriaLite, which reproduces some of the tensor contraction capabilities of FeynCalc, including the computation of the N-graviton Feynman rules for the Einstein-Hilbert lagrangian.) Stay tuned!
Motivation To measure gravitational waves produced by binary black holes and/or neutron stars as they spiral towards each other, gravitational wave observatories such as GEO, LIGO, TAMA, and VIRGO need the effective lagrangian of 2 point masses up to 3 PN and beyond: O[(v/c)6], and higher, relative to Newtonian gravity, where v is the typical speed of the binaries in its center of energy frame and c is the speed of light. The effective lagrangian is used to construct theoretical templates so that the raw data can be compared against them to see if there is significant enough correlation to claim detection; see Blanchet for a review. For now, I am focusing on the integer PN order, conservative portion of the dynamics.
On the other hand, experiments such as APOLLO, GTDM, LATOR, BEACON, etc. are beginning to probe the non-Euclidean nature of the solar system's geometry beyond the currently well tested O[(v/c)2], by measuring the timing and deflection of light propagation within the solar system to higher accuracy than before. Knowing the geometry of the solar system at a theoretical level amounts to knowing the effective lagrangian for n point masses, and vice versa.
In view of the gravitational wave detection efforts, because the calculation at such a high order is very arduous, it is imperative that the necessary software be developed to automate the computation as far as possible.
Code for post Newtonian diagrams, related toolsThis section contains the code I used to compute the n-body effective lagrangian up to O[(v/c)4]. Please do let me know if you find errors / bugs.
Update 28 Jan 2009: I have added in the 0 thru 2 PN Mathematica notebooks some description for FeynD, the notation used to represent Feynman diagrams.
Future developmentsTo push our knowledge of binary dynamics beyond the currently known 3.5 PN, O[(v/c)7], using field theory, the first steps to take would be to improve the efficiency of the codes in IntegerPN_FullyConnectedDiagrams.nb and EinsteinHilbertLagrangianFeynmanRules_LinearizeddeDonderGauge.nb.