Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation

Abstract

The present paper addresses open questions regarding the handling of the spin supplementary condition within the effective field theory approach to the post-Newtonian approximation. In particular it is shown how the covariant spin supplementary condition can be eliminated at the level of the potential (which is subtle in various respects) and how the dynamics can be cast into a fully reduced Hamiltonian form. Two different methods are used and compared, one based on the well-known Dirac bracket and the other based on an action principle. It is discussed how the latter approach can be used to improve the Feynman rules by formulating them in terms of reduced canonical spin variables.

arXiv comment42 pages, document changed to match published version, in press; Ann. Phys. (N. Y.) (2012)

References in corpus (42)

• The Dynamics of General Relativity
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• An Effective Field Theory of Gravity for Extended Objects
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Gravitational waves from inspiraling compact binaries: The quadrupole-moment term
• An improved effective-one-body Hamiltonian for spinning black-hole binaries
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Next to Leading Order Spin(1)Spin(1) Effects in the Motion of Inspiralling Compact Binaries
• Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
• Spin(1)Spin(2) Effects in the Motion of Inspiralling Compact Binaries at Third Order in the Post-Newtonian Expansion
• Hamiltonian of a spinning test-particle in curved spacetime
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order
• Next to leading order spin-orbit effects in the motion of inspiralling compact binaries
• Effective field theory calculation of conservative binary dynamics at third post-Newtonian order
• Effective field theory calculation of second post-Newtonian binary dynamics
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order
• Spin-squared Hamiltonian of next-to-leading order gravitational interaction
• Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction
• The next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form
• Non-Relativistic Gravitation: From Newton to Einstein and Back
• ADM canonical formalism for gravitating spinning objects
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• Effective one body Hamiltonian of two spinning black-holes with next-to-next-to-leading order spin-orbit coupling
• Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance
• Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates
• Canonical Formulation of Spin in General Relativity
• Equations of Motion for Spinning Particles in External\\Electromagnetic and Gravitational Fields
• Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
• Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries
• Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries
• The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theory
• Canonical formulation of self-gravitating spinning-object systems
• Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for n gravitating spinning compact objects
• Canonical formulation of gravitating spinning objects at 3.5 post-Newtonian order
• Dressing the Post-Newtonian two-body problem and Classical Effective Field Theory
• Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction
• Leading-order spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians
• Subleading Spin-Orbit Correction to the Newtonian Potential in Effective Field Theory Formalism
• Rosenfeld, Bergmann, Dirac and the Invention of Constrained Hamiltonian Dynamics

Cited by in corpus (17)

• Amplitudes, Observables, and Classical Scattering
• The Effective Field Theorist's Approach to Gravitational Dynamics
• Spinning gravitating objects in the effective field theory in the post-Newtonian scheme
• Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order
• Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
• Influence of internal structure on the motion of test bodies in extreme mass ratio situations
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Spacetime dynamics of spinning particles - exact electromagnetic analogies
• Spin supplementary conditions for spinning compact binaries
• Fourth post-Newtonian effective-one-body Hamiltonians with generic spins
• On the comparison of results regarding the post-Newtonian approximate treatment of the dynamics of extended spinning compact binaries
• Spin gauge symmetry in the action principle for classical relativistic particles
• Canonical Angles In A Compact Binary Star System With Spinning Components: Approximative Solution Through Next-To-Leading-Order Spin-Orbit Interaction for Circular Orbits
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole