Spin supplementary condition in quantum field theory: covariant SSC and physical state projection

Abstract

The spin supplementary conditions are constraints on spin degrees of freedom in classical relativity which restricts physical degrees of freedom to rotations. It is argued that the equivalent constraints in quantum field theory are the projection conditions on polarisation tensors, which remove timelike/longitudinal polarisations from the physical spectrum. The claim is supported by three examples of massive spinning particles coupled to electromagnetism: Dirac and Proca fields in quantum field theory, and $\mathcal{N}=1$ worldline QFT for classical worldline theory. This suggests a resolution to the apparent discrepancy between effective field theory description of massive higher-spin fields~\cite{Bern:2020buy,Bern:2022kto} and post-Newtonian effective field theory of spinning classical particles~\cite{Levi:2015msa}, where the former admits more unfixed parameters compared to the latter; the additional parameters are fixed by projection conditions and therefore are not tunable parameters.

version accepted to JHEP; title modified; footnote 1 on spin tensor definitions with boost-subtraction added; appendix D on classical EOM derivation from WQFT added; references added; 27 pages

References in corpus (23)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order
• Effective field theory calculation of second post-Newtonian binary dynamics
• Static two-body potential at fifth post-Newtonian order
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Canonical Formulation of Spin in General Relativity
• Classical observables from coherent-spin amplitudes
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Completing the Fifth PN Precision Frontier via the EFT of Spinning Gravitating Objects
• A note on the absence of $R^2$ corrections to Newton's potential
• Light bending from eikonal in worldline quantum field theory
• N${}^3$LO Quadratic-in-Spin Interactions for Generic Compact Binaries
• N${}^3$LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects
• Classical Double Copy of Spinning Worldline Quantum Field Theory
• Factorization in Graviton Scattering and the "Natural" Value of the g-factor

Cited by in corpus (3)

• Observables from the Spinning Eikonal
• Massive twistor worldline in electromagnetic fields
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes