Asymptotic structure of the Pauli-Fierz theory in four spacetime dimensions

Abstract

The asymptotic structure of the Pauli-Fierz theory at spatial infinity is investigated in four spacetime dimensions. Boundary conditions on the massless spin-$2$ field that are invariant under an infinite-dimensional group of non-trivial ``improper'' gauge symmetries are given. The compatibility of these boundary conditions with invariance of the theory under Lorentz boosts is a subtle issue which is investigated in depth and leads to the identification of the improper gauge symmetries with the pure BMS supertranslations. It is also shown how rigid Poincaré transformations and improper gauge symmetries of the free Pauli-Fierz theory merge into the full BMS group as one switches on the gravitational coupling. Contrary to the massless spin-$1$ case, where invariance under boosts is implemented differently and where important differences between the free and the interacting cases have been exhibited recently, the free Pauli-Fierz theory and general relativity show very similar behaviours at spatial infinity.

arXiv comment36 pages

References in corpus (23)

• Aspects of the BMS/CFT correspondence
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• New Symmetries of Massless QED
• Asymptotic Symmetries of Yang-Mills Theory
• Low's Subleading Soft Theorem as a Symmetry of QED
• Holographic Renormalization of Asymptotically Flat Spacetimes
• Bondi-Sachs Formalism
• The $\Lambda$-BMS${}_4$ Charge Algebra
• The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$
• Subleading soft photons and large gauge transformations
• BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
• BMS Supertranslations and Not So Soft Gravitons
• Null infinity, the BMS group and infrared issues
• Einstein-Yang-Mills theory : I. Asymptotic symmetries
• Asymptotic $U(1)$ charges at spatial infinity
• The BMS4 algebra at spatial infinity
• Asymptotic symmetries of electromagnetism at spatial infinity
• Remarks on Asymptotic Symmetries and the Sub-leading Soft Photon Theorem
• Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity
• Relaxing the Parity Conditions of Asymptotically Flat Gravity
• On higher-spin supertranslations and superrotations
• BMS4 Algebra, Its Stability and Deformations
• Asymptotic symmetries of Yang-Mills fields in Hamiltonian formulation

Cited by in corpus (7)

• Logarithmic supertranslations and supertranslation-invariant Lorentz charges
• Local supersymmetry and the square roots of Bondi-Metzner-Sachs supertranslations
• The (super)conformal BMS${}_3$ algebra
• Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis
• Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity
• BMS algebra as an extension of the Poincaré symmetry in light-cone gravity
• Conserved asymptotic charges for any massless particle