The Quantization of Maxwell Theory in the Cauchy Radiation Gauge: Hodge Decomposition and Hadamard States
arXiv:2401.08403 · doi:10.1112/jlms.70020
Abstract
The aim of this paper is to prove the existence of Hadamard states for the Maxwell equations on any globally hyperbolic spacetime. This will be achieved by introducing a new gauge fixing condition, the Cauchy radiation gauge, that will allow to suppress all the unphysical degrees of freedom. The key ingredient for achieving this gauge is a new Hodge decomposition for differential k-forms in Sobolev spaces on complete (possibly non-compact) Riemannian manifolds.
arXiv comment38 pages -- to appear in J. Lond. Math. Soc
References in corpus (18)
- Renormalized Quantum Yang-Mills Fields in Curved Spacetime
- A Quantum Weak Energy Inequality for Spin-One Fields in Curved Spacetime
- The Necessity of the Hadamard Condition
- Green-hyperbolic operators on globally hyperbolic spacetimes
- Construction of Hadamard states by pseudo-differential calculus
- Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry
- Classical and Quantum Fields on Lorentzian Manifolds
- Linear bosonic and fermionic quantum gauge theories on curved spacetimes
- Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states
- Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times
- Initial value problems for wave equations on manifolds
- Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry
- Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime
- On Wick polynomials of boson fields in locally covariant algebraic QFT
- A new class of Fermionic Projectors: Møller operators and mass oscillation properties
- Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
- The quantization of Proca fields on globally hyperbolic spacetimes: Hadamard states and Møller operators
- Hadamard states for linearized gravity on spacetimes with compact Cauchy surfaces