IR dynamics and entanglement entropy

Abstract

We consider scattering of Faddeev-Kulish electrons in QED and study the entanglement between the hard and soft particles in the final state at the perturbative level. The soft photon spectrum naturally splits into two parts: i) soft photons with energies less than a characteristic infrared scale $E_d$ present in the clouds accompanying the asymptotic charged particles, and ii) sufficiently low energy photons with energies greater than $E_d$, comprising the soft part of the emitted radiation. We construct the density matrix associated with tracing over the radiative soft photons and calculate the entanglement entropy perturbatively. We find that the entanglement entropy is free of any infrared divergences order by order in perturbation theory. On the other hand infrared divergences in the perturbative expansion for the entanglement entropy appear upon tracing over the entire spectrum of soft photons, including those in the clouds. To leading order the entanglement entropy is set by the square of the Fock basis amplitude for real single soft photon emission, which leads to a logarithmic infrared divergence when integrated over the photon momentum. We argue that the infrared divergences in the entanglement entropy (per particle flux per unit time) in this latter case persist to all orders in perturbation theory in the infinite volume limit.

arXiv comment33 pages, added references and discussions; accepted in Physical Review D; added clarification, corrected typos

References in corpus (44)

• Soft Hair on Black Holes
• On BMS Invariance of Gravitational Scattering
• BMS supertranslations and Weinberg's soft graviton theorem
• New Symmetries of Massless QED
• Holographic Entanglement Entropy
• Entanglement entropy, conformal invariance and extrinsic geometry
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• Low's Subleading Soft Theorem as a Symmetry of QED
• Infrared Factorization, Wilson Lines and the Heavy Quark Limit
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Entanglement entropy in de Sitter space
• Momentum-space entanglement and renormalization in quantum field theory
• Infrared Divergences in QED, Revisited
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• Shaving off Black Hole Soft Hair
• More on Soft Theorems: Trees, Loops and Strings
• The cusp anomalous dimension at three loops and beyond
• Soft Hair as a Soft Wig
• Entanglement Entropy of Scattering Particles
• Large Gauge Symmetries and Asymptotic States in QED
• Asymptotic symmetries of gravity and soft theorems for massive particles
• Infrared quantum information
• BMS Supertranslation Symmetry Implies Faddeev-Kulish Amplitudes
• Variation of Entanglement Entropy in Scattering Process
• Evaluation of Entanglement Entropy in High Energy Elastic Scattering
• On the need for soft dressing
• Dressed infrared quantum information
• Comments on Lorentz Transformations, Dressed Asymptotic States and Hawking Radiation
• Subleading soft dressings of asymptotic states in QED and perturbative quantum gravity
• The Super BMS Algebra, Scattering and Holography
• Holographic Space-time and Black Holes: Mirages As Alternate Reality
• Dressed states from gauge invariance
• Scattering and momentum space entanglement
• Equations of Motion as Constraints: Superselection Rules, Ward Identities
• Infrared Divergences and Quantum Coherence
• Holographic Theory of Accelerated Observers, the S-matrix, and the Emergence of Effective Field Theory
• The Scales of the Infrared
• Holographic Space-time, Newton's Law and the Dynamics of Black Holes
• Scattering with partial information
• On the logarithmic divergent part of entanglement entropy, smooth versus singular regions
• Entangled Scent of a Charge
• Graviton Emission and Loss of Coherence
• The Temperature/Entropy Connection for Horizons, Massless Particle Scattering, and the Origin of Locality

Cited by in corpus (13)

• In-in formalism for the entropy of quantum fields in curved spacetimes
• Entanglement and scattering in quantum electrodynamics: S-matrix information from an entangled spectator particle
• Infrared acceleration radiation
• Black hole evolution in quantum-gravitational framework
• Infrared dressing in real time: emergence of anomalous dimensions
• Larmor Temperature, Casimir Dynamics, and Planck's Law
• Some measures for fermionic entanglement in the cosmological de Sitter spacetime
• Dress code for infrared safe scattering in QED
• Soft photon radiation and entanglement
• Ultralight dark matter or dark radiation cosmologically produced from infrared dressing
• On the infrared divergence and global colour in N=4 Yang-Mills theory
• Threshold and infrared singularities: time evolution, asymptotic state and entanglement entropy
• Subleading soft radiation during scattering of dressed states in QED