Mañana, JUEVES, 24 DE ABRIL, el sistema se apagará debido a tareas habituales de mantenimiento a partir de las 9 de la mañana. Lamentamos las molestias.
Quantum foundation of infrared physics
Author
Letschka, Raoul AlexanderAdvisor
Gómez López, CésarEntity
UAM. Departamento de Física Teórica; Instituto de Física Teórica (IFT)Date
2019-12-13Subjects
Radiacion infrarroja - Tesis doctorales; Teoría cuántica de campos - Tesis doctorales; FísicaNote
Tesis doctoral inédita leída Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 13-12-2019Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
In this thesis we will take a look on the infrared (IR) and collinear limit of QED and perturbative
gravity. First we study the infrared regime with its connection to the memory effect
and to the decoherence of density matrices. Lastly, we study the consistency of QED with
massless electrons.
First we investigate the memory effects in scattering processes which are described in
terms of the asymptotic retarded fields. These fields are completely determined by the scattering
data and the zero mode part is set by the soft photon theorem. The dressed asymptotic
states defining an infrared finite S-matrix for charged particles can be defined as quantum
coherent states using the corpuscular resolution of the asymptotic retarded fields. Imposing
that the net radiated energy in the scattering is zero leads to the new set of conservation laws
for the scattering S-matrix which are equivalent to the decoupling of the soft modes. The
actual observability of the memory requires a non-vanishing radiated energy and could be
described using the infrared part of the differential cross section that only depends on the
scattering data and the radiated energy. This is the IR safe cross section with any number
of emitted photons carrying total energy equal to the energy involved in the actual memory
detection.
Secondly, we investigate on possible decoherence of the density matrix in QED or perturbative
gravity due to entanglement with soft radiated modes and use thereby the two standard
approaches to cancel infrared divergences coming from soft loop contributions. In the inclusive
way only rates that include emitted soft radiation are non-vanishing. Independently of
detector resolution, finite observables can only be obtained after integrating over the IRcomponent
of this radiation. This integration can lead to some loss of quantum coherence.
We argue that it should in general not lead to full decoherence. Based on unitarity, we suggest
a way to define non-vanishing off-diagonal pieces of the IR-finite density matrix. For
this IR-finite density matrix, we estimate the dependence of the loss of quantum coherence
i.e. of its purity, on the scattering kinematics. In the coherent state approach we dress the
initial and final states with a cloud of infinite many photons to achieve a not fully decoherent
density matrix. The inclusive way and the coherent state approach both yield the same IRfinite
rates, but we point out that they are not equivalent since they encode different infrared
scales. In particular, dressing states are independent of the resolution scale of radiation.
Instead, they define radiative vacua in the von Neumann space. We present a combined formalism
that can simultaneously describe both dressing and radiation. This unified approach
allows us to tackle the problem of quantum decoherence due to tracing over unresolved radiation.
We again obtain an IR-finite density matrix with non-vanishing off-diagonal elements
and again estimate how its purity depends on scattering kinematics and the resolution scale.
Along the way, we comment on collinear divergences as well as the connection of large
gauge transformations and dressing.
Lastly, we work out in the forward limit and up to order e6 in perturbation theory the
collinear divergences. In this kinematical regime we discover new collinear divergences that
we argue can be only cancelled using quantum interference with processes contributing to
the gauge anomaly. This rules out the possibility of a quantum consistent and anomaly free
theory with massless charges and long range interactions. We use the anomalous threshold
singularities to derive a gravitational lower bound on the mass of the lightest charged
fermion
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