Electrodynamic absorber theory

This work deals with questions that arise in classical and quantum electrodynamics when describing the phenomena of radiation reaction and pair creation. The two guiding ideas are the absorber idea of Wheeler and Feynman (i.e. all emitted radiation will be again be absorbed by matter) and the electron sea idea of Dirac. In the first part classical dynamics are studied which allow for a description of radiation reaction without the need of renormalization. The starting point are the coupled Maxwell and Lorentz equations without self-interaction. Based on the notion of absorber medium, it is shown how the so-called Lorentz-Dirac equation for radiation reaction emerges and the intimate connection to the famous Wheeler-Feynman action at a distance electrodynamics is explained. Based on this, the mathematical problem of the existence of solutions to the Wheeler-Feynman theory, which is given by a functional differential equation, is rigorously analyzed. In the second part the phenomenon of pair creation is discussed from a thermodynamic perspective in which the Dirac sea satisfies the absorber condition. Taking Dirac's original idea seriously, the vacuum is to be regarded as an equilibrium state in which all net-electron-electron interactions vanish. Small departures of this equilibrium can be effectively described by introducing pair creation. For the mathematical discussion these seas are considered to consist of infinitely many electrons (in the thermodynamical limit). The mathematical implementation of the quantum mechanical time-evolution for such infinitely many electron seas subject to prescribed external four-vector fields is then carried out in detail. The main result is that the probability amplitudes induced by this time-evolution are well-defined and unique. In a last part we give a perspective on the quantization of Wheeler-Feynman-like inter- action. Based on the proposed equations, a derivation of the Dirac-Barut equation is given, which seems to predict QED corrections in accordance with the experiment

Relationalism about mechanics based on a minimalist ontology of matter

This paper elaborates on relationalism about space and time as motivated by a minimalist ontology of the physical world: there are only matter points that are individuated by the distance relations among them, with these relations changing. We assess two strategies to combine this ontology with physics, using classical mechanics as example: the Humean strategy adopts the standard, non-relationalist physical theories as they stand and interprets their formal apparatus as the means of bookkeeping of the change of the distance relations instead of committing us to additional elements of the ontology. The alternative theory strategy seeks to combine the relationalist ontology with a relationalist physical theory that reproduces the predictions of the standard theory in the domain where these are empirically tested. We show that, as things stand, this strategy cannot be accomplished without compromising a minimalist relationalist ontology

Authors’ Response: the virtues of minimalism in ontology and epistemology

The paper sets out and defends against criticism the claims argued for in the book A minimalist ontology of the natural world

Ground states in the Many Interacting Worlds approach

Recently the Many-Interacting-Worlds (MIW) approach to a quantum theory without wave functions was proposed. This approach leads quite naturally to numerical integrators of the Schr\"odinger equation. It has been suggested that such integrators may feature advantages over fixed-grid methods for higher numbers of degrees of freedom. However, as yet, little is known about concrete MIW models for more than one spatial dimension and/or more than one particle. In this work we develop the MIW approach further to treat arbitrary degrees of freedom, and provide a systematic study of a corresponding numerical implementation for computing one-particle ground and excited states in one dimension, and ground states in two spatial dimensions. With this step towards the treatment of higher degrees of freedom we hope to stimulate their further study.Comment: 16 pages, 8 figure