# Causality in the Classical Limit for Quantum Electrodynamics

Causality in the Classical Limit for Quantum Electrodynamics We use the path integral form of quantum electrodynamics (QED) to show that a causal classical limit to QED can be derived by functionally integrating over the photon coordinates, starting from an initial photon vacuum and ending in a final coherent radiation state driven by the anticipated classical charged particle trajectories. The resulting charged particle transition amplitude depends only on particle coordinates. When the $${\hbar} \, \to \,0$$ ħ → 0 limit is taken, only those particle paths that are not constrained by the final radiation state are varied. These results demonstrate that the collapse from an infinity of charged particle paths, a path integral description, to causally interacting classical trajectories, a stationary-action description, is critically dependent on including final coherent state radiation and maintaining the distinction between particle paths that are free to vary and those trajectories that can be monitored by the final state radiation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Foundations of Physics Springer Journals

# Causality in the Classical Limit for Quantum Electrodynamics

, Volume 48 (6) – Mar 22, 2018
8 pages

/lp/springer_journal/causality-in-the-classical-limit-for-quantum-electrodynamics-Px0Mvl9gL8
Publisher
Springer US
Subject
Physics; History and Philosophical Foundations of Physics; Quantum Physics; Classical and Quantum Gravitation, Relativity Theory; Statistical Physics and Dynamical Systems; Classical Mechanics; Philosophy of Science
ISSN
0015-9018
eISSN
1572-9516
D.O.I.
10.1007/s10701-018-0158-z
Publisher site
See Article on Publisher Site

### Abstract

We use the path integral form of quantum electrodynamics (QED) to show that a causal classical limit to QED can be derived by functionally integrating over the photon coordinates, starting from an initial photon vacuum and ending in a final coherent radiation state driven by the anticipated classical charged particle trajectories. The resulting charged particle transition amplitude depends only on particle coordinates. When the $${\hbar} \, \to \,0$$ ħ → 0 limit is taken, only those particle paths that are not constrained by the final radiation state are varied. These results demonstrate that the collapse from an infinity of charged particle paths, a path integral description, to causally interacting classical trajectories, a stationary-action description, is critically dependent on including final coherent state radiation and maintaining the distinction between particle paths that are free to vary and those trajectories that can be monitored by the final state radiation.

### Journal

Foundations of PhysicsSpringer Journals

Published: Mar 22, 2018

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