# Continuous Transitions Between Quantum and Classical Electrodynamics

## TL;DR

This paper develops a gauge-invariant framework that smoothly transitions between quantum and classical electrodynamics, revealing similarities and differences in energy flow patterns in specific experimental setups.

## Contribution

It introduces an interpolating field theory that models continuous quantum-classical transitions in electrodynamics, extending the understanding of gauge invariance and energy flow.

## Key findings

- Energy flow lines are identical in quantum and classical cases for double-slit experiments.
- Differences in energy flow are observed in vortex beam configurations.
- The theory provides a unified description bridging quantum and classical regimes.

## Abstract

The Maxwell equations in the presence of sources are first derived without making use of the potentials and the Hamilton-Jacobi equation for classical electrodynamics is written down. The manifestly gauge invariant theory is then quantized to write down the Hamilton-Jacobi equation in quantum electrodynamics. Finally, an interpolating field theory is proposed that describes continuous transitions between quantum and classical electrodynamics. It is shown that energy flow lines are identical for quantum and classical fields in the case of the double-slit arrangement but differ in the case of vortex beams.