# Generalized Abraham Forces on Molecules: from classical to quantum

## TL;DR

This paper revises the classical and quantum formulations of Abraham forces on molecules, highlighting the inaccuracies of the standard derivative approach and exploring new manifestations and quantum descriptions of these forces.

## Contribution

It introduces a corrected classical framework for Abraham forces considering induced-dipole effects and provides a quantum perspective applicable to complex molecules.

## Key findings

- Standard Abraham force derivative is generally incorrect due to induced-dipole contributions.
- Multiple manifestations of Abraham forces and torques are identified, some violating dual symmetry.
- Quantum description of Abraham forces is developed, enabling future studies on molecules with spin and quantum vacuum effects.

## Abstract

Abraham forces are defined as electromagnetic forces on neutral objects caused by the presence of slow, time-dependent, homogeneous electromagnetic fields. Only a few experimental observations have been reported, and different formulations exist in literature. The ``standard" Abraham force is usually associated with the full derivative $\partial_t(\mathbf{E} \times \mathbf{B})$ of homogeneous electric and magnetic fields. We show that this full derivative is wrong in general, since the classical Maxwell theory contains subtle induced-dipole forces that contribute to the Abraham force, which thus breaks the dual symmetry between electric and magnetic components. We investigate other manifestations of Abraham forces and torques and estimate orders of magnitude, e.g related to chiral, moving or rotating matter. Some of them are also severely violating dual symmetry. We provide a quantum description of the Abraham force. Apart from being more elegant and less technical, this quantum treatment paves the way for future studies of Abraham forces on complex molecules involving spin and spin-orbit coupling, and also facilitates the inclusion of the quantum vacuum.