# Velocity, temporal and generalized Kirchhoff gauges

## TL;DR

This paper derives and analyzes the Green's functions for generalized velocity and Kirchhoff gauges in electromagnetics, unifying many gauge choices and showing their relationships in different limits.

## Contribution

It introduces a unified framework for velocity and Kirchhoff gauges, deriving their Green's functions in time and frequency domains, connecting them to classical gauges.

## Key findings

- Green's functions derived for generalized velocity gauge in time domain.
- Green's functions for generalized Kirchhoff gauge in frequency domain.
- Unified framework encompasses most vector/scalar potential gauges.

## Abstract

We derive the dyadic Green's function for the generalized velocity gauge in the time domain with an arbitrary parameter v and show that it reduces to the Lorenz and the Coulomb gauge Green's functions in the limit as v goes to the speed of light c and to infinity, respectively. We also derive the Green's function for the generalized Kirchhoff gauge in the frequency domain and show that it reduces to the results of the Coulomb and the temporal gauges as special cases. Together the generalized velocity and Kirchhoff gauges encompass most gauges in vector/scalar potential form in electromagnetics.