Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I was reading the http://en.wikipedia.org/wiki/Quanti...d#Electromagnetic_field_and_vector_potential" and I am a little bit confused.

In this equation defining the vector potential

[itex]\mathbf{A}(\mathbf{r}, t) = \sum_\mathbf{k}\sum_{\mu=-1,1} \left( \mathbf{e}^{(\mu)}(\mathbf{k}) a^{(\mu)}_\mathbf{k}(t) \, e^{i\mathbf{k}\cdot\mathbf{r}} + \bar{\mathbf{e}}^{(\mu)}(\mathbf{k}) \bar{a}^{(\mu)}_\mathbf{k}(t) \, e^{-i\mathbf{k}\cdot\mathbf{r}} \right)[/itex]

are the [itex]a^{(\mu)}_\mathbf{k}(t)[/itex] and [itex]\bar{a}^{(\mu)}_\mathbf{k}(t)[/itex] complex or real?

On my first reading I assumed complex as the text says the bar indicates complex conjugates but the vector potential is later defined as a linear addition with complex [itex]\mathbf{e}^{(1)}(\mathbf{k})[/itex] and [itex]\mathbf{e}^{(-1)}(\mathbf{k})[/itex] basis vectors so why would these vectors have complex multipliers? They are also not in bold font which would indicate scalers.

Is the bar in this case simply a label for the scaler?

Please help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Fourier components of vector potential

**Physics Forums | Science Articles, Homework Help, Discussion**