- #1

dkin

- 5

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Hi all,

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!

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!

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