# Questions about the Casimir energy equation

1. Sep 3, 2015

### space-time

I've been studying the Casimir effect and zero point energy recently. In a scholarly article, I came across this formula for the electromagnetic quantum vacuum energy:

E= (i / 2τ) Tr ln Γ where Γ is Green's dyadic that satisfies the equation:

[(1/ω2 * ∇) × (1/μ * ∇) - ε ] Γ

Here is a link to the article where you can see the equation in the beginning of the article:
http://www.worldscientific.com/doi/pdf/10.1142/S2010194512007325

1. First I just want to verify whether or not the term "i" in the equation refers to the imaginary number i or some other variable i. Is this i the square root of -1 or is it something else (and if so what is it)?

2. The article said that τ is the "infinite" time that the configuration exists. What is this "configuration exactly"? I assumed that it was the configuration of the two uncharged conducting parallel plates that is used to invoke the Casimir effect, but I wanted to make sure of this.

3. I assume that the term Γ is a matrix because from what I read in the formula, it seems that you are taking the trace of the natural logarithm of Γ. Is this correct? Are you taking the trace of the natural log of a matrix?

4. What are ω, μ, and ε? Is ε some electric permitivity vector? I assume ε is a vector quantity since it wouldn't make sense to subtract a scalar from a cross product (which is a vector).

Thank you.

2. Sep 7, 2015

### space-time

Sorry to bug people. It's just that it has been multiple days since I posted this and nobody has replied , so I thought I'd just bump up the thread a little to see if anyone may reply now.