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For questions where the dynamical variables are fields, that is, functions of several variables (typically, one time coordinate and several space coordinates). Comprises both classical field theory and quantum field theory. Use this tag when the question applies to both classical and quantum phenomena. Otherwise, use the specific tag instead.

2 votes
1 answer
55 views

How to calculate the Hodge dual of a two-form defined in self-dual BF theory?

I am trying to calculate the Hodge dual of the two form \begin{align}\Sigma^i=e^0\wedge e^i+\epsilon^i{}_{jk}e^j\wedge e^k,\quad (i,j,k \in \{1,2,3\}),\end{align} where Hodge dual with respect to inte …
mortimer's user avatar
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How to calculate the Hodge dual of a two-form defined in self-dual BF theory?

I found the solution thanks to the comments. There seems to be a factor of $\frac{1}{2}$ missing from the second term in the reference as well. Adding this factor will resolve the issue. \begin{align} …
mortimer's user avatar
2 votes
1 answer
113 views

What is the Lie derivative of Ashtekar connection and its conjugate momentum in LQG?

I am using the reference Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons for this question. I am trying to understand the two equations (30) that give the variation …
mortimer's user avatar