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Mar
30
revised What is the problem with quantizing GR in the Effective Field Theory approach?
Fixed grammatical error
Mar
30
suggested approved edit on What is the problem with quantizing GR in the Effective Field Theory approach?
Mar
29
comment Implementing Category Theory in General Relativity
Well, one problem is how do you even model GR category-theoretically? The category of smooth manifolds is not nice (hence the fascination with diffeological spaces --- because they do form a "good" category). Or do we model it as a gauge theory with beins as the field? Or are the connections the field? How do you categorify either one? These are nontrivial problems...
Feb
24
comment GR Tetrads & ZAMO example
One's the "inverse" of the other (if we pretend they're both square matrices), recall ${e^{\mu}}_{m}{e^{\nu}}_{n}g_{\mu\nu}=\eta_{mn}$, then ${e^{\mu}}_{m}{e^{m}}_{\nu}=\delta^{\mu}_{\nu}$.
Jan
28
comment The cosmological constant as a Lagrange multiplier?
One might be interested in perusing Appendix X.7 in Zee's Einstein Gravity in a Nutshell which cites arXiv:gr-qc/0505104 and arXiv:0711.3170.
Jan
2
answered Is causality a total order?
Nov
19
answered Can a neutron decay to the gravitons?
Nov
3
revised Simple QFT simulation - how to do it
Improved TeX formatting
Nov
3
suggested approved edit on Simple QFT simulation - how to do it
Oct
27
revised Deriving the Poisson bracket relation of the Ashtekar variables
added 706 characters in body
Oct
22
comment Deriving the Poisson bracket relation of the Ashtekar variables
But look, the only reason you have the symmetry problem is because you arbitrarily introduced it into Eq (3). If you instead rewrite it as $\gamma_{ab} = {e_{a}}^{i}{e_{b}}^{j}\delta_{ij}$ without explicitly symmetrizing the RHS, you're golden. (Your reasoning and counter-example is quite excellent, though.)
Oct
22
comment Deriving the Poisson bracket relation of the Ashtekar variables
no, look at Eq (4), it should read $\delta^{a}_{(c}\delta^{b}_{d)} = \partial\gamma_{cd}/\partial\gamma_{ab}$, which fixes your problem.
Oct
21
comment Deriving the Poisson bracket relation of the Ashtekar variables
You didn't symmetrize the LHS of Eq (4), which leads to the discrepency. If you match the downstairs indices, you end up with (10) and hence (13).
Oct
20
comment Deriving the Poisson bracket relation of the Ashtekar variables
@thenumbernine It's just the product rule: $\delta_{jk}({e_{c}}^{j} (\partial {e_{d}}^{k}/\partial_{ab}) + {e_{d}}^{k} (\partial {e_{c}}^{j}/\partial_{ab}))$, then set it equal to $\delta^{(a}_{c}\delta^{b)}_{d}$, and you're done.
Oct
20
answered Deriving the Poisson bracket relation of the Ashtekar variables
Oct
20
revised Deriving the Poisson bracket relation of the Ashtekar variables
Improved the TeX
Oct
20
suggested approved edit on Deriving the Poisson bracket relation of the Ashtekar variables
Oct
14
revised Lagrangian isn't unique
Improved the TeX formatting
Oct
14
suggested approved edit on Lagrangian isn't unique
Oct
11
answered What is meant by a “c-number”?