Removing terms of a definite order?

[NotoGrav]

Hello Folks,

Here is attached a file where I am trying to implement perturbation for a Lagrangian.

In the last term Lflat1, how can I get rid of all the terms which have order of h^3 (h, PD[h], PD[PD[h]] all permutations combined). I would like to keep ONLY the terms of combined order of h^2.

Thanks in advance.

[Thomas Bäckdahl]

Hi!

I suppose you mean powers of h, regardless of perturbation order.
For that I would do something like
DefConstantSymbol[\[Sigma]]
Coefficient[Series[Lflat1 /. gpert[args__] :> \[Sigma]*gpert[args], {\[Sigma], 0, 2}], \[Sigma], 2]

This idea is easily to adapt to other situations where you want to collect or extract terms with a specific total power defined multiplicatively.

By the way, I would write Sqrt[Scalar[g[-a, -b] v[a] v[b]]] instead of Sqrt[g[-a, -b] v[a] v[b]].

Regards
Thomas

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[Mehbub Khan]

Hello Thomas,

Thanks for your helpful feedback. I have two related questions.

1. Following what you mentioned, after doing so can I do the same to collect the terms which include h(1) terms ONLY?

2. In my expression for Lflat1, I am seeing Minkowski metric eta to be in two forms, one with the imaginary i, the other just eta.

Can you comment on whether I made any error while converting the general metric to eta metric?

Your feedback would be highly appreciated.

 

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