Derivative expansions

[fetchinson]

This is more like a support question than any coding issue.

I'm guessing FORM could be used for various derivative expansions like the heat kernel expansion of the covariant Laplacian. In this case one expands the heat kernel with the covariant Laplacian around the free Laplacian heat kernel and one gets increasingly complicated expressions in the field strength tensor organized as a polynomial.

Are there example packages using FORM where something like this is done? One would need identities involving derivatives, several derivatives in several variables, non-commuting nature of the field strength, etc.

Any ideas would be greatly appreciated, my problem seems to be that the name FORM is not very googleable :)

[vermaseren]

From what you describe, it should be very doable in Form, but I am sure there are more details, and I do not know anything about heat kernel expansions. You could pm me with some more details/information. If it looks possible, I could help you set up such a program.

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On 8 Oct 2025, at 22:33, Daniel Fetchinson ***@***.***> wrote: fetchinson created an issue (form-dev/form#728) <#728> This is more like a support question than any coding issue. I'm guessing FORM could be used for various derivative expansions like the heat kernel expansion of the covariant Laplacian. In this case one expands the heat kernel with the covariant Laplacian around the free Laplacian heat kernel and one gets increasingly complicated expressions in the field strength tensor organized as a polynomial. Are there example packages using FORM where something like this is done? One would need identities involving derivatives, several derivatives in several variables, non-commuting nature of the field strength, etc. Any ideas would be greatly appreciated, my problem seems to be that the name FORM is not very googleable :) — Reply to this email directly, view it on GitHub <#728>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABJPCEVIJDWQ4BUZJ5GXWI33WVYI5AVCNFSM6AAAAACIVHOKQGVHI2DSMVQWIX3LMV43ASLTON2WKOZTGQ4TMOBQHE2DGMI>. You are receiving this because you are subscribed to this thread.

[reinle]

This is more like a support question than any coding issue.

I'm guessing FORM could be used for various derivative expansions like the heat kernel expansion of the covariant Laplacian. In this case one expands the heat kernel with the covariant Laplacian around the free Laplacian heat kernel and one gets increasingly complicated expressions in the field strength tensor organized as a polynomial.

Are there example packages using FORM where something like this is done? One would need identities involving derivatives, several derivatives in several variables, non-commuting nature of the field strength, etc.

Any ideas would be greatly appreciated, my problem seems to be that the name FORM is not very googleable :)

I'm also implementing some covariant derivative expansion method and I guess I've reached the limit of mathematica, have you started doing something in FORM ? Would be nice to get in touch to help each other. Have a nice day