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MathGroup Archive 2003

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Re: Functional differentiation on the lattice

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39824] Re: Functional differentiation on the lattice
  • From: Rolf Mertig <rolf at mertig.com>
  • Date: Sat, 8 Mar 2003 02:48:13 -0500 (EST)
  • Organization: Mertig Consulting
  • Reply-to: rolf at mertig.com
  • Sender: owner-wri-mathgroup at wolfram.com

Hi there,
Hi,
for the continuum case I once programmed this, see:
http://www.feyncalc.org/FeynCalcBook/FunctionalD/
http://www.feyncalc.org/FeynCalcBook/FeynRule/

You may have to modify it for lattice calculations.
Just download FeynCalc, look at the source and adapt it 
to your needs (and contribute if you want).

Regards,

Rolf Mertig
Mertig Consulting
http://www.mertig.com


================
I've just recently decided that the maths I have to do at the moment really
demand the use of a CAS. I'm absolutely new to Mathematica, but the problem
I have is probably a bit hard to get moving on. Perhaps someone can give me
a simple solution to start out on?

What I need to do could probably be called a "Functional differentiation on
a lattice". To give one very simply example:

I have the functional

        S[A] := sum_x (A(x+1)-A(x))^2

(where x is integer - in my case there are periodic boundaries, but that
does not matter at that point)

now I want to calculate

        dS/dA(y)

which should result in

        - 2(A(y+1)-A(y)) + 2(A(y)-A(y-1))

or simplified

        -2A(y+1) + 4A(y) - 2A(y-1)

Lateron, the whole thing will get 4-dimensional and A will get indices that
will be summed over as well.

Is there a simple way to do that in Mathematica? I would really appreciate a
piece of code to get me started on.

Thanks,
Nobbi




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