[newbie] Scalar field's eq. of motion (itensor)

It just occurred to me that since you're using a flat metric, using covdiff
is unnecessary overkill. A simpler solution is to tell Maxima that the
metric is constant, and to use indicial differentiation instead of covdiff:

load("itensor")$
imetric(g)$
declare(g,constant)$
ishow(L:-g([-u,-v],[])*idiff(S([],[]),u)*idiff(S([],[]),v)-m^2*S([],[])^2)$
ishow(rename(contract(diff(L,S([],[]))-idiff(diff(L,idiff(S([],[]),l)),l))))
$

By the way, if you are using covdiff, I recommend (for now) using
g([],[u,v]) instead of g([-u,-v],[]). Since the metric tensor is symmetric,
it makes no difference mathematically, but as I just discovered, there are
some bugs when the "new" notation for contravariant indices is combined with
covariant differentiation. (Ideally, itensor should be able to deal with
contravariant ordinary derivatives, but it can't; however, some of the code
produces contravariant derivatives, which lead to errors.)


Viktor



-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Viktor T. Toth
Sent: Tuesday, December 09, 2008 12:08 AM
To: 'Victor Stabile'; maxima at math.utexas.edu
Subject: Re: [Maxima] [newbie] Scalar field's eq. of motion (itensor)

Try this:

load("itensor")$
imetric(g)$
ishow(L:-g([-u,-v],[])*covdiff(S([],[]),u)*covdiff(S([],[]),v)-m^2*S([],[])^
2)$
ishow( diff(L,S([],[])) - covdiff( diff(L, covdiff(S([],[]),l) ),l ) )$
%,ichr2$
flushd(%,g)$
ishow(rename(contract(%)))$


The fifth line evaluates ichr2 in terms of the metric; the sixth line
eliminates all terms that include (ordinary) derivatives of the metric; and
finally, the last line contracts and displays the result.


Viktor
 

-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Victor Stabile
Sent: Monday, December 08, 2008 9:12 PM
To: maxima at math.utexas.edu
Subject: [newbie] Scalar field's eq. of motion (itensor)

Hi,
 
I want to calculate the free real scalar field's equation of motion (flat
space-time), so I go like:
 
load("itensor")
imetric(g)
ishow(L:-g([-u,-v],[])*covdiff(S([],[]),u)*covdiff(S([],[]),v)-m^2*S([],[])^
2)$
ishow( diff(L,S([],[])) - covdiff( diff(L, covdiff(S([],[]),l) ),l ) )$
 
Now the problem: covdiff is differentiating the metric. How can I avoid
that?
 
Thanks
 
Victor


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