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From: Viktor T. T. <vt...@vt...> - 2017-01-10 02:26:59
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Dear Dimiter,
If L is a general field Lagrangian, all you know is that
T_{\mu\nu} = -2/\sqrt{-g} \partial (L\sqrt{-g})/\partial g^{\mu\nu}.
That's all you know. To work out T_{\mu\nu}, some specific form of L must be given.
The itensor package has the ability to compute functional derivatives with respect to fields, including g^{\mu\nu}. But depending on the specific form of the Lagrangian, it may take quite an effort to set up the problem and simplification rules in order to obtain a meaningful result.
Viktor
> -----Original Message-----
> From: Dimiter Prodanov [mailto:dim...@gm...]
> Sent: Monday, January 9, 2017 4:25 AM
> To: Viktor T. Toth <vt...@vt...>
> Cc: max...@li...
> Subject: Re: [Maxima-discuss] energy-momentum tensor
>
> Hi Viktor,
>
> Actually, I have in mind a general field lagrangian.
> So starting from an input lagrangian to compute the energy-momentum tensor according to the noether theorem.
>
> best regards,
>
> Dimiter
>
> On Mon, Jan 9, 2017 at 7:39 AM, Viktor T. Toth <vt...@vt... <mailto:vt...@vt...> > wrote:
>
>
> Dear Dimiter,
>
> No, I do not. The canonical energy-momentum depends on whatever fields we are dealing with. I am assuming
> that you have in mind the electromagnetic field and its energy-momentum tensor? In itensor, it would be something
> like
>
> load(itensor);
> imetric(g);
> igeowedge_flag:true;
> components(F([i,j]),extdiff(A([i],[]),j));
> components(F([i,-k],[]), g([-j,-k])*F([i,j]));
> components(F([-l,-k],[]),g([-i,-l])*F([i,-k]));
> components(T([-m,-n]),F([-m,-a])*F([-n,a])-1/4*g([-m,-n])*F([a,b])*F([-a,-b]));
> ishow(T([-m,-n]))$
>
> (Note the use of the negative sign for contravariant indices; this notation was implemented specifically to
> ensure that index ordering is preserved when indices are raised/lowered, as in this case.)
>
>
> Viktor
>
>
>
>
>
>
> > -----Original Message-----
> > From: Dimiter Prodanov [mailto:dim...@gm... <mailto:dim...@gm...> ]
> > Sent: Friday, January 6, 2017 11:45 AM
> > To: max...@li... <mailto:max...@li...>
> > Subject: [Maxima-discuss] energy-momentum tensor
> >
> > Dear Viktor,
> >
> > do you have code for compuation of the canonical energy-momentum tensor?
> > I would like to implement it in clifford so I want to compare it with reference implementation.
> >
> > best regards,
> >
> > Dimiter
>
>
>
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