P-forms

[sanctus]

In my general relativity course I'm following there is heaps of differential geometry...

 

My question is are the so-called p-forms (p any positive integer) just applications from R^p to R p linear in every coordinate?

[Qfwfq]

No, a p-form takes p vectors as arguments and, I seem to remember (sheeeeeeesh 'twas a good while ago!) it is by definition antisymmetric for exchange of any two of them:

 

[math]F(v_1, v_2, v_3, v_4...) = -F(v_1, v_3, v_2, v_4...)[/math]

 

Therefore, if your manifold is n dimensional (4, perhaps?) then you could say it's like a function [math]\norm f:\, \Re^{np} \rightarrow\, \Re[/math]

[sanctus]

Thanks Qfwfq,

 

I was tempted to already say this phrase above in the first post because usually it's always you who answers this questions...:)

Don't get me wrong, I really appreciate it

[Alon]

sanctus, can i gather that youre at graduate physics level right now? (cause GR is usually a course given in graduate studies).

[Qfwfq]

Your welcome Sanctus.

 

Well, Alon, it has been creeping "downward" if you know what I mean. When I took it, yes, it was a Ph. D. course shared with the degree ones so I was able to choose it as a fourth year course. Another such course I took was field theory based on functional methods and including QCD, the recomended textbook was Ramond.

 

In past decades quantum mechanics was "usually" a Ph. D. course but it has long been compulsory in the third year, just like special relativity.

[Alon]

nowadays SR, is the first course with classical mechanics in your first year in physics.

i take physics and maths in my uni, but for those who take only physics can choose to take intro to general realtivity, i guess it just covers tidbit of this extraordinary theory, ill try squeezing someday intro to GR if i can. (but the schedule is already tight, i think it would be shame to have a bsc in physics and maths but not having done any course on GR).

[sanctus]

Alon, I'm now donig my last semester before finishing the courses for the master in physics, after I've got the paper to write (no idea of how you call it in english).

The GR course depends on two things here:

1) because we are not many students it is given only every two years (so there is people doing the bachelor who follow it as well);

2) The prof who gives it is very theoretical (without many intuitive examples), so this scared off quite a few people and makes the course interesting only for those interested in theoretical physics.

 

By the way what is a good book also with the modern approach to GR (I mean as well with the Cartan calculus)?

[Erasmus00]

By the way what is a good book also with the modern approach to GR (I mean as well with the Cartan calculus)?

 

Misner, Wheeler, Thorne's big black book Gravitation covers nearly everything you'd want to know and uses Cartan's forms.

-Will

[sanctus]

thanks I'll look into it on tuesday when I get back to university (and its library).