What Math Do I Need for SR and Classical Relativistic Field Theories?

[magicfountain]

I read basic stuff about relativity (time dilitation etc.) in a HS textbook.
I want to do some relativistic dynamics and go up to Einsteins field equations (GR). For GR I will definitely need tensor analysis. However, what is the math involved in the SR that I need to get to classic relativistic field theories (Electromagnetic),which I want to do before doing GR?

 

[alialice]

I want to do some relativistic dynamics and go up to Einsteins field equations (GR). For GR I will definitely need tensor analysis.

However, what is the math involved in the SR that I need to get to classic relativistic field theories (Electromagnetic),which I want to do before doing GR?

For GR you need some basis of differential geometry.
For the second question, I think you refer to Classical Electrodynamics? For it you need vector calculus, and to know something about tensor if you use covariant formalism.

Is this what you were asking?

 

[magicfountain]

As far as my understanding goes, maxwells basic equations describe the EM field without relativistic effects (I have done them already, as well es basic vec. calc. (div. grad. rot.)). I just had a look at some lecture notes from the internet and it had a lot of tensors for relativistic maxwelltheory. not really following it (because I know few about tensors in relativity) i saw langrange densities coming up while going through it.
I know the how to derive lagrange densities in mechanics (they can be nonrelativistic) and thought, there was a way to have maxwell field theory in lagrangian form, but this probably corresponds to relativistic forms only. (is this correct?)
should I start doing tensors and relativity first to get to relativistic maxwelltheory?

 

[haushofer]

As far as my understanding goes, maxwells basic equations describe the EM field without relativistic effects.

Maxwell's equations are inherently relativistic. So why do you say this?

Of course one can take a non-rel. limit, giving "Galilean Maxwell theories", but that's a different cookie.

 

[magicfountain]

Maxwell's equations are inherently relativistic. So why do you say this?

Ok, if you mean relative motion (B-field for moving etc.).
Maybe it was wrong, that with relativistic I referred to time dilatation and doing Lorentztransformations.

 

[alialice]

should I start doing tensors and relativity first to get to relativistic maxwelltheory?

Maxwell theory is relativistic( in the sense of special relativity): it predicts for example that the speed of an electromagnetic wave is c.
What are you looking for, I think it is electrodynamics. You can study the motion of particles in electromagnetic field, and for this you need special relativity and tensors.

 

[alialice]

http://arxiv.org/abs/physics/0311011/
I've just found this notes, try to look at them, even if they are more mathematic than physics.
The standard reference for the subject is a book called Classical Electrodynamics by Jackson.

 

[magicfountain]

I think it is electrodynamics. You can study the motion of particles in electromagnetic field.

Thanks, this helps!
So is this also what the Langrangians are for?

 

[harrylin]

Ok, if you mean relative motion (B-field for moving etc.).
Maybe it was wrong, that with relativistic I referred to time dilatation and doing Lorentztransformations.

Maxwell's equations relate to a single inertial frame. The change with SR was that the equations are valid for any inertial frame - this doesn't affect the equations at all.

 

[alialice]

Thanks, this helps!
So is this also what the Langrangians are for?

Yes :)