# Lorentz transforms and distribution functions

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1. Oct 7, 2015

### Reed Kartye

Hi there, kinda new here so please let me know if this question has been answered. I am hoping to get a link or two to some good sources of information on Lorentz transforms and distribution functions (as used in physics). I understand DF's in class and I understand the math behind them I just have a hard time applying it to my homework. My textbooks makes a lot of jumps and I can't follow what is going where. It's the same thing with the Lorentz transforms, I understand the concept and examples. But have a hard time doing a problem type I've never seen before. I think my big problem is with putting the values into the equations and which equations to use. I'm hoping someone can share with me a few reasources that can help me better understand the concept and how to put those concepts into practice in problems. This is just an intro class so I don't need anything too high level, thanks in advance for all the help.

2. Oct 8, 2015

### BvU

Hello Reed, welcome to PF !

Your description reminds me of early years at university: in lectures everything is crystal clear and you understand every step. And then when you try to do some exercise it turns out you have no clue whatsoever. All I can help with is to advise you to do as many exercises as possible. If you don't like your textbook, find some other that suits you better. (As long as it has lots of exercises ). The investment is worth it (and if you don't want to spend the money you can use the library for free).

And (if necessary with help from your institution) work on problem solving skills.

3. Oct 9, 2015

### vanhees71

You must be a bit more specific, which distribution functions you are discussing. If it's the phase-space distribution function in relativistic statistical physics or kinetic theory, it's a pretty delicate subject concerning the Lorentz-transformation properties. The short answer is that it is defined by a clever convention used to define the phase-space volume element $\mathrm{d}^3 \vec{x} \mathrm{d}^3 \vec{p}$ as an invariant quantity, making the phase-space distribution function a scalar field (for "onshell" particles, i.e., with four-momenta obeying $p^0=E_{\vec{p}}=\sqrt{m^2+\vec{p}^2}$ (using natural units with $c=1$). For details, see my "Kolkata Lectures":

http://fias.uni-frankfurt.de/~hees/publ/kolkata.pdf

4. Oct 9, 2015

### BvU

Reed hasn't reacted yet. I reconsidered my first impression that he/she wanted to know about DFs as applied in LTs before I posted #2 -- mainly from the wording "it's the same thing with the LTs" I gathered we have to do with a first year student who gets all this stuff thrown at him/her. Please correct me if wrong.

For LTs I can recommend Leonard Susskind's excellent Stanford lecture video series.

5. Oct 9, 2015

### vanhees71

Hm, let's see. I'd not through phase-space distribution functions within relativistic theory to a 1st-year student when introducing SRT. It's a very subtle subject. Many of my colleagues are involved in using relativistic transport codes to simulate heavy-ion collisions at RHIC and LHC. There from time to time we come back to the problems of the covariant definition of phase-space distribution functions and the correct realization of the collision term within the test-particle methods. It's pretty delicate, and we have many very lively discussions about it. It's definite not a topic for an undergrad. intro to SRT!