I am an MPhys graduate currently reading Joseph Polchinski’s, String Theory, Vol. 1. Unsurprisingly I’m stuck on the first real bit of maths… :p(adsbygoogle = window.adsbygoogle || []).push({});

I quote from page 10, heh:

“The simplest Poincaré invariant action that does not depend on the parametrization would be proportional to the proper time along the world line,

S_pp = -m∫dτ(- δX¬μ/δτ δX_μ/δτ )^1/2 “

Where X¬μ is a covariant tensor of time dependent equations describing the position of the particle in all space time dimensions and X_μ is the contravariant tensor. (I don't know how to write subscripts or superscripts in this btw).

Now I understand basic tensor rules, and know that a Poincare invariant action is given by: dS = L dt. My questions are: why does the negative mass come into the equation? ; why does the negative in front of the derivative come into it?; why is the term in brackets square rooted?; and where does the pp subscript come from? Perhaps someone could point me to an article or web page that could help, or if you know the answers and would be so kind, perhaps explain this equation to me.

Any help will be much appreciated. Thanks.

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# Poincare invariant action of a point particle

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