String Theory

String Theory is one of the most exciting theory among other physics theories.Main idea is really basic.Particles are not a distinct form or point particles,and they are not excitations of quantum fields.They are strings and fluctiating from here to there. String theory is candidate of a grand unified theory.Because it allows a definition of combining general relativity and quantum field theory.Why it is important?why physicists are searching a unified theory?I think we can answer these questions in many ways. Firstly,in state of extremely massive and relativistic regime,There is not a theory that describe physical phenomena.We can list these regime blackhole and early age of our universe.There are quantum fluctiotions,singularities,mini blackholes,matter and anti matter pairs,etc.String theory a mathematical frame work which describe iteractions,particles and spacetime.Gravity is natural consequence of string theory. To study string theory,one must follow A first course in string theory book by Barton Zwiebach. It is an introduction text book for undergraduate students.If you haven't any background in quantum field theory and general relativity,it is a good course boook for introducing string theory. General relativity describes gravity with a interesting and challenging way.Gravity is curvature of spacetime continuum.And objects follows curve paths.This is an anology between Newtonian motion.Because in classical mechanics,we define free particles,and these particles not in effect under a force.So they follow a straight paths.However,in general teory of relativity,free particles follow a curve or mathematically,geodesics.Geodesics are shortest way that particles follow. We can see that gravity is a geometrical appearence. Quantum field theory,an attempt quantization of fields,describe particles with fields excitations.So it is not directly geometrical theory.

Cartan's Structure Equations

         We have already use Tensor algebra for constructing General Relativity,that is,Einstein Field Equations.Tensor algebra is useful when we define a physical law in coordinate independend form.However,it is difficult to compute some metric with tensor algebra.So Cartan's Structure Equations allows us very useful and short computations.I will introduce some basic properities of CSE(Cartan's Structure Equatons) here.First of all this text an attempt at writing in english language.Thanks for your tolerance,and please advice me for any mistakes.
Now we will dive into most elegant form of mathematical structure of our universe.
Major motivation of construction of structure equation is transformation of coordinate basis to non coordinate basis.We know from elementary physics only cartesian coordinate is orthogonal.Therefore we want build a framework that have orthogonal basis and independent from chosen coordinate frame.
        To describe a mathematical framework that belong to physical phenomena one has to take a coordinate system and approach a description of experimental fact that valid every time and independend from where experments performed.From this consequences we want orthogonal basis and to be converted between different coordinates.Special relativity and General relativity are coordinate independent theories.And they are valid any referance frame.
        Next chapter we will introduce basics of CSE.