For example you have a cell or already a bunch of cells. Those cell(s) divide and after several week you have a grown organism, for example a human with limbs, several different organs etc. 
However, how do cells know where up, down, left, right etc. is?
I know left and right can be defined clearly in physics. However how do cells define those directions and what are mechanisms for them to grow into a certain direction? 
Is there a paper or a longer article dealing with that question/problem?

I don't think my knowledge on Biology goes far beyond high school level maybe 1. term at a university. If I have to, I would read and learn everything I need to know to understand the matter. 


Question: Spin matrices in Dirac equation
Answer: Particles in the standard model are in principle massless and acquire mass through interactions via the Lagrangian. This poses a problem if you want to use the 3x3 matrix generators of angular momentum because massless particles have different lie group representations as particles with mass.

The 3x3 generators for particles of spin 1 acts on three states, -1, 0 +1. In the massless case only two states remain.

With fermions and the 2x2 SU(2) matrices  this issue doesn't exist. The two chiral components $\psi_L$ and $\psi_R$ propagate lightlike and the two states of each chiral component correspond with spin up and down where the spin is parallel or anti parallel to the direction of propagation.

Hans