Checklist for VL-01:

slide 5:

(1)
How many elementary particles do we know in the SM, distinguishing left-, right-
handed, particles and anti-particles? How many of these are matter particles and 
how many particles arise from the gauge interactions or Higgs mechanism? 

(2)
Ordering matter and interaction particles by spin one observes that matter 
particles are fundamental fermions with spin 1/2 and the particles associated 
to the gauge interactions are vector-like bosons with spin 1. This is true for 
the photon, the W and Z bosons and the gluons. From where do you see this 
requirement on the spin of the gauge particles?

slide 19:

(3)    
What does the approximation of collinearity of the partons in the colliding 
protons mean for the transverse momentum of the partons relative to the proton 
direction? What do you think, how well is this approximation justified?

slide 20:

(4)
Can you calculate the transition from rapidity to pseudo-rapidity starting 
from the assumption of small particle mass and the first equation on slide 
20 (the one with the ln)? 

(5)
The rapidity is not invariant, but _form invariant_ under Lorentz boosts along 
the z-axis. I.e. rapidity distribution of particles keep its form when boosted 
along the z-axis, but it shifts as a whole smaller or larger values of y. Can 
you show this form invariance starting form the definition of y and the Lorentz 
boost along the z-axis? What value of the boost vector beta corresponds to a 
shift of one unit in y?

slide 26:

(6)
(Pseudo-) scalars, (axial) vectors, tensors are defined according to their 
behavior under Poincare transformations. The same is true for a spinor, which 
is an object on its own on the same footing as a vector. Note the transforma-
tion behavior for scalars, vectors, tensors of second order, and spinors. What 
is the peculiar characteristic of a spinor under rotations?

slide 28:

(7)
What happens if the operator PL/R is executed twice upon a spinor?  

slide 30:

(8)
The action h is 1 in natural units. Does a spinor have a unit in natural units?