Question

How to transform Dirac fermion coupled with $SU(2)/Z_2$ gauge field to the real fermion coupled with $SO(3)$?

Answer 1

. If we assume that our problem has a well-defined field theory model coupled to SO(3)SO(3) gauge field, then the solution seems unique. From the point of view of the dimension of the representation, the only two possible solutions are just the (1)+(3) representation of SO(3)SO(3) or (1)+(1)+(1)+(1) where (1) and (3) are spin-0 and spin-1 representation, respectively. In addition, considering the number of the nonzero generators, which should be 4, we can only have (1)+(3) representation as solution.

Answer 2

The experiment consists of releasing a steel ball from various heights hi and measuring corresponding free fall times τi . We used a variant of the Atwood’s machine for the measurement The information about the release and about the impact is transferred to the timer via connectors

the resolution of the measurement is 0.01[s]

Air resistance is disregarded for calculation

then I have to calculate the magnitude of the acceleration due to gravity including its uncertainty

By comparing this relation

h=1/2g

t

2

+

V

0

t

h=1/2gt2+V0t