2,515 reputation
11535
bio website berkeley.academia.edu/…
location Berkeley, CA
age 25
visits member for 4 years
seen May 21 at 16:58

Currently a graduate student in mathematics at the University of California - Berkeley.

Previously obtained a MASt. in Applied Mathematics from the University of Cambridge (2013), and a B.S. in Mathematics and a B.A. in Physics from the University of Chicago (2012).


Nov
9
comment Derivation of the irreducible representations of SO(3)
Suppose that the representation has spin $n/2$ with $n\in \mathbb{Z}^+$. Then, in particular, this representation will contain an element $v$ such that $S_zv=\frac{n}{2}v$. This is at the level of the Lie algebra. At the level of the Lie group, $R_z(\theta )=\exp (-i\theta S_z)$ is a rotation about the $z$-axis by an angle $\theta$. Hence, $R_z(\theta )v=\exp (-i\theta \frac{n}{2})$. For $\theta =2\pi$, we had better have that $R_z(2\pi )=R_z(0)$; however, using the formula above, $R_z(2\pi )=\exp (-i\pi)=-1$. Thus, this does not give us a representation of $SO(3)$ for half-integer spin.
Nov
9
revised Derivation of the irreducible representations of SO(3)
added 19 characters in body
Nov
9
comment Derivation of the irreducible representations of SO(3)
The spherical harmonics give you all the irreducible representations of $SO(3)$, but it does not give you all those of $SU(2)$. You'll note this does not make any direct reference to the Lie algebra of $SO(3)$
Nov
9
answered Integral over scalar product of eigenfunction of momentum operator and harmonic oscillator one
Nov
9
answered Calculation mistake some place in finding stress-energy tensor
Nov
9
revised Calculation mistake some place in finding stress-energy tensor
added 10 characters in body
Nov
9
answered Derivation of the irreducible representations of SO(3)
Nov
9
answered Why does the acceleration $g$ due to gravity not affect the period of a vertically mounted spring?
Nov
8
answered Neutrino-Neutron Interaction Feynman Diagram (W Boson Direction)
Oct
21
awarded  Notable Question
Oct
15
awarded  Nice Question
Sep
30
awarded  Explainer
Sep
28
revised What are great circles of 2-sphere?
deleted 2 characters in body
Sep
27
answered What are great circles of 2-sphere?
Jul
23
awarded  Good Question
Jul
22
awarded  Famous Question
Jul
2
awarded  Curious
Jun
11
revised The relation between classical and quantum vacua
added 36 characters in body
Jun
11
revised The relation between classical and quantum vacua
added 36 characters in body
Jun
10
asked The relation between classical and quantum vacua