Recent content by Shen712

We are taught that all fermions have spin ##\frac{1}{2}##, short for spin angular momentum ##\frac{\hbar}{2}##, which can be added to the orbital angular momentum. Considering spin is a kind of angular momentum, it must be dependent on the mass (or moment of inertia) of the particle. However...

I got the idea of fraction because I believe electrons have substructure, and each component of the electron must have a spin smaller than $\frac{\hbar}{2}$, say, $\frac{\hbar}{4}$ or $\frac{\hbar}{6}$. But this would violate our convention that fermions have spin $\frac{\hbar}{2}$. As I try to...

The Schrödinger equation is $$ i\hbar \frac{\partial\Psi}{\partial t} = -\frac{\hbar^{2}}{2m} \frac{\partial^{2}\Psi}{\partial x^{2}} + V \Psi $$ Why is the coeffient on the left-hand side ##\hbar##, not ##\frac{\hbar}{2}## or ##i\frac{\hbar}{3}## or something like these Besides, in quantum...

Under the entry "Quantum electrodynamics" in Wikipedia, the Dirac equation for an electron is given by $$ i\gamma^{\mu}\partial_{\mu}\psi - e\gamma^{\mu}\left( A_{\mu} + B_{\mu} \right) \psi - m\psi = 0 ,\tag 1 $$ or $$ i\gamma^{\mu}\partial_{\mu}\psi - m\psi = e\gamma^{\mu}\left( A_{\mu} +...

I read somewhere that, suppose a scalar field Σ transforms as doublet under both SU(2)L and SU(2)R, its general rotation is δΣ = iεaRTaΣ - iεaLΣTa. where εaR and εaL are infinitesimal parameters, and Ta are SU(2) generators. I don't quite understand this. First, why does the first term have...

Can you explain more clearly? How are the linear compositions different? And how does one lead to a - sign while the other lead to a + sign?

The composition of the π0 is (uu_bar - dd_bar/√2; while the composition of the η meson is (uu_bar + dd_bar)/√2. Why is there a - sign in π0 while is there a + sign in η? How are the signs determined? By the way, can I type Latex symbols on this site? I tried to type the anti up quark by typing...

My thoughts are: Since the SM generator Y is proportional to identity, the required linear combination of the LRS generators must also be proportional to identity. Considering that the generators of SU(2)R are TaR = τa/2, where τa are the Pauli matrices, only the combination of T3R and X is...

This is a homework problem in a course in particle physics at Cornell University. Assume the Left Right Symmetric (LRS) model for leptons. The gauge group is GLR = SU(2)L×SU(2)R×U(1)X. The Standard Model group SU(2)L×U(1)Y has to be included in the LRS group. Namely, U(1)Y ⊂ SU(2)R×U(1)X. Find...

We often use SO(N) and SU(N) to describe symmetries in particle physics. I am not clear which one to choose when I try to discuss a symmetry. For example, why do we use SU(3) but not SO(3) to describe the symmetry of the three colors of quarks? Similarly, why do we use SU(2) but not SO(2) to...

The covariant derivative in standard model is given byDμ = ∂μ + igs Gaμ La + ig Wbμ Tb + ig'BμYwhere Gaμ are the eight gluon fields, Wbμ the three weak interaction bosons and Bμ the single hypercharge boson. The La's are SU(3)C generators (the 3×3 Gell-Mann matrices ½ λa for triplets, 0 for...

How do we know the spin of an elementary particle? For example, a fermion has spin 1/2; a photon has spin 1; and even the ficticious graviton has spin 2. How do we know these spins? In other words, how are these spins determined?