phymath999: QED is involved massless photon, which is related to gauge invariant.

Monday, December 8, 2014

Deep Fact about Nature

Today we will tell you deep fact about nature between like objects which have same charge, and are indeed different.

We know Newton’s force is attractive whereas Coulomb’s force is repulsive. We may ask why they behave like this.

Many years later since they are discovered, we can answer part of this question with QED, quntum electrodynamics.

QED is involved massless photon, which is related to gauge invariant. However, since people have spent decades to

understand this and there are lots of subtlety in gauge theory, we will not talk about it untill later lectures. Today,

we will just use Sidney Coleman’s method to bypass discussing gauge invariance.

Lecture Notes of Quantum Field Theory

Prof. Anthony Zee. (recorded by Gao Ping)

July 11, 2012

Lecture 5

5.1 Two Questions about m → 0

In last class, we have met two questions about m = 0 case and they are essentially different from the coleman’s

trick: m → 0. Since last weekend, some students sent e-mails to me to discuss this problem, here I will just make

some comments on this issue.

According to equipartition of energy theorem, the energy per degree of freedom is averaged to 1

2kT. Thus we can

immediately know whether photon is massless or not will result very different results in specific heat, whose ratio

should be 2 : 3. Experimentalists can thus measure the specific heat to judge the mass of photon. However, they

can only give an upper bound at most. The reason is that when m → 0, the longitudal component will decouple to

all physical process. This means we have to wait for infinite long time to get the thermal equilibrium of longitudal

polarization photon with detector. Since the intensity of coupling is proportional to m(see Chap II.7 in my book),

if m is small enough, the time will be still so long that no experimentalist can wait until thermal equilibrium. Then

even if m ̸= 0, experimentalists are only able to measure the specific heat of two transverse polarized components of

equilibrium plus longitudal component of unequilibrium(whose specific heat is not defined). Thus, experimentalists

can only give an upper bound for the mass of photon.

The other comment is about graviton. We know the

Anthony Zee. 規範場論 的結果 (無引號)：

phymath999