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):
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