n********s
发帖数: 150 | 1 I am reading a paper "Class of scalar-field soliton solutions in three space
dimensions" (Phys.Rew.D 13 2739) by T.D.Lee. When the authors try to
quantize the soliton, they said "....Q is the total charge operator. Because
x is a cyclic variable with a period = 2 pi, the eigenvalue of its
conjugate momentum Q are all integers: 0, 1,2....".
I cannot understand this point. What does it means "cyclic variable"? why
its eigenvalue must be integers?
Thanks a lot. | e**********n
发帖数: 359 | 2 cyclic is another way of saying periodic boundary condition, here Q is
identified with Q+2 pi.
Similar to crystal momentum, when the variable is periodic, its conjugate
momentum, which is the generator of its translation, has integer eigenvalues
. You probably need to familiarize yourself with Luttinger liquid theory in
1D before going to 3D solitons. There are lots of good tutorials on
Luttinger liquid on the web. | n********s
发帖数: 150 | 3 Hi, eventhorizon,
Thanks a lot.I got it, and it makes sense to me now.
The Q is the charge of the soliton and it must be integer to any quantum
soliton. |
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