t***s
发帖数: 88 | 1 In a 1952 paper(DOI: 10.1103/PhysRev.85.631), Dyson made an argument that
the purterbation series after renormalization has zero convergence radius.
So even for coupling parameters as small as 1/137, any series calculated
from Feynman diagrams will blow up to infinity eventually. How to interpret
this divergence? If the series is divergent, how do we define the physical
quantity we are calculating in the first place? |
q*d
发帖数: 22178 | 2 等你又算到无穷大了再说,至少目前还没有吧
interpret
【在 t***s 的大作中提到】
: In a 1952 paper(DOI: 10.1103/PhysRev.85.631), Dyson made an argument that
: the purterbation series after renormalization has zero convergence radius.
: So even for coupling parameters as small as 1/137, any series calculated
: from Feynman diagrams will blow up to infinity eventually. How to interpret
: this divergence? If the series is divergent, how do we define the physical
: quantity we are calculating in the first place?
|
Q******g
发帖数: 607 | 3 almost all purterbation series are diverged.
it does not stop one to abstract sensible rsults.
interpret
【在 t***s 的大作中提到】
: In a 1952 paper(DOI: 10.1103/PhysRev.85.631), Dyson made an argument that
: the purterbation series after renormalization has zero convergence radius.
: So even for coupling parameters as small as 1/137, any series calculated
: from Feynman diagrams will blow up to infinity eventually. How to interpret
: this divergence? If the series is divergent, how do we define the physical
: quantity we are calculating in the first place?
|
l*******g
发帖数: 14 | 4 It just state the fact that we will need the second renormalization to
remove this divergence.
For UV divergence we have give their explicit form with dimensional
regularization or momentum cutoff. Then physicist find some way of removing
them as renormalization. But since physicist is not able to sum over all
perturbation series and expressed the divergence, they cannot give
corresponding subtraction method to removing this divergence.
However, this doesn't invalidate the use of perturbation se
【在 t***s 的大作中提到】
: In a 1952 paper(DOI: 10.1103/PhysRev.85.631), Dyson made an argument that
: the purterbation series after renormalization has zero convergence radius.
: So even for coupling parameters as small as 1/137, any series calculated
: from Feynman diagrams will blow up to infinity eventually. How to interpret
: this divergence? If the series is divergent, how do we define the physical
: quantity we are calculating in the first place?
|
w****1
发帖数: 4931 | 5 I'm disappointed that none of the previous replies to your post got to the
point. Come on guys, this is something you should have learned in a decent
quantum field theory course. The answer is nonperturbative effects, which
are of order exp(-1/g^2) where g is the coupling constant. The perturbation
series starts to diverge precisely when the perturbative contributions are
comparable to the order of the nonperturbative effects, e.g. from instantons
. So this is when you can no longer trust the pe
【在 t***s 的大作中提到】
: In a 1952 paper(DOI: 10.1103/PhysRev.85.631), Dyson made an argument that
: the purterbation series after renormalization has zero convergence radius.
: So even for coupling parameters as small as 1/137, any series calculated
: from Feynman diagrams will blow up to infinity eventually. How to interpret
: this divergence? If the series is divergent, how do we define the physical
: quantity we are calculating in the first place?
|
w******0
发帖数: 1404 | 6 What will happen when you add up all the purterbation expansion?
interpret
【在 t***s 的大作中提到】
: In a 1952 paper(DOI: 10.1103/PhysRev.85.631), Dyson made an argument that
: the purterbation series after renormalization has zero convergence radius.
: So even for coupling parameters as small as 1/137, any series calculated
: from Feynman diagrams will blow up to infinity eventually. How to interpret
: this divergence? If the series is divergent, how do we define the physical
: quantity we are calculating in the first place?
|
e**********n
发帖数: 359 | 7 Dirt under the rug, dirt is still dirt. |
w****1
发帖数: 4931 | 8 It may look like dirt but it's really gold. If you were Steve Shenker and
thought hard enough about the analogous divergence of the asymptotic series
in string perturbation theory, you would have discovered D-branes years
before Polchinski did.
【在 e**********n 的大作中提到】
: Dirt under the rug, dirt is still dirt.
|
x******i
发帖数: 3022 | 9
举个小学水平的例子来说明一下收敛半径：
1 + x + x^2 + x^3 + ...
如果x>1，就算你全加起来，也加不出正确答案：
1/(1-x)
【在 w******0 的大作中提到】
: What will happen when you add up all the purterbation expansion?
:
: interpret
|
r****y
发帖数: 1437 | 10
you mean abs(x) < 1 ba.
【在 x******i 的大作中提到】
:
: 举个小学水平的例子来说明一下收敛半径：
: 1 + x + x^2 + x^3 + ...
: 如果x>1，就算你全加起来，也加不出正确答案：
: 1/(1-x)
|
|
|
x***u
发帖数: 6421 | 11 显然他要说>1
【在 r****y 的大作中提到】
:
: you mean abs(x) < 1 ba.
|
N***m
发帖数: 4460 | 12 =1的情形怎么算阿
【在 x***u 的大作中提到】
: 显然他要说>1
|
x***u
发帖数: 6421 | 13 那就是1＋1＋1＋1＋。。。呗，去掉最大值1，再去掉最小值1，结果是0。
【在 N***m 的大作中提到】
: =1的情形怎么算阿
|
w******0
发帖数: 1404 | 14 I mean renormalization to all order.
【在 x******i 的大作中提到】
:
: 举个小学水平的例子来说明一下收敛半径：
: 1 + x + x^2 + x^3 + ...
: 如果x>1，就算你全加起来，也加不出正确答案：
: 1/(1-x)
|
w****1
发帖数: 4931 | 15 It looks like you need a lesson in calculus. The divergence of perturbation
series has nothing to do with renormalization.
I suggest you do the following exercise. Consider the integral \int_{-\infty
}^\infty dx \exp(-x^2 - g x^4).
Calculate it perturbatively in powers of g, and show that the series in
powers of g has zero radius of convergence. Next, show that the if you cut
off the series at the point where it starts to diverge, the error is
comparable to the contribution from instantons, whic
【在 w******0 的大作中提到】
: I mean renormalization to all order.
|
