1,344 reputation
215
bio website
location Nanjing, China
age 27
visits member for 1 year, 7 months
seen Sep 19 at 9:05

I'm a graduate student studying theoretical condensed matter physics in Nanjing university, China.

My current interest is in the topics of symmetry, gauge theory, and topology in condensed matter theory.


Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer
Sep
19
comment Is there a critical order of the Abelian gauge theory in (2+1)D
@Everett You Dear Everett, I have a naive comment here. I don't know whether the group $Z_n$ has a well-defined limit $\lim_{n\rightarrow \infty}Z_n$ at the mathematical level. For example, if $Z_n\equiv \left \{exp(il\frac{2\pi}{n});l=1,2,...,n\right \}$, then it seems that $\lim_{n\rightarrow \infty}Z_n=U(1)$; while, if $Z_n\equiv \left \{ (-\frac{n}{2})^*,(-\frac{n}{2}+1)^*,...,0^*,1^*,2^*,...,(\frac{n}{2}-1)^*\right \}$($n$ is even for example), where $m^*\equiv \left \{ m,m\pm n,m\pm 2n,...\right \}$, then it seems that $\lim_{n\rightarrow \infty}Z_n=Z$($Z$ represents all the integers).
Sep
19
comment Some questions about anyons?
I'm sorry that I just saw your answer, thank you. I can not understand your explanation immediately, but I just found a related article.
Aug
6
comment Naive questions on the concept of effective Lagrangian and equations of motion?
I think I can answer my Q3 now: Classically, without the path integral method, express $x$ in terms of $E$ by solving the Euler-Lagrangian equation for $x$ derived from the total Lagrangian $L$, then substitute $x$ back into $L$, and we will obtain the same effective Lagrangian $L_{eff}$ containing only $E$.
Aug
4
comment Naive questions on the concept of effective Lagrangian and equations of motion?
And mathematically speaking, $OE=0$ does not always give the correct equation of motion. For example, let's take $O=\partial _t$, then $OE=0$ gives the equation $\partial _tE=0$, while the Euler-Lagrangian equation gives a trivial equation $\partial _tE=\partial _tE$. And here $O=\partial _t$ is NOT positive.
Aug
4
comment Naive questions on the concept of effective Lagrangian and equations of motion?
If $O$ is not positive, then there exists a function $f(t)$ such that $\int dtfOf<0=\int dtEOE$, where $OE=0$, which means that the solution $E$ does NOT correspond to the minimal action $S_{eff}$.
Aug
3
comment Naive questions on the concept of effective Lagrangian and equations of motion?
:Inspired by your comment, if there exists a least action principle for the effective action $S_{eff}=\int dtL_{eff}$, and further the operator $O$ is assumed to be positive, then $OE=0$ may be one possible solution. So what's your opinion?
Aug
2
comment Naive questions on the concept of effective Lagrangian and equations of motion?
♦ Yes. And I wonder whether we could define an effective Lagrangian containing only the electric field $E$ from the classical point of view? Thanks.
Aug
2
revised Naive questions on the concept of effective Lagrangian and equations of motion?
edited tags
Aug
2
comment Naive questions on the concept of effective Lagrangian and equations of motion?
♦ Thanks for your answer. You have given the classical equations of motion using normal coordinates. But I'm not interested in how to solve the classical harmonic oscillators, instead, here what I concerned is the concept of effective Lagrangian, either quantum version or classical version.
Aug
2
comment Naive questions on the concept of effective Lagrangian and equations of motion?
Wow, your explanation to Q2 is very clear, thank you very much. BTW, I'm not clear how you get Eq(2) from Lagrangian (1)? I only know the so-called Euler-Lagrangian equation derived from an ordinary Lagrangian $L(E,\dot{E})$ which is a function of only coordinate and velocity variables.
Aug
2
accepted Naive questions on the concept of effective Lagrangian and equations of motion?
Aug
1
asked Naive questions on the concept of effective Lagrangian and equations of motion?
Jul
8
revised Naive questions on the classical equations of motion from the Chern-Simons Lagrangian
added 186 characters in body; edited tags
Jul
8
revised Naive questions on the classical equations of motion from the Chern-Simons Lagrangian
added 19 characters in body
Jul
8
asked Naive questions on the classical equations of motion from the Chern-Simons Lagrangian
Jul
2
awarded  Inquisitive
Jul
2
awarded  Curious
Jun
29
revised Degenerate perturbation theory applied to topological degeneracy?
added 138 characters in body