What is chern-simons: Definition and 16 Discussions
In mathematics, the Chern–Simons forms are certain secondary characteristic classes. The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose.
Hey all,
I am reading David Tong's notes on Chern-Simons: https://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf
and he makes the following statement that doesn't make much sense to me: "Because the Chern-Simons theory is first order in time derivatives, these Wilson loops are really parameterising...
I believe this boils down to lack of familiarity on my part with wedge products of forms, so the answer is probably simple - but it's better to ask a stupid question than to remain ignorant! I've been looking at <https://arxiv.org/abs/hep-th/9505027>, and the idea that the BF [1] action...
I was reading Dunne's review paper on Chern-Simons theory (Les-Houches School 1998) and I don't get how he decomposes the gauge potential on the torus. My own knowledge of differential geometry is sketchy. I do know that the Hodge decomposition theorem states that a differential form can be...
I've been studying the Witten-Reshetikhin-Turaev (WRT) invariant of 3-manifolds but have almost zero background in physics. The WRT of a 3-manifold is closely related to the Chern-Simons (CS) invariant via the volume conjecture. My question is, what does the CS invariant of a 3-manifold...
Dear All
It is known that pontryagin densities are defined in even dimension space, let's say i am concerned with 4 dim space time. We also have a certain group G. What is the formula of pontryagin densities for arbitrary group? Larger group?
I have the Chern Simons action, and I've found the equations of motion ##\epsilon^{\mu\nu\rho}F_{\nu\rho}=0##. A problem I was looking at said show that the e.o.m. is "gauge equivalent to the trivial solution". I understand what this means. Obviously the e.o.m. is manifestly gauge invariant, and...
Hi PF,
I'm still very much a novice when it comes to QFT, but there's a particular calculation I'd like to understand and which (I suspect) may be just within reach. In short, the result is that after coupling a system of fermions to an external U(1) gauge field, one obtains a Chern-Simons...
Hi, I am struggling with a problem in field theory:
We are looking at a Chern-Simons Lagrangian describing a massive A field:
L = -\frac{1}{4} F^{\mu\nu}F_{\mu\nu}+\frac{m}{4}\epsilon^{\mu\nu \rho}F_{\mu\nu}A_{\rho}
I find those field equations:
\partial_{\mu}F^{\mu\lambda}=-\frac{m}{2}...
I've encountered chern-simons forms several times in papers of general relativity, such as in "actions based on the chern-simons form". I don't really understand where that form comes from. Is it simply some mathematical quantity? Can someone explain to me? or at least send me a reference?
Spin networks describing BH have a central node with label taken from an intertwiner Hilbertspace of high dimension (corresp. to hole entropy). Horizon area corresponds to the network links that pass through the horizon. The horizon Hilbertspace turns out to have the same high dimension (again...
Hi dudes.
I'm studying the paper of Witten: 2+1 Dimensional gravity as an exactly soluble system.
Before eq (2.8) the author justifies as a way to find the inner product the fact that in this theory we have the casimir \epsilon_{abc}P^aJ^b. Then he introduce the invariant quadratic form...
Homework Statement
Imagine a spatially 2d world. The electromagnetic field could be richer here, because you could add to the Lagrangian L an additional term (known as the Chern-Simons Lagrangian)
L_{CS} = \epsilon_{0}\frac{\kappa}{2}\epsilon^{\alpha \beta...
Hi everybody!
Is there someone that can help me to prove that
\omega^2E-k^2E=-ip_0k\times E+i\omega p\times E
imply that the dispersion relation is
(k^\mu k_\mu)^2+(k^\mu k_\mu)(p^\nu p_\nu)=(k^\mu p_\mu)^2
Thanks in advance ;)
p.d. The reference for this formula is the...