Weyl Definition and 91 Threads

Hi, I was wondering if someone wouldn't mind breaking down the geometrical differences between the Riemann, Ricci, and Weyl tensor. My current understanding is that the Ricci tensor describes the change in volume of a n-dimensional object in curved space from flat Euclidean space and that if we...

Homework Statement Show that all Robertson - Walker models are conformally flat. Homework Equations Robertson Walker Metric: ds^{2}=a^{2}(t)\left(\frac{dr^{2}}{1-Kr^{2}}+r^{2}(d\theta^{2}+(sin\theta)^{2}d\phi^{2} )\right)-dt^{2} Ricci Tensor: R_{\alpha\beta}=2Kg_{\alpha\beta} Ricci...

Hello, sorry for my english.. I have a problem with weyl's spinors notation. I'm confused, becouse i read more books (like Landau, Srednicki and Peskin) and it's seems to me that all of them use different and incompatible notations.. If i define...

In his article The Ricci and Weyl Tensors John Baez states that the tidal stretching and squashing caused by gravitational waves would not change the volume as there is 'only' Weyl- but no Ricci-curvature. No additional meaning is mentioned. But, beeing not an expert I still have no good...

I am readin Belinte's book about Lie algebras (I have also the Cahn) . And I try to understand this. He writes "Each basic weight is invariant under all but one of the simple Weyl reflections since w_i l_j = l_j for i<>j while w_i l_i = l_i - alpha_i (alpha_i is simple by definition of...

I've been watching Sidney Coleman's QFT lectures (http://www.physics.harvard.edu/about/Phys253.html, with notes at http://arxiv.org/pdf/1110.5013.pdf), and I'm now on to the spin 1/2 part of the course. We've gone through all the mechanics of constructing irreducible representations D^{(s1,s2)}...

I just started studying supersymmetry, but I am a little bit confused with the superspace and superfield formalism. When expanding the vector superfield in components, one obtains therms of the form \theta^{\alpha}\chi_{\alpha}, where \theta is a Grassmann number and \chi is a Weyl vector. I...

Hi guys! I'm having some problems in understanding the direct products of representation in group theory. For example, take two right weyl spinors. We can then write\tau_{0\frac{1}{2}}\otimes\tau_{0\frac{1}{2}}=\tau_{00}\oplus\tau_{01} Now they make me see that...

Hi , I can't understand the general formula for weyl ordering of the hamiltonian . It is written in Srednicki field theory book in page 68 . Can someone explain how to derive this formula ?

Hello, Can someone please give me the form of the "Weyl" version of the Rarita-Schwinger equation. Thanks

Homework Statement The task is to show the invariance of a given Lagrangian (http://www.fysast.uu.se/~leupold/qft-2011/tasks.pdf" ), but my problem is just in one step (which i got from Peskin & Schröder, page 70) which i can not reproduce due to my lack of knowledge regarding spinors. The...

Hi, I'm getting used to the anti-symmetric bracket notation used with indices and I can't seem to find the Weyl Tensor written fully out. So I want to make sure I get it. Here is my attempt in dimension 4...

How is Weyl Tensor associated with tidal force? I checked my book, the acceleration in tidal effect can be expressed as: ac=-RabdcZawbZd Note: Za is the tangent of geodesics, wb is the separation vector I cannot see from this equation how Weyl Tensor affects tidal force. It is...

hello everyone, following the book of Landau&Lifsitz I managed to understand the Schwarzschild solution. At the end, it finds this formula for the mass of the spherical body generating the gravitational field: M=\frac{4\pi}{c^2} \int^a_0 \epsilon(r) r^2 dr in which \epsilon(r) is...

I hope someone can help me cite the right reference that explains how to arrive at Weyl rule in the next paper, in the second page (eq. (1)). http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry340.pdf Thanks in advance.

Hi, I'm new on this forum. I have a doubt regarding helicity and Weyl spinors: I can't understand when I have to use left or right-handed Weyl spinors in order to describe particles or antiparticles. What i have understood is that a charged current is described by left-handed Weyl fields...

Hey guys, something that puzzles me everytime I stumble across spinors is the following: I know that i can express Dirac spinors in terms of2-component Weyl spinors (dotted/undotted spinors). Now, if i do that, i can reexpress for instance the Lorentz or conformal algebra in terms of Weyl...

Can anyone explain to me what is the difference between a Weyl spinnor and a Majorana spinnor? Thanks

Homework Statement Using (\sigma^{\mu \nu})^{\beta}_{\alpha} (\sigma_{\mu \nu})^{\delta}_{\gamma} = \epsilon_{\alpha \gamma} \epsilon^{\beta \delta} + \delta^{\delta}_{\alpha} \delta^{\beta}_{\gamma} show that \Psi_{\alpha} X_{\beta} = \frac{1}{2} \epsilon_{\alpha \beta} (\Psi X) +...

Amusingly, a search on these three words here in PF does not show a lot of postings, so I am creating this thread so you can ask all your doubts about N-dimensional Majorana, Weyl and Dirac particles, their representations, their Lagragians, masses, and whatever you have always wanted to know...

If we take the the Dirac Lagrangian and decompose into Weyl spinors we find \mathcal{L} = \bar{\psi} ( i \gamma^\mu \partial_\mu - m ) \psi = i U^\dagger_- \sigma^\mu \partial_\mu u_- + i u^\dagger_+ \bar{\sigma}^\mu \partial_\mu u_+ - m(u^\dagger_+ u_- + u^\dagger_- u_+ ) =0 So far I have...

What is the difference between left and right Weyl spinors? (probably they transform differently under boosts or rotations). Thanks for answer.

I'm a bit confused about this and would like for someone to help me get this straight. I read in wikipedia that a manifold with more than three dimensions, like spacetime, is conformally flat if its Weyl tensor vanishes. I think all FRW metrics are conformally flat, so I guess our universe is...

Hey guys, I have a question about said spinors. In supersymmetry introductions one finds (e.g. for two left-handed spinors \eta , \nu ) that \eta\nu=\nu\eta due to their Grassmannian character and the antisymmetry of the spinor product. If I look, however, at modern field theoretical...

Can Conformal Weyl Gravity be considered a viable cosmological theory?

I found the formula for the number of independent components of Weyl tensor in n-dimensional manifold: (N+1)N/2 - \binom{n}{4} - n(n+1)/2~~~~~N=(n-1)n/2 This expression implies that in 3 dimension Weyl tensor has 0 independent components, so it's 0. Does it implies that any three-dimensional...

This question is a follow-up to the one I asked last week in the thread called, "about tidal forces". In that thread the question came up: what would happen to a sphere of free-falling particles (a "ball of coffee grounds") in a gravitational field described by the Rindler metric? After some...

In discussions of questions related to gtr, it is often useful to know that one can in fact "create solutions to order" in gtr, when one wishes to model specific physical scenarios. Sort of, not really--- and herein lies a tale which illustrates some of the many thorny technical and conceptual...

Hey! I have a problem with problem 5.6 (b) from Peskin + Schroeder. Maybe I just don't see how it works, but I hope somebody can help me! Homework Statement We are asked to calculate the amplitude for the annihilation of a positron electron pair into two photons in the high-energy limit. The...

A Dirac field can be written as two Weyl fields stacked on top of each other: \Psi= \left( \begin{array}{cc} \psi \\ \zeta^{\dagger} \end{array}\right) , where the particle field is \psi and the antiparticle field is \zeta. So a term like P_L\Psi=.5(1-\gamma^5)\Psi=\left( \begin{array}{cc}...

Kip Thorne says (Lecture in 1993 Warping Spacetime, at Stephan Hawking's 60th birthday celebration, Cambridge, England,) Comments, interpretations, appreciated. I thought classical time was always symmetric ...apparently not. Is this same description applicable to a "big crunch" as...

Weyl spinors are not eigenstates of the helicity operator when the mass is not zero. But they have well-defined chiralities no matter what the mass is. Yet, it seems to me that references keep talking of Weyl spinors as if they have well-defined helicities, regardless of the mass...

I'm not sure if this is the right place for this question, so feel free to move it. Anyway, my question is, is there any good reason why the following field theory should be Weyl invariant in an arbitrary dimension d>1: S = \int d^d x \sqrt{g} \left( g^{\mu \nu} \partial_\mu \phi \partial_\nu...

This is a very very simple question and I am sure it will look dumb because I won't be using the correct terminology but here I go. Consider the points in a manifold. Now we assign coordinates to those points. ne thing that I find confusing about any type of transformation is whether a)...

Could someone show me a derivation of the Weyl tensor or link me to a good site?

Hello, I wish to show that on 3-dimensional manifolds, the weyl tensor vanishes. In other words, I want to show that the curvature tensor, the ricci tensor and curvature scalar hold the relation Please, if anyone knows how I can prove this relation or refer to a place which proves the...

Hello, I wish to show that on 3-dimensional manifolds, the weyl tensor vanishes. In other words, I want to show that the curvature tensor, the ricci tensor and curvature scalar hold the relation Please, if anyone knows how I can prove this relation or refer to a place which proves the...

A "Weyl" theory of dark matter http://web.mit.edu/people/cabi/index.html by Hung Cheng of MIT, showing that if physics is locally conformal (independent of scale choice) then there is a vector particle he calls S which couples to a scalar particle like the hypothetical Higgs, or to a tensor...

What's the actual status of the Weyl curvature hypothesis? Is there any best explanation to the early low entropy?

I have been reading that the quantity called "Weyl curvature" can exist independently of any matter, or energy, in the universe? :confused: This seems to contradict Heisenberg uncertainty which says there can be no 100% vacuum, because uncertainty in position and uncertainty in momentum...

I was reading about Weyl Transformations in Polchinski's book and I have a little doubt: Is it correct to say that under a Weyl transformation the scalars are invariant, i.e., that a weyl transformation preserves the scalar product?