Vertex Definition and 136 Threads

Hi, I'm trying to prove that the conformal weight of the bosonic vertex operator :e^{ik\cdot X}: is \left(\frac{\alpha'k^2}{4},\frac{\alpha'k^2}{4}\right). I've done some algebra but I think I am making some mistake with a factor of 2 somewhere because I get a 1/2 instead of a 1/4. My attempt...

There is a Theorem that states that if G = (V, E) is a graph, then S is an independent set $\Leftarrow\Rightarrow$ V - S is a vertex cover. Suppose the vertices have positive integer weights. Does it follow from the theorem that: S is an independent set with maximum weight...

Hi all, I wonder if anyone here is familiar with Feynrules package to implement new model by Mathematica. Actually I'm a new user for and try to implement Yukawa Lagrangian for new charged Higgs scalar called X and the charge conjugate Xbar with the SM fermions, I wrote the Lag. as : LX := X...

The general equation of the parabola has the form $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ with $B^2 = 4AC$ what is the coordinate of the vertex of the parabola or in other word how to determine the vertex of a given parabola for example $4x^2 + 4xy + y^2 - 5x + 7y + 11 =0 $ Thanks.

I was looking at a homework question posted here requiring proof that the vectors from the vertices of a triangle to the midpoint of the opposite edge sum to zero, and it struck me that there is a more general property: Consider a set of points, \{A_0, A_1, \ldots A_n\}. The midpoint of...

I have a unique problem that I'm struggling with with regards to surveying. Because my surveying equipment is much more accurate at measuring angles than distances I'd like to find an analytic solution using only the angular measurements. Let the surveyor sit at the origin of the...

I need to know the relation of wave function and vertex function of mesons. Any one give me an explanation of them. Are they same? in some journals their expressions are the same and in other papers the wave function expresses as a function of the vertex function of meson. Which one is the...

Homework Statement Let P, Q, and R be the vertices of a parallelogram with adjacent sides PQ and PR. Find the other vector S. P (2, 0 ,-1), Q (-2, 4, 1), R (3, -1, 0) Homework Equations PR = QS PQ = RS The Attempt at a Solution I took the two equations and solved both of them...

I have the following function and I'm supposed to find the vertex of its graph. f(x)=-3(x-2)2-3 Why is the vertex (2,-3) instead of (-2,-3)? Edit: Bah, nevermind. I just realized the formula has (x-h) in it, not (x+h) in it...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 11) Find the vertex of f(x) = -2x^2 - 8x + 3 algebraically. My Answer: (-2,0) 12) Multiply and simplify: (6 - 5i) (4 + 3i) My Answer: 39 - 2i

Is there a proof or obvious reason why the vertex function is related to the current via: S(p')\Gamma^\mu(p',p)S(p)=-\int \int dxdy e^{ipx}e^{-ipy} \langle T \psi(x) j^\mu(0) \bar{\psi}(y)\rangle In the free-field case one can see it's true. But the interacting case?

In a group of n people, each pair are friends or strangers. No set of three people are mutually friends. For any partition of the n people into two groups, there exists two people in a group that are friends. Prove that there exists a person who is friends with at most 2n/5 people in the group...

Hi I am studying qft with worldwidely used text, written by Peskin and Schroeder, An introduction to qft. I have trouble with the calculation of thr numerator on pp. 192. I got additional term ## 2m(z-xy)(mγ^μ - p^μ) ## between spinors, which seems not vanishing. Is there any idea to treat this...

Hi. I have trouble understanding an argument in Lewis H. Ryder's QFT (second edition) at page 325 where he wants to write down an equation similar to the renormalization group equation which expresses the invariance of the vertex function \Gamma^{(n)} under the change of scale. The relevant...

Hi, I'm wondering if anyone can give me some advice on working out the vertex factor from a lagrangian. I think I know what I should be doing however it isn't quite getting the right answer so if anyone could guide me that would be great. \mathcal{L}_{W^-e^-\nu_e} =...

Homework Statement Four similar rods of uniform density are connected with frictionless hinges, and this frame is placed to a horizontal smooth tabletop, such that its shape is a square. Vertex P is acted upon by a horizontal force in the direction of the diagonal, and due to this force it...

Is there a reason that one-loop corrections to vertex functions seem to always be logarithmic? If you write the vertex as a Taylor series in the external momenta, then the first couple of terms (say the constant and linear terms) diverge, but these divergence gets subtracted off, so you now...

Hello. The vertex form is y= a(x-h)^2+k, in general. Could it also be defined as y= a(x+h)^2+k? I am wondering about that minus sign. I see no particular use of it. Is it there because of tradition or am i missing something?

1. The Problem I am trying to find the feynman rule which corresponds to the addition of an interaction term to the QED lagrangian which couples the electromagnetic field to a neutral massive vector boson field. In this problem, $$k^\mu$$ corresponds to the photon 4-momentum and $$q^\mu$$...

Alright, this is a pretty low level / silly question but I am having some issues. I would like to get the vertex rule for an interaction that has a field tensor involved like this... \partial_\mu Z_\nu -\partial_\nu Z_\mu do I treat the two Z's as separate fields? For a generic field...

Not sure if anyone has any experience with chiral perturbation theory, but I'm trying to see what all of the vertices are for interactions with a single Z boson. I've looked at the lagrangian up to order p^4 so far, and it seems that the Z only interacts with charged pions/kaons. I'm using...

I have a mesh with unstructured triangular grid. I need to find neighboring triangles of each vertex. How can I do it? Thanks before :D

Homework Statement Folks, I wish to construct a quadratic expression from a graph which has the following 2 coordinates. ##(0,0)## and the vertex ##(\alpha h_e,1)## where ##0<\alpha<1## Homework Equations Using the following ##y(x)=a(x-h)^2+k## The Attempt at a Solution...

Hello, I stumbled across the following equation in a presentation about collider physics: tcorrWV =(tiRV - tiWV) + (TOFRV - TOFWV), where tcorrWV is the corrected time for the wrong vertex, tiRV is the initial time of the right vertex, tiRV is the initial time of the wrong vertex...

Look at the page 256. relation (6.93). http://books.google.rs/books?id=vrcHC9XoHbsC&pg=PA256&lpg=PA256&dq=Nolting+spin+product+of+graphs&source=bl&ots=5uRIg5aDIj&sig=sawJYioGHevsuCjxs-NNv_OxSrY&hl=sr#v=onepage&q=Nolting%20spin%20product%20of%20graphs&f=false What is even vertex? Can you...

The Feynman diagram you'd naively draw for a beta decay such as p\rightarrow n + e^++\bar{\nu} would have four lines joined at a vertex, but in reality there's a virtual W or Z involved, which makes it into two 3-vertices. Is there any fundamental reason why all the vertices in a field theory...

I've been scratching my head over this one. I'm trying to find a system of equations to solve for points R and S. The known parameters are: Point Q, tangent vector t and the axis vector a. The following vectors are perpendicular to each other: a,d a,b b,c c,t d,t The other known...

given 3 vectors : a=(1,3,4) b=(2,5,3) c=(1,0,0)

Homework Statement Evaluate \lim_{z \to 0}:e^{ik \cdot X(z)}:|0\rangle where X(z) is a free chiral scalar field in the complex plane. Homework Equations In Conformal Field Theory, the free chiral scalar field in the complex plane is given by: \begin{array}{rcl} X(z) &=& \frac{1}{2}q -...

I am lost and confused. I have been on the same problem for 2 hours. I know all the formulas, but I'm not doing something right...

Points (6,0) and (O,8) are the endpoints of the hypotenuse of a right-angled triangle, whose other vertex is at (x,y). What equation relates x and y?Attempt at solution: So What I am thinking is that the line will be perpendicular to the line with end points 6,0 and 0,8. So The gradient of...

Points (6,0) and (O,8) are the endpoints of the hypotenuse of a right-angled triangle, whose other vertex is at (x,y). What equation relates x and y?Attempt at solution: So What I am thinking is that the line will be perpendicular to the line with end points 6,0 and 0,8. So The gradient of...

Dear Folks: Suppose \Gamma is a discrete subgroup of SL2(R), which acts on the upper half complex plane as Mobius transformation. F is its fundamental domain. If z is a vertex of F which does not lie on the extended real line ( that is R\bigcup\infty ) ,then must x be an elliptic point...

[Closed] Question on the form of a vertex operator in a proof Ok, never mind - I decided to find the solution in a different way.. This is a little too specialized anyway. (Is there a way to delete the thread?) Hi, I am reading paper [1] and I found that formula (33), \psi(xy)\psi^*(y)=\frac...

I have to find the vertex, axis, domain, & range of this quadratic equation: f(x)= -1/2(x+1)^2 -3 I can't remember how to do the vertex. Is it y= -b/2a? Also, I tried factoring the equation, but I think I messed up. I ended up with: f(x)= .25x^2 +.5x-2.75 Thanks

Hi, I am trying to find the last vertex coordinates of a triangle given that Vertex 1 = (2,10) Vertex 2 = (3,6) Angle at Vertex 1 = 75.9638 degrees Angle at Vertex 2 = 70.3462 degrees. I have tried using the equations based on the length of each side, as well as using the cos dot...

Have a look at http://arxiv.org/abs/1202.5039 Degenerate Plebanski Sector and its Spin Foam Quantization Authors: Sergei Alexandrov (Submitted on 22 Feb 2012) Abstract: We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and...

1. Write an equation of the quadratic function f whose graph has x-intercepts 3 and 7 and f(5) = 8. 2. I really don't know where to go from here :frown: 3. obviously, is the x-int. are 3 and 7 that means they are points (3,0) and (7,0). Also, f(5) = 8 becomes the point (5,8) which i have found...

Hi forum, The weak force vertex factor is γu(1-γ5). Am I right that the axial component only couples to left handed fermions? Does the vector component couple to both left and right-handed fermions? Thanks, Mark

Hi there. I did this problem, and I wanted to know if my solution is ok. The problem says: Three equal charges are situated at the vertex of an equilateral triangle, and we want to cancel out the forces exerted by each other. What charge q' of opposite sign should be placed at the center of the...

i.e. thank you very much in advance

hi in "Introduction to Elementary Particles" ed. 2 / David Griffiths the writer states that a bilinear vertex in two different fields is always impossible (my words). or in other words: theoretically we can't have a fundamental vertex with one particle coming in and one going out. and...

Homework Statement Find the equation of a parabola with a vertex of (1,-3) and focus of (1,-1)? Homework Equations The Attempt at a Solution

Homework Statement Can someone assist me with number 3 please... Homework Equations The Attempt at a Solution I went ahead and rewrote f(x) in vertex form in terms of a,b, and c but I'm having a hard time writing down how f can be thought of as a transformation of g.

I just began to read Do Carmo's Differential Geometry book and having breezed through most of the chapter 1, I am finding it difficult to see how the four vertex theorem for a convex figure is proved? Could someone please provide a simple and easy to understand proof?

Anyone know a reference in the literature that computes the correction to the 3 gluon vertex due to a quark loop with non-zero quark-mass?

Homework Statement A regular tetrahedron has the vertices of its base A(1,1,0) B(3,1,0) C(2,1+(3^(1/2),0). Find coordinate of vertex S? Homework Equations The Attempt at a Solution If this is a tetrahedron Then we know the length by caclulating the distance formula, which gives...

I am getting apparently conflicting statements about the conformal transformation law of the vertex operator appearing in and 2D QFT (such as in bosonic string theory). For example, according to http://en.wikipedia.org/wiki/Conformal_field_theory" (eqn 64 on page 15), the transformation law is...

Hi guys, I have a question regarding a point in the QFT book of peskin and schroeder. Iv been working through renormalisation in QED, The 2-point corrections are simple enough, however in this book the 3-point function is a little more involved and I have some issues. Essentially id to...

Homework Statement Find the vertex of the parabola y = (a-b)(a+b) Homework Equations x = -b/2a The Attempt at a Solution This question was extra credit on my Pre-Calc test today. I got the answer and it took almost a page to do it. But I'm very anxious and I just can't wait until i get my...