Scalar Definition and 777 Threads

Homework Statement Show that [\hat{\phi}(x_1),\hat{\phi}^\dagger(x_2)] = 0 for (x_1 - x_2)^2 < 0 where \phi is a complex scalar field Homework Equations \hat{\phi}=\int\frac{d^3 \mathbf{k}}{(2\pi)^3 \sqrt{2\omega}}[\hat{a}(k)e^{-ik\cdot x} + b^\dagger(k)e^{ik\cdot x}]...

Homework Statement I'd like to figure out the moment at pt A using the scalar approach, not vector Homework Equations Vector M = r x f Scalar M = fd The Attempt at a Solution I think I might be missing some concept that would make my life easier... I figured out how to...

Hello, I am confused how vectors that are coplanar will give a triple product of zero? Or is it the case that all 3 vectors must be coplanar for a triple product of zero, or is 2 sufficient? I.e. the vector being dotted with one of the vectors being crossed in the same plane, will this...

equipotential surface / electric scalar potential problem (why!) Homework Statement A potential field is given by V = 3x^2*y - y*z. Is the following statement valid? "A unit normal to the equipotential surface V = -8 at P(2,-1,4) is <-0.83,0.55,0.07>"Homework Equations Gradient of a scalar...

"scalar gravity" -Feynman lectures on gravitation Hi all, I'm trying to understand the following claim from Feynman's lectures on gravitation, section 3.1 (p.30 in my edition). He's considering how heating or cooling two clouds of gas would change their mutual gravitational attraction. I...

I read that scalar matrices are the center of the ring of matrices. How would I prove this? Tips are appreciated. It is already obvious that scalar matrices commute with all matrices, but the converse seems tricky. BiP

I've been wrestling with this for a few days (not literally). I got confused because I read in a book that E = - ∇ \phi where E is the electric field and \phi is the scalar potential. However in my notes I had that for a conservative force F = -∇\phi. I got confused because electric force and...

In the equation x = vt it is generally accepted that x and v are vectors and that they have a common eigenvector. Each vector is the product of a scalar and a unitary eigenvector. Dividing both sides by v works because in x/v = t the x and v vectors have identical and canceling eigenvectors...

Sorry for reopening a closed thread. But I have exactly the same doubt as this guy: https://www.physicsforums.com/showthread.php?t=346730 And the answer doesn't actually answer his question. I do get delta(p+p'), but they just help me in getting a_{p}a_{-p} and a_{p}^{\dagger}a_{-p}^{\dagger}...

Homework Statement Problem 7.15 from Aitchison and Hey, Volume I, 3rd Edition. Verify the forum (7.139) of the interaction Hamiltonian \mathcal{H_{S}^{'}}, in charged spin-0 electrodynamics. Equation 7.139 is \mathcal{H_{S}^{'}}= - \mathcal{L}_{int} - q^2 (A^0)^2 \phi^{\dagger} \phi...

Homework Statement I am studying inflation theory for a scalar field \phi in curved spacetime. I want to obtain Euler-Lagrange equations for the action: I\left[\phi\right] = \int \left[\frac{1}{2}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi + V\left(\phi\right) \right]\sqrt{-g} d^4x Homework...

momentum, position vector dot (scalar) product "action" Hello, I was playing with single mass point classical mechanics, when I realized that the dot product of the position vector and momentum vector, p.r , has action dimension. Furthermore, its time derivative, d/dt(p.r) = F.r + p.v, has...

First I didn't know where to open new tread, so I open hear, if I put in wrong section please teach me where is the write place. As amateur in Physics I saw somewhere that with scalar waves you can communicate in transmitter-receiver way of course if resonance between t-r is good. Can we, and...

Homework Statement Let V be the real vector space of all real symmetric n × n matrices and define the scalar product of two matrices A, B by (Tr (A) denotes the trace of A) Show that this indeed fulfils the requirements on a scalar product. Homework Equations Conditions for a scalar...

Homework Statement Consider the vector space of continuous, complex-valued functions on the interval [−∏, ∏]. Show that defines a scalar product on this space. Are the following functions orthogonal with respect to this scalar product? Homework Equations The Attempt at a...

Homework Statement Find the equation of scalar curvature for homogenous and isotropic space with FLRV metric. Homework Equations ## R=6(\frac{\ddot{a}}{a}+\left( \frac{\dot{a}}{a}\right )^2+\frac{k}{a^2}) ## The Attempt at a Solution ##G_{AB}=R_{AB}-\frac{1}{2}Rg_{AB}##

Hello! Im currently reading Ryder's QFT book and am confused with the variation of a scalarfield. He writes that the variation can be done in two ways, \phi(x) \rightarrow \phi'(x) = \phi(x) + \delta \phi(x) and x^\mu \rightarrow x'^\mu = x^\mu + \delta x^\mu. This seems...

hi why only scalar cam build with second order of derivative of metric is Ricci scalar? thanks

I have been trying to get my head around this topic for a while. As I go through the description of scalar fields, the inflation and the potential inflaton, (in description as in ned.ipac.caltech.edu), I constantly miss a concept. There must be a fundamental difference between the type of...

Say ##V_{out}=4e^{j\frac {\pi}{6}}##, what is this mean? It is a scalar voltage. Does this means: 4e^{j\frac {\pi}{6}}=4\left(\cos \frac {\pi}{6}+j\sin \frac {\pi}{6}\right) = 4(0.866+j0.5) = 3.4641+j2=4\angle 30^o What is the phase shift means, reference to input? Thanks

hello Can you perhaps explain what does the Riemann curvature scalar R measure? or is just an abstract entity ? What does the Ricci tensor measure ? I just want to grasp this and understand what they do. cheers, typo: What DO they measure in the title.

Hello, I am a 15 year old high school student, We were being taught about current, My teacher said its a scalar quantity, I had a doubt on that that since wires bound the charges, we shouldn't say that since wire's orientation doesn't change the magnitude of current, its Scalar quantity. For...

Hello. I don't know how to prove that a certain function is a solution to the scalar wave equation in cylindrical coordinates. The scalar wave equation is \left(\nabla^2+k^2\right)\,\phi(\vec{r})=0,which in cylindrical coordinates is...

hello For the same Friedmann metric, Landau (Classical theory of fields) finds a value for the Riemann curvature scalar which is given in section 107 : R = 6/a3( a + d2(a)/dt2) whereas in MTW , in box 14.5 , equation 6 , its value is : R = 6(a-1 d2(a)/dt2 + a-2 (1 + (d(a)/dt)2 ) ) The...

Im having trouble understanding this property my book states that: a.(bxc) = b.(cxa) = c.(axb) it also states that a.(ax(anything)) = 0 I understand the second point and why that's true, what I don't understand is why a.(bxc) = b.(cxa) = c.(axb) is true If I name any 3 vectors a b...

1.a. Show that ∇F[u(x,y,z),v(x,y,z)] = Fu∇v + Fv∇u 1.b. Show that a necessary and sufficient condition that u and v are functionally related by the equation F(u,v) = 0 is ∇u x ∇v = 0 Homework Equations ∇ = \frac{\partial}{\partial x}\widehat{i} + \frac{\partial}{\partial y}\widehat{j} +...

Homework Statement Hi. This one I really am lost on :/ In my mind it seems rather easy, but I still can't figure it out. I have been given the E-field: \mathbf{E}\left( t,\,\,\vec{r} \right)=\frac{\kappa }{{{\varepsilon }_{0}}}\left[ \begin{matrix} ctx+{{x}^{2}}-{{y}^{2}} \\...

One can show that at around ##p \approx m## where m is the physical mass the full propagator ##D_F## is something like $$D_F = \frac{Z}{p^2 - m^2}.$$ Where ##Z = (1 - \Sigma '(m))^{-1}##, ##\Sigma## is the self energy and m is the physical mass of the particle. If i were now to write a...

Is there conventional terminology to distinguish between scalars that transform between frames and those that don't? For example, energy is a single-component quantity but it isn't the same in every frame, whereas the length of a vector is also a scalar but is the same in every frame. Do we just...

I am not able to understand how to go about this problem: Find the minimum mean square estimator for the scalar parameter w based on the scalar observation z = ln w + n where f(w) =1 if 0<=w<=1; 0 else: and f(n) =e^-n if n>= 0; 0 else I did f(z/w) = (f(n))...

Homework Statement Given the vectors: P = 8i +5j-Pzk m and Q = 3i -4j-2k m Determine the value of Pz so that the scalar product of the two vectors will be 60m2Homework Equations Sure seems like we will need to use the following equation: P * Q = |P| * |Q| * cos ∅ But I don't recall being able...

as i understand it the higgs field is a spin-0 scalar field that gives mass to elementry particles. How is it a scalar field? I thought it was homogenous.

Homework Statement The following is a passage from a quantum mechanics textbook: "We find empirically that the electron behaves like a simple scalar wave (i.e., not like a vector wave, such as electric field, E, but like asimple acoustic [sound] wave with a scalar amplitude; in acoustics...

Where should I start from to show that curvature scalar (RiemannScalar) is 2\frac{R_1212}{det (g_μ√)} ?

Homework Statement Let M2 denote the set of all 2x2 matrices. We define addition with the standard addition of matrices, but with scalar multiplication given by: k \otimes [a b c d] = [ka b c kd] (note that they are matrices) Where k is a scalar. Which of the...

This is a really basic question, but... Say I have a massive scalar field obeying the Klein-Gordon equation linearized about flat space, \partial_t^2 \phi + (k^2 + m^2)\phi = 0. This has solutions \phi \sim e^{\pm \sqrt{k^2 + m^2}t} and the sound speed should be \omega_k/k =...

Homework Statement Determine the vector(s) whose vector projection on u =< 1,2,2 > is v =< 3,6,6 > and its scalar projection on w =< 1,1,1 > is √3. Homework Equations Vector Projection of b onto a: (|b.a| \ |a|) * (1/ |a|) * a Scalar Projection: (|b.a| \ |a|) The Attempt at a...

Homework Statement a dot (b-c)* (a dot b) x c (a-b) x c Which results would yield a scalar, vector, or none? The Attempt at a Solution Please give me some guidance, I know that a dot product produces a scalar and a cross product yields a vector but what about the addition and subtractions?

Hi can I just check that i haven't done anyhting foolish here whe quantising the scalar field; \ddot{\phi} - \frac{1}{a^2}\nabla \phi + 3H\dot{\phi} - 3\frac{H}{a^2}\nabla \phi + m^2 \phi with \phi = \int \frac{d^3 K}{(2\pi)^{\frac{3}{2}}}(\chi \exp(+ikx) +\chi \dagger \exp(-ikx))...

According to Carroll, \nabla \phi is covariant under rotations. This really confuses me. For example, how could equations like \vec{F}=-\nabla V be rotationally covariant if force is a contravariant vector? I know this is strictly speaking more of a mathy question, but I still figured this...

what is flux...?? is it a scalar or a vector and difference bet flux and flux density i have read the articles where the flux (either in case of electric flux or magnetic )is described as the no of lines passing through a surface area ( open in case of magnetic characterized by boundary and...

Hi All, I'm trying to solve the following derivative with respect to the scalar parameter \sigma $$\frac{\partial}{\partial \sigma} \ln|\Sigma|,$$ where \Sigma = (\sigma^2 \Lambda_K) and \Lambda_K is the following symmetric tridiagonal K \times K matrix $$ \Lambda_{K} = \left(...

Here and there I come across the following formula for the Lagrangian density of a real scalar field, but not a deriviation. \mathcal{L} = \frac {1}{2} [ \dot \phi ^2 - ( \nabla \phi ) ^2 - (m \phi )^2 ] Could someone show me where this comes from? The m squared term in particular...

"Del" operator crossed with a scalar times a vector proof Homework Statement Prove the following identity (we use the summation convention notation) \bigtriangledown\times(\phi\vec{V})=(\phi \bigtriangledown)\times\vec{V}-\vec{V}\times(\bigtriangledown)\phi Homework Equations equation for...

"Quantum" gravity -- Planck's constant as a scalar field? I was just reading about a fascinating new theory on the solution to the quantum gravity problem: http://arxiv.org/pdf/1212.0454.pdf I really like it, but I have one big problem with it: The author states that G = \frac{\hbar...

Homework Statement I didn't really know if this belonged here or in the math section but it is from a physics book so what the heck =D. I have to show that the directional derivative of the ricci scalar along a killing vector field vanishes i.e. \triangledown _{\xi }R = \xi ^{\rho...

I know that the electric flux is a scalar quantity, but the concept of the Electric flux seems to confused me. If the electric flux density is a vector quantity, how come the electric flux is a scalar quantity? For example, I have the electric flux density: D=20i+2j. Isn't it means...

Homework Statement For some scalar field f : U ⊆ Rn → R, the line integral along a piecewise smooth curve C ⊂ U is defined as \int_C f\, ds = \int_a^b f(\mathbf{r}(t)) |\mathbf{r}'(t)|\, dt where r: [a, b] → C is an arbitrary bijective parametrization of the curve C such that r(a) and r(b)...

Hi. Let's say we have a complex scalar field \varphi and we separate it into the real and the imaginary parts: \varphi = (\varphi1 + i\varphi2) It's Lagrangian density L is given by: L = L(\varphi1) + L(\varphi1) Can you tell the argument behind the idea that in summing the densities of...

Scalar multiplying a set?? Homework Statement Let A and B be two finite non-empty sets such that A \subset B and n({C : C \subset B\A}) = 128. Then what is the value of n(B) - n(A)? Homework Equations The Attempt at a Solution I actually got to 7 by assuming that n was...