Scalar Definition and 829 Threads

say i have some vector ##\vec{v}## multiplied by a scalar k. the norm of ##\vec{v}## would be just ##||\vec{v}||## and the norm of ##k\vec{v}## is claimed to be ##|k|||\vec{v}||## ie, ##||k\vec{v}||=|k|||\vec{v}||## ie the sign of the constant is irrelevant. when i work it out...

What happens to a particle in a scalar potential U(t,x)? I have been living under a belief that the equation of motion would be \frac{d}{dt}\frac{m\dot{x}(t)}{\sqrt{1- \frac{\|\dot{x}(t)\|^2}{c^2}}} = -\nabla_x U(t,x(t)) but I just proved that this isn't Lorentz invariant, and therefore...

This is a short question. I don't know why, but somehow I have the impression that scalar in adjoint representation should be real. Now I highly doubt this statement, but I have no idea how to disprove it. Can anyone give me a clear no? Thanks,

Mathematically, Scalar V_m Magnetic Potential is given by \overline{H}=∇V_m and Vector Magnetic Potential \overline{A} is given by \overline{B}=\overline{∇}X\overline{A} Is there any way I can explain it or define it in words?

What is the Lagrangian of interaction of photon and spin zero charge scalar?The vertex of photon and spin 1/2 charge fermion is proportional with e multiplied vertor gamma matrix,but I do not know what is the vertex of photon and charge scalar.I hear that a vertex is proportional with polynomial...

Hi, I know this question may seem a little trivial, but is there any real difference between \left (\partial_{\mu} \phi \right)^{\dagger} and \partial_{\mu} \phi^{\dagger} and if so, could someone provide an explanation? Many thanks. (Sorry if this isn't quite in the right...

In scalar QED, there are two noether currents ##J_{global}## and ##J_{local}##corresponding to the global and local gauge transformations respectively. In QED, the two currents are exactly the same. But in scalar QED, they are totally different. $$J_{global}^\mu=i e (\phi^\dagger...

Homework Statement Calculate ∫∫ f(x,y,z)dS for the surface G(r,θ) = (rcosθ,rsinθ,θ), 0<r<1, 0<θ<2pi. f(x,y,z) = (x^2+y^2)^(1/2) = r Homework Equations The Attempt at a Solution so the surface is given so I have to find the normal vector... G_r = cos(θ),sinθ,0 G_θ =...

The Vector A points 17° counterclockwise from the positive x axis. Vector B lues in the first cuadrant of the xy plane. The magnitudes of the cross product and the dot product are the same: i.e, |AXB|= |A(times)B| What Angle does B make with the positive x axis? 2. Is ti a scalar...

Homework Statement For what values of k is (scalar product of vectors a and b) = a_{1}b_{1}-a_{1}b_{2}-a_{2}b_{1}+ka_{2}b_{2} a valid scalar product? The vectors a and b are defined as: a = a_{1}e_{1} + a_{2}e_{2} b = b_{1}e_{1} + b_{2}e_{2} where e_{1} and e_{2} are unit vectors...

Hi! I have encountered a little problem. I want to show that the explicit form of the Feynman propagator for massless scalar fields is given by: \begin{align} G_F(x) & = - \lim_{\epsilon \to +0} \int \dfrac{\mathrm{d}^{4}k}{(2 \pi)^{4}} \dfrac{1}{k^{2} + i \epsilon} \mathrm{e}^{- i k...

I am having trouble understanding why energy is a scalar. (1/2 mv^2, mgh, 1/2kx^2, etc). Can someone just briefly hit over why? I tried asking a few people but I still don't get it. Thanks.

Homework Statement Evaluate the scalar field ##f(r, \theta, \phi)= \mid 2\hat{r}+3\hat{\phi} \mid## in spherical coords. Homework Equations Law of Cosines? ##\mid \vec{A} + \vec{B} \mid = \sqrt{A^2+B^2+2ABCos(\theta)}## The Attempt at a Solution I'm not sure the law of cosines...

Good afternoon fellow scientists,i have a small problem in evaluating the propagator for the complex Klein-Gordon field. Although the procedure is the one followed for the computation of the propagator of the real K-G field, a problem comes up: As known: <0|T\varphi^{+}(x)\varphi(y)|0> =...

Hi, can somebody help me with the problem: Suppose that in a vector space over field of real numbers a positive defined norm is defined for each vector which satisfies the triangle inequality and ||aU||=|a|*||u||. Show that a real valued scalar product can de defined as follows...

What is the "equation for the amplitude of scalar perturbations"? I am studying inflation now, and in a book I read "equation for the amplitude of scalar perturbations", in the paper the author does not explain what is it, could anyone give some detail on this equation or any reference? Thanks...

Consider a triangulated discrete manifold (a polyhedron) with known vertices (i.e. each vertex is given in terms of its $$(x,y,z)$$ coordinates ). Assign scalar values (some kind of potentials) to each vertex (i.e. at each vertex, a $$k_t(\mathbf{v})$$ is known through its value, no...

I got asked how the scalar product can be used to find the length of a vector? Could someone please explain

hi Guys, i Needed your help to prove out the following, thanks in advance; Let u1,u2,...,ut be vectors in $\Re^n$ and $k\in\Re ,k\neq0.$ Prove that $Span\{u_1,u_2,...,u_t\}=Span\{ku_1,u_2,...,u_t\}$

I hope this fits this section. This doesn't all fit into the title, but this comes from a homework on conformal field theory, and I am slightly stumped on it. I just can't seem to get anything sensible out of it at the end, but it may be because I've just done something wrong (even though I've...

Homework Statement Hi all, Here's the problem: Prove, in tensor notation, that the triple scalar product of (A x B), (B x C), and (C x A), is equal to the square of the triple scalar product of A, B, and C. Homework Equations The Attempt at a Solution I started by looking at the triple...

Hello, I'm really stuck, I don't know how to start ! Homework Statement In the regions where Jl=0, we have ∇x H=0, so we can introduce a magnetic scalar potential Vm such as H=-∇Vm. A long cylinder of radius R of linear magnetic material of permeability μr. The cylinder axis is in z...

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 am trying to determine my scalar function \(f(u_1, u_2, u_3)\) of elliptical cylindrical coordinates. \begin{align*} x &= a\cosh(u)\cos(v)\\ y &=...

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...

Hi to all! I have the following transformation \tau \to \tau' = f(\tau) = t - \xi(\tau). Also I have the action S = \frac{1}{2} \int d\tau ( e^{-1} \dot{X}^2 - m^2e) where e = e(\tau) . Then in the BBS String book it says that $$ {X^{\mu}}' ({\tau}') = X^{\mu}(\tau)$$ and...

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} +...