Scalar Definition and 829 Threads

In mathematics and physics, a scalar field or scalar-valued function associates a scalar value to every point in a space – possibly physical space. The scalar may either be a (dimensionless) mathematical number or a physical quantity. In a physical context, scalar fields are required to be independent of the choice of reference frame, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory.

View More On Wikipedia.org
Recent contents Top users
  1. I

    Correct my simple error (property of scalar multiplication)

    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...
  2. J

    Point particle in scalar potential

    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...
  3. K

    Is scalar in adjoint representation always real

    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,
  4. N

    Magnetic scalar and vector potential

    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?
  5. N

    What is the Lagrangian of interaction of photon and spin zero scalar?

    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...
  6. D

    Question on derivatives of Hermitian conjugate scalar fields

    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...
  7. K

    The interpretation of noether currents in scalar QED

    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...
  8. PsychonautQQ

    Scalar Surface Integral over parameterized surface

    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 =...
  9. D

    Is it a scalar product? I'm kind of lost

    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...
  10. H

    Math Methods: help with scalar product properties.

    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...
  11. P

    Explicit form of scalar propagator

    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...
  12. O

    Why is Energy a Scalar? A Simple Explanation

    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.
  13. B

    Evaluating Scalar Field in Spherical Coordinates

    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...
  14. Ace10

    Complex scalar field propagator evaluation.

    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> =...
  15. F

    MHB Defining Real-Valued Scalar Product in Vector Spaces

    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...
  16. P

    What is the equation for the amplitude of scalar perturbations ?

    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...
  17. T

    Computing a discrete surface integral of a scalar function

    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...
  18. P

    Scalar product used for length?

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

    MHB Proving span of a Set with Scalar attached to First Element

    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 $Span\{u_1,u_2,...,u_t\}=Span\{ku_1,u_2,...,u_t\}$
  20. H

    Solutions to equations of motion for free scalar field

    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...
  21. F

    Tensor Notation for Triple Scalar Product Squared

    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...
  22. D

    How Do Scalar Magnetic Potentials Relate to Cylindrical Fields?

    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...
  23. E

    Lorentz Invariance of Propagator for Complex Scalar Field

    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}]...
  24. W

    Easy 3d Moment with Couples question, Scalar approach.

    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...
  25. M

    Is the Triple Scalar Product Always Zero?

    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...
  26. FOIWATER

    Equipotential surface / electric scalar potential problem (why )

    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...
  27. M

    Scalar gravity -Feynman lectures on gravitation

    "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...
  28. B

    Proving the scalar matrices are the center of the matrix ring

    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
  29. D

    MHB Gradient and scalar function question

    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 &=...
  30. D

    Can you miss out a factor in scalar potential?

    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...
  31. J

    Does relativity change the rules for time being a vector or a scalar?

    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...
  32. G

    Total momentum operator for free scalar field

    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}...
  33. A

    Interaction Hamiltonian of Scalar QED

    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...
  34. R

    Scalar field lagrangian in curved spacetime

    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...
  35. M

    Momentum, position vector dot (scalar) product action

    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...
  36. O

    Exploring Scalar Wave Communication

    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...
  37. U

    Trace of Matrix Product as Scalar Product

    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...
  38. U

    Prove scalar product of square-integrable functions

    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...
  39. E

    Solving Scalar Curvature for Homogenous & Isotropic FLRV Metric

    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}##
  40. K

    The variation of a scalar field (from Ryder's QFT book)

    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...
  41. S

    Why is Scalar Cam Built with Second-Order Derivative of Metric Ricci Scalar?

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

    Early Universe scalar field, inflaton and analogies in electric field

    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...
  43. L

    Transformation question; first order shift of a scalar field

    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...
  44. Y

    What is scalar voltage potential with phase shift means?

    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
  45. Z

    Riemann curvature scalar, Ricci Scalar.What does they measure ?

    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.
  46. A

    Current vector or scalar different in different books

    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...
  47. IridescentRain

    Solution to the scalar wave equation in cylindrical coordinates

    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...
  48. Z

    Riemann Curvature Scalar Differs in Landau & MTW

    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...
  49. P

    Understanding Triple Scalar Product and Its Properties: Explained Simply

    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...
  50. B

    Showing scalar functions u(x,y,z) and v(x,y,z) are related

    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} +...
Back
Top