What is Scalar: Definition and 828 Discussions

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.

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  1. Y

    Solving for Vector & Scalar Potential of a Rotating Line Charge Density

    Homework Statement This is not a home work, I actually make this problem up and work on it. I want to verify whether I am correct in the step and I need help to solve the final integration. The question is: Given a plastic circular ring radius = a with line charge density glued on...
  2. 7

    Exact differential of scalar field

    Suppose I have the scalar field f in the xy-plane and that it is smooth. Its total derivative is given the normal way, i.e. df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy and the gradient of f is given the normal way as well. I read in a paper that, due to the...
  3. L

    Scalar Vector Tensor Decomposition

    My notes are talking about this scalar vector tensor decopmosition business. Unfortunately, they are not online but they seem to follow this wikipedia article fairly closely: http://en.wikipedia.org/wiki/Scalar-vector-tensor_decomposition So our perturbed metric is of the form...
  4. A

    Is This Calculation of Grad \(\psi\) for \(\psi(x,y,z) = (y-1)z^2\) Correct?

    For the following scalar field: \psi(x,y,z) = (y-1)z2 Find grad \psi Here is my attempt at: Multiplying out brackets: yz2 - z2 Therefore grad \psi = 0+Z2 J -2ZK Is this correct??
  5. Y

    Question about retarded scalar potential and Coulomb Gauge.

    This is exact copy from Griffiths Introduction to Electrodynamics 3rd edition page 421. This is regarding to information travel in space. In time varying situation, E depend not only on V, but on A also.
  6. M

    Calculating Vector & Scalar Projection of a & b

    Homework Statement i have to find the scalar and vector projection of a=i-j+k and b=2i-j-2k and i got: Vector proj = (1/3)(i-j+k) = i/3 + j/3 + k/3 scalar proj = (1/9)(2i-j-2k) = 2i/9 - j/9 - 2k/9 is this correct?
  7. D

    Triple scalar product question

    Homework Statement Is it possible to use the triple scalar product to solve anything greater than a 3x3 matrix? Homework Equations Ax + By + Cz + D = 0 The Attempt at a Solution In terms of planes, the triple scalar product can be used to determine if the NORMALS of the planes...
  8. B

    Kinetic Energy and Momentum Scalar

    This is a conceptual problem that I'm sure is pretty common. How can kinetic energy (1/2mv^2) be a scalar quantity when it includes a vector quantity like velocity?
  9. D

    Convert from plane equation to scalar equation

    Homework Statement When we're given an equation in form r = r0 + sa + tb, how do we convert it to scalar form Ax + By + Cz + D = 0? I've been having trouble with plane form, but I can do it fine when its given in 2- or 3-D form.
  10. E

    Electric Scalar Potential and Electric Field Intensity

    Homework Statement A uniform line charge of -4π x 8.85 pCm^-1 is situated between the points (-5,0) and (-2,0) m and another such line of positive charge between (2,0) and (5,0) m. A) Find the electric scalar potential V at (1,0) m. B) Find the electric field intensity E at the same...
  11. B

    Finding scalar equation of a line with a vector and a point given

    I would really appreciate the help, I've been trying to figure this out for the last three hours no joke. Homework Statement Write the scalar equation the line given the normal vector [3,1] and point (2,4) Homework Equations R=[X0,Y0]+ T[M1,M2] The Attempt at a Solution...
  12. S

    Scalar Functions Explained - 65 characters

    scalar functions :( First of all I'm sorry for posting new thread about for this simple topic. I know scalars are quantities that are fully described by a magnitude or numerical values. For example i setx related scalar function and named it f(x) suppose that f(x)=5 and how about if...
  13. 0

    What is the Equation for the Scalar and Vector Products of Two Vectors?

    what can be defined by the following equation? im new to calculus, and I'm totally lost now :(
  14. A

    The scalar partner of Majorana particle in SUSY

    For example, the right-handed sneutrino. It can decay into both (s)leptons and anti-(s)leptons, so it is also the anti-particle of itself. I wonder how it looks like mathematically. If it is the same as normal scalar field, we can still distinguish its anti-particle (the complex conjugate)...
  15. L

    Proof Scalar action is conformally invariant

    Hi, So if we have the Lagrange density for a massless scalar field: L=\sqrt{-g}\left(-\frac{1}{2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi-\frac{(n-2)}{4(n-1)} R\phi^2\right) Then under a conformal transformation g_{\mu\nu}=\omega^{-2}\tilde{g_{\mu\nu}} , then the Ricci sclar goes to...
  16. A

    Puzzle of scalar dynamic in the early universe

    Sometimes we need to calculate the evolution of the scalar field \phi with the equation of motion \frac{\partial^2 \phi}{\partial t^2}+3H\frac{\partial \phi}{\partial t}+m_\phi^2 \phi = 0. And we can get the field \phi=Ae^{im_\phi t} where A is the amplitude of the scalar field (damped by...
  17. E

    Feynman rules of scalar QCD (colour ordered)

    Hey guys, does any of you know where I could find the Feynman rules for scalar QCD? If they where colour ordered, even better! Cheers, earth2
  18. O

    What is the difference between scalar and vector functions?

    Hi all :) can anybody help me out in understanding scalar function and vector function? the difference between them
  19. F

    Scalar particle scattering amplitude

    Homework Statement I have simplified the expression -i\int d^4xie[\phi'^*(\partial_{\mu}A^\mu + A^\mu\partial_\mu)]\phi to -i\int d^4xie[\phi'^*(\partial_\mu\phi) - (\partial_\mu\phi'^*)\phi]A^\mu under the conditions A^0 \rightarrow 0, t \rightarrow \pm \infty |A^i| \rightarrow 0, |x_i|...
  20. L

    Calculating the Effective Action of a Scalar Field Theory

    The effective action Γ[ϕ] for a scalar field theory is a functional of an auxiliary field ϕ(x). Both Γ and ϕ are defined in terms of the generating functional for connected graphs W[J] as W[J] + \Gamma[\phi] = \int d^dx J \phi , \quad \frac{\delta}{\delta J(x)} W[J] = \phi(x) Show - \int...
  21. S

    Is the Defined Complex Scalar Product a Valid Scalar Product?

    Homework Statement This is what we are given in the assignment: Recall a definition of scalar product on complex numbers. Let A = [[3,1],[1,2]]. Prove that the product as defined by: * => dot product u * v := uT * A * conjugate(v) ( = Sum from i,j=1 to 2; uiAijconjugate(vj) )...
  22. J

    Curl of the partial derivative of a scalar

    I have a problem where part of the solution involves taking the Curl of the partial derivative of a scalar. If A is a scalar function, then wouldn't taking the partial derivative of A with respect to time "t" just give another scalar function?
  23. L

    Vector and scalar magnitude problem

    Homework Statement The vector -1.90A has a magnitude of 59.1 m and points in the positive x direction. Calculate the x component of the vector A. Calculate the magnitude of the vector A. Homework Equations 3. The Attempt at a Solution I understand vectors but having a...
  24. T

    Adding Scalar Multiples of Vectors Graphically

    Homework Statement Draw the vector C = 1.5A -3B (Mastering Physics problem) A is 4.5 and B is 1.0 The Attempt at a Solution I've tried it 4 times and still can't do it. I've looked at some sites but I guess I just don't understand it. I've heard of the head to tail method, or something...
  25. F

    Scalar Curvature, R, for Dummies

    Is it possible to explain, in one or two paragraphs, what the scalar curvature, R, is as it applies to General Relativity (the Einstein Field Equation, specifically?). This needs to be understandable to a high school AP-C physics student. Signed, Me - the high school AP-C physics student...
  26. C

    Differentiating the complex scalar field

    Basic question on scalar filed theory that is getting on my nerves. Say that we have the langrangian density of the free scalar (not hermitian i.e. "complex") field L=-1/2 (\partial_{\mu} \phi \partial^{\mu} \phi^* + m^2 \phi \phi^*) Thus the equations of motion are (\partial_{\mu}...
  27. C

    Is the true for any scalar function?

    Homework Statement If \phi depends on a single position only, \phi=\phi(x,y,z) Can I say that: \oint{\frac{\partial\phi}{\partial{x}}dx=\oint{d\phi}=[\phi]_{a}^{a}=0 Provided that the point a lies on the closed path being integrated around? Homework Equations The Attempt at a Solution I...
  28. B

    Integration by parts of a dot product scalar integrand

    Homework Statement Is this true or false? \int_V {\vec \nabla \Phi \bullet {\bf{E'}} \cdot {d^3}x} = \vec \nabla \Phi \bullet {\bf{E'}} - \int_V {\Phi \cdot \vec \nabla \bullet {\bf{E'}} \cdot {d^3}x}
  29. N

    Differentiating the matrix exponential with respect to a scalar

    Homework Statement Let's say A is a 7x7 matrix which is defined as [a b c 0 0 0 0; b a 0 d 0 0 0; c 0 a b e 0 0; 0 d b f 0 e 0; 0 0 d 0 f b g; 0 0 0 d b f h; 0 0 0 0 0 0 0] where semicolon (;) represent a new row and a space is a new column.Homework Equations If y = expm (A*t), where expm...
  30. S

    Lagrangian, scalar or pseudo-scalar?

    Hi, My question is. Can in principle, a Lagrangian density for some theory be a pseudo-scalar. Normally people say that the Lagrangian needs to be a scalar, but it case it is a pseudo-scalar it would also be a eigaen function of the parity operator. This topic could well be on the...
  31. T

    Yukawa [3 Dirac - 8 scalar] interaction lagrangian

    Homework Statement Given an interaction lagrangian L = i \, g \, \bar \psi(x)_i (\lambda^a)_{ij} \gamma_5 \, \psi(x)_j \phi(x)_a where \psi_i are three Dirac fermions with mass M and \phi_a are eight real scalar fields of mass m and \lambda_a are the generators of SU(3). I have to find...
  32. A

    What is the Difference Between Vector and Scalar?

    Hi I was reading a physics book and i came to the part where the started to explain vectors and scalars and i got really confuzzled(confused/puzzled) please help
  33. arivero

    Are there scalar partners for the Z and W particles in massive SUSY multiplets?

    Does anybody remember some reference to models where the Z and W particles are in massive susy multiplets of vector type? Such models should predict, besides the zino and wino, scalar partners for the Z and W, as well as new chiral fermion for each (probably the later should be able to...
  34. D

    Scalar Product of Momentum Eigenvectors in terms of Little Group Representation

    I'm trying to derive the equation for the scalar product of one particle momentum eigenvectors \Psi_{p,\sigma} ( p is the momentum eigenvalue and \sigma represents all other degrees of freedom), in terms of the little group of the Lorentz group with elements W that take the standard four...
  35. S

    Group: most general scalar potential out of 2 doublet irreps of S3.

    Group Theory: Most general scalar potential out of 2 doublet irreps of S3. I'm taking a course on group theory in physics, but the teacher is really bad at making the bridge between the maths and the physics. As homework I have to do the exercise below. I think I know how to do it but I'm...
  36. A

    Exploring the Scalar Gradient and Unit Vectors

    greetings in a scalar gradient why does the unit vector has appeared?scalar gradient only represent the change in that scalar quantity along x,y and z axis.then why unit vector along x, y and z comes in picture? advanced thanks.
  37. S

    No uncertainty principle for scalar particles?

    hi, I do wonder if the Higgs boson is a quantum object because since it is the (only) particle with spin 0, then it should not behave like a wave(since the wave aspect is connected to the fact that it is spinning) and therefore not experience the uncertainty principle. Or am I wrong?
  38. B

    Inverse matrices with scalar multiplication.

    I was surprised that I have never had to do this in so long and forgot the basic way to factor out a scalar multiple when a matrix is raised to a certain power (for example -1 for inverse matrices). Basically, I just want some confirmation: (λT)^n= λ^n (T^n ) ∶ for λ ϵ F and Tϵ L(V)...
  39. S

    The SUSY F and D terms, and the scalar potential

    Hello all. Again, thank you for the help so far. Forgive the lack of tex in this post, it somehow was creating errors no matter what I tried. My question this time involves understanding the F and D terms in SUSY theories. From what I understood, they were introduced as auxiliary fields (EOM...
  40. P

    Understanding Gradient Vector of Scalar Field (grad)

    Dear All I am having trouble understanding the gradient vector of a scalar field (grad). I understand that you can have a 2D/3D space with each point within that space having a scalar value, determined by a scalar function, creating a scalar field. The grad vector is supposed to point in...
  41. N

    Are Scalar Energy Pendants Safe and Effective for Medical Benefits?

    Hello to all, Greetings! i know there are really great minds here in this forum, I just wanted to know if any of you have heard of these scalar energy pendants? are they safe? and what medical benefits do they give? I work in CT and MRI so i know a little bit of physics. from my...
  42. zomgwtf

    Does a speedometer measure a scalar or vector quantity?

    This is a pretty elementary question but I had it on a quiz and it made me think... does a speedometer measure a scalar or vector quantity? I answered that it measures a vector quantity my rational being that it is the instantaneous speed in a forward direction, always. It doesn't matter if...
  43. C

    BRS: Static Axisymmetric Gravitationless Massless Scalar Field Solutions

    BRS: Static Axisymmetric "Gravitationless" Massless Scalar Field Solutions This thread is an (easy and amusing) companion to a previous BRS, "The Weyl Vacuums" www.physicsforums.com/showthread.php?t=378662 I. The Family of "Gravitationless" Solutions I will describe a family of...
  44. K

    Independent solutions of scalar wave equations

    Hi, This has been bothering me for a while now.. The scalar wave equation is a 2nd order differential equation. So we would expect two independent solutions for it. However when you try to find the solution of the scalar wave equation (in spherical coordinates) by employing the separation...
  45. S

    ResourcesHelp|Close Moment of a Force: Scalar Formulation

    Homework Statement A pipe is anchored to a wall at point A. During the pipe's installation, several forces are applied to the pipe at different locations. If F1 = 14.7 lb, F2 = 18.5 lb, F3 = 12.6 lb, F4 = 10.9 lb, d1 = 0.400 ft, d2 = 0.800 ft, and d3 = 0.800 ft, what is MRA, the net moment...
  46. I

    Vectors- scalar products - statements true/false

    Homework Statement 7 statements about vectors. Which two statements are incorrect? Question: A The result of the vector product of two vectors is a scalar quantity. B A vector can have a magnitude of zero. C A vector is completely specified by its magnitude and direction. D Two...
  47. L

    Multivariable Calculus - Scalar projection

    Homework Statement Find the scalar and vector projection of the vector b=(3,5,3) onto the vector a=(0,1,-5) . Homework Equations The Attempt at a Solution What I've tried is multiplying all the i's and j's and k's together and adding up everything because you get a scalar...
  48. D

    Finite differences on scalar? Matrix?

    Hi, In a paper I have v_{n,k} = \Delta^K ( (-1)^n n^k y_n ) with n = K, \dots , N-1, k = 0, \dots, K and N = 2K where \Delta^K is the Kth finite difference operator. As you can see, all v_{n,k} consistute an (N-K) \times (K+1) matrix. So without the \Delta's, each v_{n,k} would be a...
  49. T

    Scalar projection of b onto a (vectors)

    Homework Statement If a = <3,0,-1> find the vector b such that compaB = 2 Homework Equations None. The Attempt at a Solution |a| =\sqrt{3^2 + 1^2} = \sqrt{10} compaB = \frac{ a\cdot b}{|a|} 2 = \frac{3(b1) - 1(b3)}{\sqrt{10}} 2\sqrt{10} = 3(b1) - 1(b3) I don't know...
  50. P

    How do I determine the minus sign in gauge transformations?

    \vec{B}=rot\vec{A} \vec{E}=-\frac{\partial\vec{A}}{\partial t}-grad\varphi If I define \varphi=\widetilde{\varphi}-\frac{\partial f}{\partial t} \vec{A}=\widetilde{\vec{A}}+gradf where f=f(x,y,z,t) I will get \vec{B}=rot\vec{A}=rot\vec{\widetilde{\vec{A}}}...
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