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.

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

    Relation between bare and full scalar booson propagator.

    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...
  2. C

    Scalar Definition: Transformations & Frames

    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...
  3. S

    Finding the Minimum Mean Square Estimator for Scalar Parameter w

    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))...
  4. S

    Physics: Vectors & their scalar product

    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...
  5. P

    Why is the Higgs field a scalar field?

    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.
  6. S

    Passage regarding vector and scalar waves

    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...
  7. G

    Why is scalar product of momentum in electron scattering conserved?

    Homework Statement Reading a textbook, I come across a situation where an electron is scattered off a nucleus. The book says p.P = p'.P', where p is the momentum of the electron and P is the momentum of the nucleus. I don't understand how it gets the conservation of scalar product. It's steps...
  8. ssamsymn

    Calculating RiemannScalar in 2-D: Where to Start

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

    Linear Algebra- Scalar Multiplication

    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...
  10. R

    Why don't scalar fields propagate superluminally?

    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 =...
  11. U

    Finding a vector using scalar and vector projections

    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...
  12. S

    Vector Scalar or Not Applicable?

    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?
  13. Mordred

    Inflationary model with exact scalar

    In my research into inflationary models I happened upon this article. http://arxiv.org/abs/1112.3005 I would like opinions and related articles pertainig to this one including any that specifically counter this article. I am not after personal opinions of inflationary models in general...
  14. P

    Is This the Correct Method for Quantizing the Scalar Field?

    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))...
  15. D

    How can the gradient of a scalar field be covarient?

    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...
  16. S

    What Is Flux? Scalar or Vector? Difference Between Flux and Flux Density

    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...
  17. F

    Derivative of Log Determinant of a Matrix w.r.t a scalar parameter

    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(...
  18. snoopies622

    Seeking derivation of real scalar field Lagrangian

    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...
  19. O

    Complex scalar field propagator

    i am trying to understand how to express contractions of field operators via propagators. we are talking about an interacting theory of 2 complex scalar fields, lets call them ψ1 and ψ2. the interaction term is: Lint=λ(ψ2)^3(ψ1) i have found the free propagator defined as...
  20. G

    Del operator crossed with a scalar times a vector proof

    "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...
  21. soothsayer

    Quantum gravity - Planck's constant as a scalar field?

    "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...
  22. WannabeNewton

    Direction derivative of Ricci scalar w.r.t. killing field

    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...
  23. O

    Electric flux, vector or scalar?

    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...
  24. R

    Line Integral of Scalar Field Along a Curve

    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)...
  25. T

    Lagrangian density for a complex scalar field (classical)

    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...
  26. V

    How Do You Calculate the Difference in Cardinalities of Sets A and B?

    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...
  27. K

    The scalar product of 4-vectors in special relativity

    Homework Statement I'm confused about the difference between the following two statements: \mathbf{V_1}\mathbf{V_2}=V_1V_2\cosh (\phi) and \mathbf{V_1}\mathbf{V_2}=\gamma c^2 Where \gamma is the Lorentz factor of the relative speed between the two vectors. Both vectors are time-like. The...
  28. S

    Feynman Factors & Relativistic Scalar Propagator

    Hey again, I have a question on a couple of things related to feynman diagrams but also the relativistic scalar propagator term. First of all, this interaction: The cross represents a self-interaction via the mass and characterised by the term: -im^2, is this just some initial state...
  29. B

    Scalar product square matrix hermitian adjoint proof

    Homework Statement If M is a square matrix, prove: (A, MB) = (adj(M)A, B) where (A, MB) denotes the scalar product of the matrices and adj() is the adjoint (hermitian adjoint, transpose of complex conjugate, M-dagger, whatever you want to call it!) Homework Equations adj(M)=M(transpose of...
  30. D

    Up+Down Scalar Meson: Isospin SU(3) & Low Energies

    Why is there no meson made up by only up and down quarks but even under parity? Is there something that forbids its existence? The pions are all axial (pseudoscalar) mesons. As we go higher in energy, there are such "flavour-pure" mesons. Is this a consequence of the almost-unbroken isospin...
  31. S

    Ricci scalar and curveture of FRW metric

    hi we know that our universe is homogenous and isotropic in large scale. the metric describe these conditions is FRW metric. In FRW, we have constant,k, that represent the surveture of space. it can be 1,0,-1. but the the Einstan Eq, Ricci scalar is obtained as function of time! and this...
  32. A

    Deriving charge for Noether current in free complex scalar field QFT

    Homework Statement Hi I a attempting to derive the expression for the conserved Noether charge for a free complex scalar field. The question I have to complete is: " show, by using the mode expansions for the free complex scalar field, that the conserved Noether charge (corresponding to complex...
  33. X

    Is Work a Scalar Quantity Despite Being Composed of Vectors?

    Why Work Is Scalar Quantity ?? I'm wondering that Why is work a scalar quantity ? Since it is the product of the force and displacement which are both vector?
  34. B

    Triple scalar product/coplanarity of

    Homework Statement Suppose that a,b,c are nonparallel nonzero vectors, and that ( a \times b) \cdot c = 0 . Show that c is expressible as a linear combination of a and b. Avoid geometric arguments (that is, try to stick to vector algebra and symbols in the proof).Homework Equations The Attempt...
  35. M

    Wick rotation, scalar field and invariants

    One point about Wick rotation is puzzling me and I can not find explanations in books. It concerns the invariants formed from scalar product and solutions to equation. So I will expose my way of reasoning to let you see if it is correct and at the end ask more specific questions. Let's start...
  36. G

    Double contraction of curvature tensor -> Ricci scalar times metric

    Double contraction of curvature tensor --> Ricci scalar times metric I'm trying to follow the derivation of the Einstein tensor through double contraction of the covariant derivative of the Bianchi identity. (Carroll presentation.) Only one step in this derivation still puzzles me. What I...
  37. K

    Scalar fields/ Scalar functions / Vector fields / Vector functions

    I know that physically, they describe relationships whereby, for instance a vector field, for each point in three dimensional space (a "vector"), we have a "vector" which has a direction or magnitude. Now I once asked what the difference between a vector field and a vector function is and the...
  38. B

    Scalar product in spherical coordinates

    Hello! I seem to have a problem with spherical coordinates (they don't like me sadly) and I will try to explain it here. I need to calculate a scalar product of two vectors \vec{x},\vec{y} from real 3d Euclidean space. If we make the standard coordinate change to spherical coordinates we can...
  39. M

    Why Can Tangential Acceleration Vector's Scalar Component Not Be Negative?

    we already know that the scalar component of the Centripetal ( Radial ) Acceleration vector is always negative because it's ALWAYS directed to the opposite direction of its unit vector ( toward the center of the circle ) , and this is satisfying to me and to the formula . however , when it...
  40. Y

    Divergence Theorem: Multiplied by Scalar Field

    Homework Statement Homework Equations Definitely related to the divergence theorem (we're working on it): The Attempt at a Solution I'm a bit confused about multiplying a scalar field f into those integrals on the RHS, and I'm not sure if they can be taken out or not. If they can be, I...
  41. B

    Is Energy Scalar or Vector, and How Does Dimensionality Affect It?

    Someones like teachers in my country says energy is vector and scalar . Is that true ? Anyone can prov that ?
  42. E

    Finding volume using the triple scalar product (vector calculus))

    Of the 3 vectors, does it matter what order I cross / dot them? <a \times b> \bullet c =? <a \times c> \bullet b
  43. D

    Fortran Divide an Array into a Scalar in FORTRAN: Get Help Here!

    How can i divide elements of an array into a scalar. I mean, i have read my data file into a matrix in FORTRAN which this matrix is 1*3414. Then, I want that each elements of this matrix is divided to (24480*2). I will be so grateful if you guide me the appropriate function. Thanks a lot
  44. I

    Transformation properties of derivative of a scalar field

    Hi all, I'm a part III student and taking the QFT course. The following seems "trivial" but when I went and asked the lecturer, the comment was that they too hate such nitty gritty details! The problem is page 12 of Tong's notes: http://www.damtp.cam.ac.uk/user/tong/qft/one.pdf All...
  45. iVenky

    Laplacian is vector or scalar?

    Here's the link that I read for Laplacian- http://hyperphysics.phy-astr.gsu.edu/hbase/lapl.html It looks as if the laplacian is scalar but the point is we know that ∇x∇xA= ∇(∇.A) - ∇2A This means that laplacian should be vector in nature which contradicts what was given in the link...
  46. M

    Potential energy, Is energy a constant scalar value?

    Hello everyone, Does everything in the universe have potential energy? I know there are two main form's of energy that are showen every day... Motion KE and potential energy and I believe all physical object's have PE and some are in KE even if they lose that motion they will return back to PE...
  47. 8

    Scalar product to prove triangle inequality?

    Homework Statement From the inequality |a.b| <= |a||b| prove the triangle inequality: |a+b| <= |a| + |b| Homework Equations a.b = |a|b| cos theta The Attempt at a Solution Making a triangle where side c = a+b. Don't know how to approach the question. Thanks.
  48. B

    Proving angle sum trig identies w/ vector and scalar products

    Homework Statement I need to prove both of these (in exercise 11) http://postimage.org/image/x7shxv11f/ Homework Equations The dot product The Attempt at a Solution
  49. F

    Magnetic scalar potential for a toroidal ferromagnetic core

    Homework Statement Given a toroidal core, with known μr, minor radius R1, major radius R2, height h (the section is not a circle, but a rectangle (R2-R1)×h), placed in a magnetic field B0 with cylindrical axisymmetries (B0r=0, B0θ=0, B0z=B0), find the magnetic field resulting by the...
  50. J

    Sum of Two Vectors: Magnitude & Scalar Product

    Homework Statement If the magnitude of the sum of two vectors is less than the magnitude of either vector, then: -the vectors must be parallel and in the same direction -the scalar product of the vectors must be negative -none of these -the scalar product of the vectors must be...
Back
Top