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. B

    Computing Scalar Product in Antisymmetric Fock Space w/ Creator Operators

    We use the antisymmetric Fock space ( "fermions"). We denote by c(h) a creator operator. I need to evaluate the following quantity: < \Omega , \big(c(h_1)+c(h_1)^{*}\big)\big(c(h_2)+c(h_2)^{*}\big) \ldots \big(c(h_n)+c(h_n)^*\big)\Omega> where \Omega is the unit vector called vaccum...
  2. I

    Basic Statics problem with scalar components and force

    Homework Statement Determine the scalar components Ra and Rb of the force R along the nonrectangular axes a and Also determine the orthogonal projection Pa of R onto axis a. Homework Equations n/a The Attempt at a Solution I tried setup rectangular coordinate but that didn't work...
  3. N

    Scalar field theory - Feynman diagrams and anti-particles

    I'm working on a "draw all possible Feynman diagrams up to order 2" problem for a scalar field that obeys the Klein-Gordon equation, and I'm wondering about a few things. When I did a course on particle physics and was first introduced to Feynman diagrams in the context of QED (but not QED...
  4. P

    Understanding Scalar, Vector and Distance Terms

    Could you please help me understand how these terms relate to one another? Scalar, Vector, Displacement, Distance, Speed, Velocity, Accelaration, Position? So Distance is a scalar Quantity, what is a Scaler? Displacement is a vector quantity, what is a Vector? Is velocity just the unit...
  5. N

    Scalar field energy for two delta function sources

    I'm trying to evaluate the energy shift in a scalar field described by the Klein-Gordon equation caused by adding two time-independent point sources. In Zee's Quantum Field Theory in a Nutshell, he shows the derivation for a (3+1)-dimensional universe, and I'm trying to do the same for an...
  6. S

    I need to calculate δR: R is Ricci scalar

    I need to calculate δR: R is Ricci scalar
  7. A

    Proving (A X B) X C = AxBxCx (i x k) + AyBxCy (j x k) | Unit Vectors

    Homework Statement Prove that (A X B) X C = AxBxCx (i x k) + AyBxCy (j x k) where i , j and k are unit vectors ? Homework Equations The Attempt at a Solution let A= Axi+Ayj B= Bxi+Byj L.H.S = (AXB)XC = (C.A) B - (C.B) A = (AxCx+AyCy)(Bxi+Byj)- (BxCx+ByCy)(Axi+Ayj)...
  8. S

    Understanding the Relation between Vector Fields, Flux, and Stokes' Theorem

    What is the relation between the flux through a given surface by a vector field? And how does stokes theorem relate to the line integral around a surface in that field
  9. B

    Magnetix flux density & Zero scalar potential

    Hi Can anybody tell how I can prove that the magnetic flux density is perpendicular to external boundaries with imposed zero magnetic scalar potential? Thanks Bag
  10. H

    Understand Why Current Is Defined as a Scalar

    Homework Statement Why has current been defined to be a scalar? Homework Equations The Attempt at a Solution No idea whatsoever!
  11. 3

    Interaction scalar field invariance

    The problem: http://www.gobigbang.nl/cft/cft.jpg An attempt of the solution: http://www.gobigbang.nl/cft/DSCN2722.JPG My problem is question c. I don't have a clue how to see that the improved current is conserved... Can anyone help me? Update I managed to solve the question by using the...
  12. H

    Scalar equation of a plane into paremetric

    Homework Statement Find a parametric equation of x-4y+2z-15 = 0 Homework Equations The Attempt at a Solution I know this is a plane in 3 space the normal of this plane is (3,-4,2) a point on this line is (15,0,0)
  13. E

    Understanding Scalar Fields: Div, Curl, RotGrad & DivGrad

    Curl div... Homework Statement f is a scalar field. What does div(f) curl(f) rotgrad(f) divgrad(f) stand for? I need to know if a scalar field can have the meanings of roration and diverge like a vector field
  14. A

    Finding Ricci Scalar Constant Nonzero Line Elements

    i need examplees where the ricci scalar is constant but nonzero . Particulary i search examples of line element. Pd: this is not a homework,
  15. Z

    Tensor gradient and scalar product

    Hi all, I need to evaluate the following equation : \mathbf{n} \cdot [\mathbf{\sigma} + \mathbf{a} \nabla\mathbf{\sigma}]\cdot\mathbf{n} where \mathbf{n} is the normal vector, \mathbf{a} a vector, and \sigma the stress tensor such that : \mathbf{\sigma} \cdot \mathbf{n} =...
  16. B

    Scalar quantity, can it be negative?

    Alright, so a friend and I have been debating if a change in speed can be negative. I state that speed is final minus initial, which if the inital is low, the the speed will have dropped in magnitude. He states that magnitude is absolute and no negatives are allowed. I was under the belief...
  17. E

    Coulomb gauge and scalar potential

    Hi there, I'm studying the interaction of one electron atom with an electromagnetic field. In every textbook the starting point is the hamiltonian of the system containing the scalar potential and the vector potential. But then the scalar potential is ignored and I don't understand why. I've...
  18. S

    Can't we say vector or scalar quantity is relative thing

    Can't we say vector or scalar quantity is relative thing! We all know that physical quantities are expressed as vector or scalar quantities.Now let consider 'area',if I say my house is 2000 sq.feet in that sense area may be called scalar but area of a surface is a vector quantity[either upward...
  19. R

    Is mass density a scalar or a scalar density of weight -1?

    Hi, I'm a little confused as to the nature of mass density. I've always seen it referred to as a scalar. Now by conservation of mass, when you integrate mass density over a volume, you get a scalar quantity. But volume transforms like a scalar density of weight 1, so shouldn't mass density...
  20. L

    Solved: Computing Potential Inside a Resistor Filled with Inhomogeneous Material

    π²³ ∞ ° → ~ µ ρ σ τ ω ∑ … √ ∫ ≤ ≥ ± ∃ · θ φ ψ Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô Homework Statement Consider the cylindrical in free space as shown below. The resistor has diameter 2a, length l, is filled with a inhomogeneous material with a z dependent electrical conductivity σ(z) and is capped by 2...
  21. Z

    Gravitational Field & Light Speed: Is Time a Scalar Quantity?

    The speed of light in a gravitational field is not a scalar quantity because at any given coordinate its speed is a function of its direction. Does general relativity treat time in a gravitational field as a scalar quantity?
  22. S

    Time dependence of scalar product

    How do I show that the scalar product is time independent? I have: \frac{d}{dt}\int\Psi^{*}_{1}(x,t)\Psi_{2}(x,t)dx = 0 And have proceeded to take the derivatives inside the integral and using the time dependent Schrodinger eq. ending up with...
  23. C

    Proving A0=0 for a Scalar and Zero Vector

    Homework Statement prove A0=0 where 0 is the zero vector and A is a scalar The Attempt at a Solution so i know we need to get it in the form A0 + A0 = A0+ 0 but I am not sure how to get there can we say A0 + 0 = 0 any input will be appreciated.
  24. R

    MATLAB Simple vector => to scalar in Matlab?

    Is there a basic function that renders a vector into its scalar component (ie, turning r1 vector into just r1) in matlab? Trying to simplify some code.
  25. P

    Scalar and vector potentials and magnetic monopoles

    Homework Statement Write down expressions oer E and B fields in terms of \varphi and \bar{A}. Demonstrate that this definition of B is consistent with the non-existence of magnetic monopoles. Homework Equations The Attempt at a Solution The first part of the question is easy...
  26. M

    Surface integral of scalar function

    Homework Statement Find the mass of a spherical surface S of radius R such that at each point (x, y, z) in S the mass density is equal to the distance of (x, y, z) to some fixed point (x_0, y_0, z_0) in S. Homework Equations Integral of a scalar function over a surface. The Attempt at...
  27. C

    Converting a Vector Equation of a Plane to a Scalar Equation

    how does one convert a vector equation of a plane to a scalar equation. This is given the parametric equations of the plane
  28. L

    Exploring Vector Operations: Scalar Multiples, Projections, and Cross Products

    [PLAIN]http://img62.imageshack.us/img62/5319/49966749.png What is the scalar multiples of a vector actually? I was thinking L = c[2 1 2]T Then I looked for projection of v on L. But I got c in my answers which are not supposed to be...
  29. Y

    Cartesian scalar equation of plane

    Just wanted to confirm. Cartesian scalar equation of plane refers to equation of plane right? As in Ax+By+Cz=D. which i think is the vector equation of a plane. I'm getting confused and need clarification thank you edit= ok sorry.. i think i got it figured out =p scalar is there because...
  30. H

    Center of Mass via Scalar Line Integrals

    Homework Statement A thin wire has the shape of the first quadrant part of the circle with center at the origin and radius a. If the density function is rho(x,y)=kxy, find the mass and center of mass of the wire. Homework Equations My parametric equation of the circle was x=a*cos(t) and...
  31. V

    Find the scalar equation for a plane perpendicular to another plane

    Find the scalar equation of a plane that contains the point P(4,9,-3) and is perpendicular to the plane 3x - 5z + 3 = 0 I know that the normal vector of the given plane is 3,0,-5. I also know that in order for two planes to be perpendicular, their normal vectors must also be perpendicular. I...
  32. M

    Exploring Scalar Work in Opposite Directions

    hello people , We know that work done is scalar because it’s the product of two vector quantities so it needs only magnitude to be defined. But look …W = Fd cos theta When the acting force is in the opposite direction to displacement then theta=180 Therefore the work done becomes...
  33. V

    Clarifying Boundary Conditions and Scalar Field Quantization in QFT

    This commmunity has so many nice people, so helpful, I am learning QFT from Srednicki I would be glad if some one can clarify, all the books talk about boundary conditions which are finite at spatial infinity and give the general solution for canonical quantization of scalar field, 1) how...
  34. F

    Reducing 3x3 Inertia Tensor to Scalar Value

    How to reduce a 3 by 3 inertia tensor to a scalor value? Hi I have the following tensor and i need to reduce it to a scalor quantity: 3 by 3 matrix 4150470.48 , 317.64, -353.42 317.64, 2047101.07,-1407556.61 -353.42, -1407566.61, 2284136.55 Please its urgent and any help would be...
  35. P

    What's the classical picture of phi^4 scalar field theory?

    I know that the classical picture of QED is Coulomb interaction, magnetic interaction etc. But what does the classical phi^4 theory look like? In particular, do particles attract or repel each other in this theory? P.S. I'm surprised that my field theory books never discuss this. (At least in...
  36. O

    Scalar Potential of a One-Dimensional Force

    Homework Statement A particle of mass m is subject to the one dimensional force F = x-x^3. Determine whether or not this force is conservative. If it is: a) write the scalar potential and find the turning points, b) write the kinetic energy and show that the sum of the kinetic and potential...
  37. M

    Divergence of a vector field is a scalar field?

    Hello. How can I show the Divergence of a vector field is a scalar field(in E^{3}) ? Should I show that Div is invariant under rotation? x^{i'}=a^{ij}x^{j},V^{'}_{i}(\stackrel{\rightarrow}{x})=a_{ij}v_{j}(\stackrel{\rightarrow}{x}) then \frac{\partial...
  38. P

    Adding Scalar Multiples of Vectors in a Graph

    Homework Statement Draw the vector \vec{C} = \vec{A}+2\vec{B} Homework Equations None The Attempt at a Solution This is what i have i don't know if it is correct P.S
  39. L

    Scalar potential in EM and Newton's Law

    Hi,all, problem is: in Electromagnetism, we introduced a scalar potential psi, such that: E = - grad Psi and In Newton's law, there is also a scar potential U, such that: F= -grad U My question is, one is the gradient of a scalar field give a field and a force?! Can anyone...
  40. R

    What is the scalar product V_1(DOT)V_2 ?

    Homework Statement Vector V_1 points along the z axis and has magnitude V_1 = 80. Vector V_2 lies in the xz plane, has magnitude V_2 = 51, and makes a -49o angle with the x-axis (points below x axis)Homework Equations A.B=ABCos(theta)=AxBx+AyBy+AzBz Cos(theta)=(AxBx+AyBy+AzBz)/AB The Attempt...
  41. A

    Scalar potential and line integral of a vector field

    Homework Statement Homework Equations Given above. The Attempt at a Solution I attempted this problem first without looking at the hint. I've defined F(r) as (B+A)/2 + t(B-A)/2, with dr as (B-A)/2 dt . Thus F(r)dr = ((B+A)/2)*((B-A)/2)+((B-A)/2)^2 dt When I integrate this from -1 to 1 I...
  42. A

    Scalar Equations: How to solve them

    Hi, My name is Abhishek Agrawal. I am a grad student in Computer Science. I know very little about scalar equations. But my research has led me to them and I am at my wits end on how to go about solving them. I have looked around every where but I am unable to start.Homework Statement...
  43. F

    Adjoint of the scalar Lie derivative?

    For every continuous linear operator A: H \rightarrow H from a Hilbert space H to itself, there is a unique continuous linear operator A^* called its Hermitian adjoint such that \langle Ax, y \rangle = \langle x, A^* y \rangle for all x,y \in H. Given that \mathcal{L}_X: \Omega^0(M)...
  44. Shackleford

    Cross Product and Triple Scalar Product

    This isn't homework, but I worked this out to become more fluent with expressing these operations using sums, indices, etc. This is from my Vector Analysis course, and the professor said understanding this would make the rest of the course smooth sailing if I get all these concepts down. I'm...
  45. B

    Interpreting g(f u\otimes u + v\otimes v) with Scalar Field f

    I know that: g(a u\otimes v) = a g(u\otimes v) where u and v are vectors and a is a constant, but what if a is a scalar field, is this rule also true? ie. how do I interpret the expression: g(f u\otimes u + v\otimes v) where u and v are vector fields and f is a scalar field?
  46. maverick280857

    Scattering of a scalar particle on a spin-1/2 particle

    Hi, Following my recent https://www.physicsforums.com/showthread.php?t=375638" with density matrix formulations of scattering theory, here's a question I faced on yesterday's particle physics exam. I did some mechanical computation, but I am not fully convinced of what I did (basically computed...
  47. snoopies622

    Understanding Scalar Curvature: Key Differences and Properties

    Is there any particular reason that scalar curvature is defined R = g^{ab}R_{ab} instead of R = R^{ab}R_{ab} ? Do both scalars share the property that they are zero if and only if every component of R^{a}_{bcd} is also zero?
  48. L

    Can I visualize three variable functions through scalar and vector fields?

    Graphics of one variable functions are two dimensional lines. Graphics of two variable functions are three dimensional surfaces. Three variable functions cannot be plotted. But can I think of the usual 3D representations of vector and scalar fields as manners of visualizing a three variable...
  49. P

    Is Y a scalar wave equation?

    Y=a+b because Y,aa+Y,bb=0
  50. P

    Scalar or Vector: How to Classify Important Quantities in Scientific Research?

    Homework Statement Classify each of the following quantities as scalar(s) or vector(v): Temperature Speed Acceleration Volume Work Area Mass Electric Field Velocity Displacement Force Homework Equations none The Attempt at a Solution Temperature - scalar Speed - scalar...
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