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.

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  1. Q

    Scalar vs Vector: Explaining the Difference

    This is a very basic question, but one I keep getting confused on nonetheless. Can someone explain to me the difference between a scalar function and a vector function? I've been told that the only difference is in the way the quantities are regarded (one as scalars, the other as elements of a...
  2. V

    Error: Conversion from scalar to nonscalar

    Hi I am writing a code and I am getting a compiler error that I can not seem to figure out. I have limited programming knowledge and I have come here for help. This is the section of code I feel is relevant. struct Player { string name; int goals; int assists; }; int find_player(Player , int ...
  3. G

    Surface with Ricci scalar equal to two

    A two-dimensional Rienmannian manifold has a metric given by ds^2=e^f dr^2 + r^2 dTHETA^2 where f=f(r) is a function of the coordinate r Eventually I calculated that Ricci scalar is R=-1/r* d(e^-f)/dr if e^-f=1-r^2 what is this surface? In this case R comes to be equal to 2 I've...
  4. G

    Surface with Ricci scalar equal to two

    A two-dimensional Rienmannian manifold has a metric given by ds^2=e^f dr^2 + r^2 dTHETA^2 where f=f(r) is a function of the coordinate r Eventually I calculated that Ricci scalar is R=-1/r* d(e^-f)/dr if e^-f=1-r^2 what this surface is? In this case R comes to be equal to 2 I've...
  5. A

    How does a scalar transform under adjoint representation of SU(3)?

    I read this in a paper: Suppose there is a theory describing fermions transforming nontrivially under SU(3) gauge symmetry. L = \Psi^{\bar}(\gamma^A D_A+Y(\Phi))\Psi. The covariant derivative is: D_A\Psi=(\partial_A-i E_A^{\alpha}T_{\alpha})\Psi. Where E_A^{\alpha} are SU(3) gauge fields...
  6. S

    MATLAB How do I calculate the triple scalar product in Matlab?

    Homework Statement i have 3 vectors a,b,and c. on matlab, i have to find the triple scalar product: b.(c x a) Homework Equations The Attempt at a Solution i typed it in the script file as: b'*cross(c,a) but i got a 3x3 matrix...shouldn't the answer be one fixed value since...
  7. B

    DEC with E/M and scalar fields

    Hi, I'm trying to show that electromagnetism and scalar field theories satisfy the DEC. I know how to find T_{\mu\nu} and all that and what I have to show (T_{\mu\nu} T^\nu_{\ \lambda} t^\mu t^\lambda\leq 0 and T_{\mu\nu} t^\mu t^\nu\geq 0 for timelike t^\mu), but I'm having trouble getting...
  8. Jim Kata

    How Do Baryons Emerge in the Standard Model Through Topological Effects?

    I'm lazy so I'm going to start bringing my questions here. Correct me if I'm wrong, but isn't it true that baryons only enter the standard model through this subtle topological effect. Now this is where I'm at. I kind of got the Goldstone boson concept, maybe someone could better explain...
  9. K

    Determinant of a matrix multiplied by a scalar

    Homework Statement it is problem 1 on the attachment Homework Equations detA = ad - bc for a 2 x 2 matrix, where the first column is a c and the 2nd column is b d The Attempt at a Solution ah i see the first part i think, but I am nto sure I am writing my answer in the most...
  10. pellman

    Why does spin 0 have to be a true scalar?

    Of course, a spin 0 field, by definition, has to be a scalar field under rotations. But what about boosts? Compare to classical charge density \rho, which must satisfy \frac{\partial\rho}{\partial t}+\nabla\cdot J=0 That is, \rho is the time-component of a four-vector under boosts...
  11. R

    Checking if Rationals are Closed Under Addition and Scalar Multiplication

    Homework Statement Check to see if the (vector space) set of rational numbers is closed under addition and scalar multiplication Homework Equations The book says this holds for addition but fails for scalar multiplication. The Attempt at a Solution Im a little confused. You can...
  12. S

    Make a value scalar or vector?

    Homework Statement no real problem statement, this isn't an equation Homework Equations same as above... The Attempt at a Solution absolutely none -- Please read this I am nowhere near the level of anyone on this board, I'm having trouble with beginning high school physics...
  13. L

    What are the differences between scalar and vector quantities?

    Hmm... I don't know the differences between the scalar and vector quantities? Help, please? I don't want to fail physics!
  14. N

    Scalar product to find angle between two vectors

    Use the definition of scalar product, a·b = ab cos , and the fact that a·b = axbx + ayby + azbz (see Problem 46) to calculate the angle between the two vectors given by a = 2.0 i + 6.0 j + 2.0 k and b = 4.0 i + 3.0 j + 6.0 k. AdotB= 8i + 18j + 12k A=sqrt(2^2 + 6^2 + 2^2)=6.63 B=sqrt(4^2 +...
  15. C

    Understanding the Scalar Product in Vector Calculus

    Homework Statement What surface is represented by r . a = conts. that is described if a is a vector of constant magnitude and direction from the origin and r is the position vector to the point P(x1, x2, x3) on the surface? The Attempt at a Solution I know that the dot product of two...
  16. M

    Do you think that scalar electromagnetic weapons are real and possible?

    www.totse.com/en/fringe/gravity_anti_gravity/162717.html http://www.prahlad.org/pub/bearden/scalar_wars.htm www.cheniere.org/books/analysis/history.htm Hi all, does anyone think this is possible? Has anyone heard of it? I read that the government has the tech to find anything deep...
  17. C

    Scalar field and spin 1/2 field

    are bosons represented by a scalar field and fermions represented by a spin 1/2 field or how does it work?
  18. C

    Transforming a Lorentz Scalar: psi-bar x psi x y_0

    i am confused why you need to write psi-bar multiplied by psi (where psi-bar is the hermitian conjugate of psi multiplied by y_0 (dirac matrix or gamma matrix)) instead of the h.c. psi multiplied by psi in order for it to transform as a lorentz scalar. Note: h.c. means hermitian conjugate
  19. B

    Synchronous Machine - Scalar Pot Solution

    My problem is defined like that. I am trying to find radial and tangential field distribution on a surface of the rotor of a large airgap synchronous machine. To do that I start from the general scalar potential equation solution in polar coordinates of the form pot = (ar+b/r)sin(teta). I take...
  20. U

    Exploring the Concept of Time as a Scalar in Mathematics and Physics

    Why is time a scalar? Sb says time is scalar because under two different FRAMES, t and t' are the same (for describing the same event?). However, if one frame is moving to the other, how can this be generally true? Isn't time RELATIVE in physicists' eyes? Therefore, " time is a scalar" is...
  21. marcus

    without resorting to scalar fields

    "...without resorting to scalar fields" http://arxiv.org/astro-ph/0703566 Co-authored by Parampreet Singh, one of the experts in Quantum Cosmology (gauged by publication trackrecord and citations by other scholars, see: https://www.physicsforums.com/showthread.php?p=1368143#post1368143 )...
  22. C

    From the scalar of curvature (Newman-Penrose formalism) to the Ricci scalar

    I calculate trace-free Ricci scalars (Phi00, Phi01,Phi02, etc) and scalar of curvature (Lambda=R/24) in Newman-Penrose formalism using a computer package. How can I find the Ricci scalar out of them? I though R was the Ricci scalar but Lambda comes non-zero for a spacetime whose Ricci scalar is...
  23. H

    Gauge group SU(5) coupled to a scalar field

    1. For a project on elementary particle physics I have to consider a gauge theory with the gauge group SU(5) coupled to a scalar field. I am to use a certain non-zero vacuum expectation value for the scalar field and check what happens to the gauge bosons. I have already done this for...
  24. R

    WHY there is no scalar equation for a line in three dimensions ?

    WHY there is no scalar equation for a line in three dimensions ? :confused:
  25. G

    Proving invariance of scalar product

    Hi everyone, How would I go about proving that the scalar product of two four-vectors (A,B) is invariant under a Lorentz transformation?
  26. U

    Is Time a Vector, Scalar, or Something Else Entirely?

    Greetings, I have pondered over this question for what seemed ages. I dared not ask for opinions of my fellow classmates for they may mock at me for being a moron. My question is: 1) What exactly is time? ( scalar? vector? units? force? ) 2) How does time past? ( Before 1s passes...
  27. J

    How Can I Use Stokes' Theorem to Show Integral of fgrad(g)*dr=0?

    Homework Statement Let S be a simple parametrically defined surface with boundary C as in Stokes' Theorem. Let f and g be two continuously differentiable scalar fields defined on S. Let n be a choice of unit normal on S. If grad(f) is perpendicular to grad(g) x n everywhere on S, show that...
  28. R

    Understanding Vector and Scalar Quantities in Physics

    No, I am not going to ask you what the difference between those two are. =P I know the differences, but at the beginning of this term, my class started to learn about electricity and magnets, and that stuff. Now, vector quantities are those that have direction and scalars are those without...
  29. C

    Solving the Triple Scalar Product: Finding the Value of a(dot)(a(cross)b)

    Homework Statement What is the value of a(dot)(a(cross)b) ? Why? I am supposed to find an actual value. Sorry I don't know code, these variables are all vectors. A is dotted with vectors a and b which are cross product. Homework Equations I know this can be written as a determinate of...
  30. J

    Can Scalar Field Redefinition Ensure Independence?

    Hello everyone. I was hoping that someone could possibly help me with a problem I've got. If you have an action for two independent scalar fields, say A and B (arbitrary functions of (x_mu), both without any zeros), then can I redefine the action in terms of two new scalar fields A and C=AB...
  31. A

    Why Pressure is a scalar quantity?

    Hi, 1. As we know that pressure is force per unit area but why it is said that pressure is a scalar quantity because force is used and force is a vector quantity. 2. Whether stress is also a scalar quantity? 3. What is basic difference between pressure and stress? Regards...
  32. A

    Is Strain a Scalar or Tensor Quantity?

    Hi, I know that strain is a unit less quantity (Tensile Strain) but whether Strain is a scalar quantity or not? If it is a scalar quantity then why? Regards, Muhammad Rizwan Khalil
  33. D

    Scalar Gravitational Theory with Variable Rest Mass

    ABSTRACT In this paper we will present the mechanical dynamics of a gravitational system resulting from a specific, rest mass, scalar potential relation, that is equivalent in predicting orbital and photon motion to that of General Relativity in the weak field solutions. The weak solutions of...
  34. Q

    Why is current considered a scalar in physics textbooks?

    current has a direction and magnitude, intuitively it should be a vector but my physics textbook describes it as a scalar. Why is that?
  35. S

    What Are Rectangular Scalar Components in Vector Analysis?

    Hey, In the question that I'm working on it says to resolve v1 and v2 into rectangular scalar components but i have no idea what a rectangular scalar component is and i can't find it in my textbook. if anyone could tell me what they are that would be very helpful! thanks
  36. A

    Determine whether work is scalar or vector.

    right the question I am finding tricky is: by considering a body doing work against gravity, moving up a hill, determine whether work done is scalar or vector? (2 mark question) so I've draw like a triangle an arrow for force at an angle theta form the horizontal which has an arrow along...
  37. S

    Scalar field pressure and energy density

    Hi all, I'm hoping someone can help me out as I'm really stuck. With reference to the top of page 7 at http://faculty.washington.edu/mrdepies/Survey_of_Dark_Energy2.pdf I'd like to know how to get the quoted energy density and pressure of phi from the stress-energy tensor. I am very...
  38. P

    Parallel vectors and scalar product rule

    hey, ive been given a problem where vector a = 2i + 3j and vector b = \lambdai + 12j and also told that these vectors are parallel of each other. i understand since the vectors are parallel of each other, the angle between them would be equal to zero, thus i could apply the scalar product rule...
  39. W

    Dot products - why does the vector become scalar

    As Gokul43281 correctly pointed out to me, the dot product of two vectors is a scalar. I looked up this page to read about this. Thing is, I think conceptually. I could simply accept that this is so, but I don't "see" why it so. As my screen name implies, I must know why something is so...
  40. P

    Solving Scalar Product Problem: Find Perpendicular Distance

    Hey, Today I was given a problem to solve in class and was told to complete it for homework. This problem is as follows: The line y=mx + c has a gradient m and cuts the y-axis at (0,c). Thus we can write the parametric vector equation of the line as: r = cj +\lambda (i + mj) Using this...
  41. C

    Physics Baisic Lab Question and Scalar Components

    Hey! New to this site, started taking physics yesterday and already need some help:frown: 1)My textbook is very complicated, is there an easy way that anyone can explain what scalar components are? 2)I did a lab with a force table and 3 pulleys. You add weight to one pully to even out a...
  42. H

    Is a Heightfield a Scalar or a Vector and How Many Dimensions Does it Have?

    Hello, I've been wondering if a heightfield is a scalar or a vector, and how many dimensions in space it has. Sure, if it's a scalar it only has a magnitude, and as a vector magnitude and direction but I cannot see either, or keep them apart in this case. Density or gravityacceleration are...
  43. S

    Proving the Relation Between Weyl Tensor, Ricci Tensor & Scalar

    Hello, I wish to show that on 3-dimensional manifolds, the weyl tensor vanishes. In other words, I want to show that the curvature tensor, the ricci tensor and curvature scalar hold the relation Please, if anyone knows how I can prove this relation or refer to a place which proves the...
  44. W

    Vector Scalar Product and KE questions

    Just a few questions from this set I have to do, I missed the class on these topics so I'm just a little confused with these last few problems. http://img161.imageshack.us/img161/2307/problem43eu.png Concerning sets 38-39, and 40-41, I've grasped how to scalar multiply these vectors, but...
  45. J

    Is torque a vector or a scalar quantity?

    Is torque a vector or a scalar quantity? Thanks.
  46. H

    How Do You Find a Scalar Equation for a Plane Through Three Points?

    The question is, Find a scalar equation that passes through the points (3,2,3), (-4,1,2) and (-1,3,2). What I did was put that into the vector equation form, using (3,2,3) as a position vector, resulting in: r=(3,2,3) +t(-7,-1,-1) + s(-5,2,0) Then I found the cross product of the...
  47. S

    Is Vm a reliable measure of magnetic fields in the presence of current?

    I'm confused about the status of Vm. We are asked under what circumstances we can write B = - Mu0*grad(Vm). I think the idea is that when there is no current density (displacement or conduction) we can write curl(B) = 0. Therefore we can write B as a grad of a scalar potential, as curl grad = 0...
  48. N

    Understanding Composite Fields and Scalar Fields

    Dear PF, Can I consider the composite field for instance psi_bar psi as a scalar filed? I mean can it be the same in all respects? Can this composite field and scalar filed treated as totally equivalent? Thks
  49. J

    Is the Scalar \( R^{ji} R_{ij} - R^2 \) Recognized in Mathematical Physics?

    In my calculations, I come across the scalar R^{ji} R_{ij} - R^2 (R_{ij} is the Ricci tensor, R is the Ricci scalar) More specifically, I come across the integral of this scalar over a compact manifold. Has anyone seen it before, and does it have any nice properties? John Schulman
  50. T

    Scalar Equations of a plane in space

    One question is bothering me.. Find the scalar equation of the plane that contains the intersecting lines (x-2)\1=y\2=(z+3)\3 and (x-2)/-3=y\4=(z+3)\2 What I've tried is doing the cross product of (1,2,3)and(-3,4,2) I get a Normal and then put it into scalar form... Substitute...
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