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. W

    Is Energy a Scalar or Vector? Understanding Energy and Work

    It's all in the title...
  2. N

    Finding an electric field from a scalar field

    Say I know an electric field E = (yz - 2x)x-hat + (xz)y-hat + (xy)z-hat How do I find the scalar field that would produce that? If I integrate each part I get Vx = xyz - x^2 Vy = xyz Vz = xyz Vt = 3xy - x^2 To find E, I would take E = gradient cross the scalar field, but that...
  3. M

    Calculating Scalar Potential for a Cube with Point Charges

    Consider a cube of edge a. There is a point charge q at each corner. Find \phi at the center of the face for which x=a. The answer to the problem is \0.707*(q/\epsilon_0*a) I have to use the the scalar potential equation, but I have been stuck on this problem for a while. I know that I have to...
  4. P

    Proving Finite Scalar Series for V and T in L(V)

    Prove: If V is a finite dimensional vector space and T is in L(V), then there exists a finite list of scalars ao,a1,a2,...,an, not all 0 such that aoX + a1T x + a2T^2 x... + anT^n x = theata for all x in V my hint for the question is: the powers of T are defined as T^0 = I, T^1 = 1...
  5. G

    Complex Scalar Field in Terms of Two Independent Real Fields

    I am working with a complex scalar field written in terms of two independent real scalar fields and trying to derive the commutator relations. So, \phi = \frac{1}{\sqrt{2}} \left(\phi_1 + i \phi_2) where \phi_1 and \phi_2 are real. When deriving...
  6. honestrosewater

    Why is scalar multiplication on vector spaces not commutative?

    (Or if you prefer: Why are things defined this way?) I noticed that, in my book's definition, scalar multiplication (SM) on vector spaces lacks two familiar things: commutativity and inverses. The multiplicative inverse concept doesn't seem to apply to SM. Can it? I can't imagine how it could...
  7. R

    Guidance in solving Scalar Field with BC's

    Hi all, I am having some problems understanding the steps in a paper. I've looked in books and asked other grad students but they have all not been of too much help and I am still stuck. I have a massive scalar field mass \mu interacting with two delta function potentials with...
  8. R

    SCALAR ELECTRO-MAGNETIC WEAPONS-Fact or Fiction?

    SCALAR ELECTRO-MAGNETIC WEAPONS? Are there such things? I have searched for data but have never gotten much of an answer. Some people claim knowledge of Russian research and development of such weapons. Does anyone know what the truth is? (Some persons even claim the latest hurricane that...
  9. O

    Understanding the Role of the Gauge in Expressing Field Situations

    There´s an assertion that the electric field depends only on Vector potential in radiation region. But I couldn´t see clearly why the contribution of scalar potential could be comparatively ignored. Could anyone give me some explanations? Thanks!
  10. Lisa!

    Neutrino scalar waves travel back and forwards in time

    what do they mean when they say "neutrino scalar waves travel back and forwards in time"?and why does it happen for neutrino?
  11. S

    If you find the scalar potential of a conservative vector field

    Should your answer include the constant of integration? I think it should but my book's answers don't, so I dunno. Example, <2xy^3, 3y^2x^2> answer is x^2y^3, but should I include the + C? (and yes I went through and made sure h(y) was in fact a constant
  12. M

    Proving Scalar Operator: Laplacian in 4 Dimensions

    According to the definition, an operator T that commutes with all components of the angular momentum operator is a scalar, or rank zero, operator. What is the mathematical definition to that statement? How can I prove that the four dimensional Laplacian is a scalar operator? Regards, :biggrin:
  13. G

    How do you differentiate a scalar n vector?

    How? I know that a scalar quantity only comprises of magnitude while a vector consist of both magnitude and direction.. But is there no definite formula to determine whether or not a quantity is a scalar or a vector.. or is there a list of scalars and vectors to show all quantities...
  14. K

    Gaining Insight into Scalar Field Theory Questions

    Greetings, I stumbled across two question that I have no idea on how to answer them. 1) The interaction term in a scalar field theory is -\frac{\lambda}{4!} \phi^4 Why should lambda be positive? (they say look at the energy of the ground state...) 2) Write down the Feynman rules for...
  15. N

    Could scalar waves do this-allow me this question for physicists and meteorologists

    Like I said I need physicists and meteorologists Could scalar waves be cause of: Artificially cause volcanoes' eruptions(because scalar waves can easily penetrate thru Earth's core,some people think that was the cause ST. Helen's volcano erupted-true or false) To artificially cause...
  16. Q

    What is the general form of the Lagrangian density for a scalar field?

    Hi, I have a question about a statement I've seen in many a Quantum Field Theory book (e.g. Zee). They say that the general form of the Lagrangian density for a scalar field, once two conditions are imposed: (1) Lorentz invariance, and (2) At most two time derivatives, is: L =...
  17. K

    Vector and scalar problem

    This one: a)Let V be a vector space and let x be a vector in V. i)Show that b0=0 for each scalar b. ii)Show that if bx=0, then either b=0 or x=0
  18. R

    Pseudo Scalar Relativistic QM problem

    Hi there, I have a problem that I could really do with a little help on. I have a spin 1/2 particle in which the dirac eqtn reads: ( i {d} - \gamma V(x) - m ) \Phi = 0 (I am new to latex - the d is SLASHED and the gamma is GAMMA5 ) In a potential V(x,t) = 0 for...
  19. R

    Calculate Scalar Product for Vectors M and N in Cartesian XY System

    Consider the two vectors M =(a,b) = ai+bj and N = (c,d) = ci +dj, where a =4, b =4, c = -1, and d = 1. a and c represent the x-displacment and b and d represent the y-displacment in a Cartesian xy co-ordinate system. Note: i and j represent unit vectors(i.e. vectors of length l)in the x and y...
  20. Reshma

    Unit vector normal to scalar field

    How do you find a unit vector normal to the surface of scalar field \phi(x,y,z)=x^2y+3xyz+5yz^2? Should you apply the \nabla operator to it?
  21. Ivan Seeking

    Scott Stevens' Response on Meteorologist Scalar Clouds

    From the thread: https://www.physicsforums.com/showthread.php?t=61472 Well Dayle, I emailed Scott Stevens http://www.kpvi.com/index.cfm?page=team/scot/content.cfm and asked about the claims at your linked site. Here is his response. I didn't think that it would take long to nip this in the...
  22. R

    Scalar Weapons? Fact or Fiction?

    I hear/read about "Scalar Weapons" from a certain website : www.cheniere.org and it's main man : retired Col. Tom Bearden. I have one of his books and he has lots to say and most seems too weird to believe. The following is part of a long paper on weapons of great power ? : Scalar...
  23. C

    Scalar multiplication(vectors)

    Hi everybody, I have a small question. I know that we have defined multiplication of a number and a vector ,for example b*A (capital letters =vectors, everything else=real numbers). We have also defined that b*(c*A)=(b*c)*A. From these two rules is a*b*c*d*...*k*Z defined (= product of n...
  24. O

    Vector valued and scalar valued functions

    Hi what is the definition and meaning (geometric) of a vector valued and scalar valued function? I read the definition in the textbook but I didn't quite get it. Thank you.
  25. A

    Weyl Transformation and Scalar Product

    I was reading about Weyl Transformations in Polchinski's book and I have a little doubt: Is it correct to say that under a Weyl transformation the scalars are invariant, i.e., that a weyl transformation preserves the scalar product?
  26. S

    Scalar & Vector Equations: What is the Difference?

    Scalar equations such as y=2x+3 actually generate POINTS which are collinear. A vector equation, as the name implies, generates VECTORS, and these vectors are definitely NOT COLLINEAR. How then can we say that an equation such as r = (2,1,3) + t(1,2,4) is the "equation of a line"...
  27. W

    Can Scalar Waves Explain Electronic Voice Phenomenon?

    can someone explain this to me please?
  28. M

    Use of curl of gradient of scalar

    I'm wondering if physics ever uses a differential equation of the form of a curl of a gradient of a scalar function. Or is this too trivial? Thanks.
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