Scalar field Definition and 207 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. 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...
  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. 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...
  4. 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...
  5. 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...
  6. 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 =...
  7. 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?
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