Scalar field Definition and 190 Threads

Dear All I am having trouble understanding the gradient vector of a scalar field (grad). I understand that you can have a 2D/3D space with each point within that space having a scalar value, determined by a scalar function, creating a scalar field. The grad vector is supposed to point in...

BRS: Static Axisymmetric "Gravitationless" Massless Scalar Field Solutions This thread is an (easy and amusing) companion to a previous BRS, "The Weyl Vacuums" www.physicsforums.com/showthread.php?t=378662 I. The Family of "Gravitationless" Solutions I will describe a family of...

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...

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...

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...

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...

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...

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?

What are the dimensions of a scalar field \phi ? The Lagrangian density is: \mathcal L= \partial_\mu \phi \partial^\mu \phi - m^2 \phi \phi So in order to make all the terms have the same units, you can try either: \mathcal L=\frac{\hbar^2}{c^2} \partial_\mu \phi \partial^\mu \phi -...

i have been given a problem for writing s matrix in second order perturbative theory for an interaction hamiltonian with phi 4 and phi 3 contributions. it is also given that our initial state is of 2 particles and final state is of three particles. now in solving that i have to take time...

I have to find the gradient of a scalar field, h, at a certain point in a direction given by a vector. I know, \vec{\nabla}h will give me the direction of maximum slope, and its magnitude is the magnitude of the slope, but i don't know where to start in finding the slope in any other...

As I know, Einstein initially tried describe the gravitational interaction as mediated by a scalar field, but he later gave up this idea because it is incompatible with the Principle of Equivalence.I don't know how this idea is incompatible with the Principle of Equivalence. Please help me. Thanks

I've recently read about Null Identities of vector analysis. I'm having a problem in understanding what is it by "taking the curl of the grad of any scalar field is equal to zero." What is by definition of scalar field then? How would it looks like? Is position vector a scalar field? If No...

Homework Statement I want to show that \mathbf{P} = -\int d^{3}x}\pi(x)\nabla\phi(x) = \int{\frac{d^{3}p}{(2\pi)^3}\mathbf{p}a_{p}^{\dagger}a_p for the KG field.Homework Equations \phi(x) = \int{\frac{d^{3}p}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p + a_{-p}^{\dagger})e^{ipx} \pi(x) =...

Homework Statement Calculate the gradient of the scalar field f(x,y) = x^{2} - y^{2} . Sketch the gradient for a few point on two straight lines y = x and y = -x on the plane and comment on the properties of the sketch. Homework Equations The Attempt at a Solution So I worked...

I'm not sure if this is the right place for this question, so feel free to move it. Anyway, my question is, is there any good reason why the following field theory should be Weyl invariant in an arbitrary dimension d>1: S = \int d^d x \sqrt{g} \left( g^{\mu \nu} \partial_\mu \phi \partial_\nu...

I wanted to ask a quick question about the complex scalar field. My question is that does the scalar field need to be complex in order to include the part for anti-particles or do you regards the scalar field for particles and anti-particles seperate. I saw this specifically when you second...

I'm not sure if this is the right place to post a graduate level course material, but I have a question about perturbative expansion of the 2n-point function of a scalar field theory. Homework Statement First, the question: In which space (position or momentum) is the topological distinctness...

Why the quantization of scalar field resolves the energy negative problem that exist in the klein-gordon equation?

Why is the Higgs field a scalar field? I understand if it is one, it will have no spin and no angular momentum. But understanding that a particle is a scalar seems to me a leap of faith. What am I not getting?

Homework Statement Find the commutators [P^\sigma,J^{\mu \nu}] The answer is part of the Poincare algebra [P^\sigma,J^{\mu \nu}]=i(g^{\mu \sigma}P^\nu-g^{\nu \sigma}P^\mu) If someone can convince me that \partial_i T^{0\mu} = 0, (i.e. the energy-momentum tensor has no explicit spatial...

Hi I have a small subtle problem with the sign of the energy-momentum tensor for a scalar field as derived by varying the metric (s.b.). I would appreciate very much if somebody could help me on my specific issue. Let me describe the problem in more detail: I conform to the sign convention...

I have seen in one paper that photon is coupled to dilaton field which is scalar and motivated by string theory. I do not understand this. Photon is carrier of electromagnetic field and so I thought it can only couple to electrically charged fields. Can anyone explain?

I've been trying to work my way through some of my lecture notes, and have hit this snag. (n.b. I use k_0 \equiv +\sqrt{\vec{k}^2 + m^2}) We have a(q) = \int d^3 x e^{iqx} \{ q_0 \phi(x) + i \pi(x) \} a^{\dagger}(q) = \int d^3 x e^{-iqx} \{ q_0 \phi(x) - i \pi(x) \} To calculate the...

Suppose you are given the Lagrangian of a scalar field \Phi(t) \mathcal{L} = \frac{1}{2} \dot{\Phi}- \nabla \Phi - V(\Phi ). By introducing covariant notation with \eta_{\mu \nu} = (1,-1,-1,-1) this reads as \mathcal{L} = \frac{1}{2} \eta^{\mu \nu} \partial_\mu\Phi \;\partial_\nu\Phi-...

Hey, this is rather involved but I hope someone can help me out. I am reading http://arxiv.org/abs/0704.3626 ( the casimir force in randall sundrum models) and am trying to get from equation 2.1 : g^{\mu\nu}\partial_\mu\partial_\nu\Phi+e^{2ky}\partial_y(e^{-4ky}\partial_y\Phi)=0 to...

Hi all, I have a little problem concerning the coupling of a fermion to CP^N (or better a 2D scalar O(3) model). Its not a mathematical type of problem. I just read on "The coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model: minimal and supersymmetric extensions"...

I've been wondering about terms you typically find in the action of a field theory, for example consider the kinetic term of a scalar field S=\int d^4x(\partial_\mu\phi\partial^\mu\phi). I've read that it can be thought of as the kinetic energy of the field - but this just doesn't sit to...

"Consider a surface S on which a scalar field f is defined" "Consider a surface S on which a scalar field f is defined" what does "on which is defined" mean phys descript answers appreciated!

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

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...

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...

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...

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...

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...

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...

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...

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...

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 =...

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?