Scalar Definition and 777 Threads

In the Kallen-Lehmann spectral representation (http://en.wikipedia.org/wiki/K%C3%A4ll%C3%A9n%E2%80%93Lehmann_spectral_representation) the interacting propagator is given as a weighted sum over free propagators. The pole of the integracting propagator is, of course, given by p^2=m^2, m being the...

I came across a problem that asked if some things were scalar or a vector. Is acceleration a vector? I thought it just gives you magnitude and not direction at all. For example when velocity and acceleration are put together, velocity gives you the direction and the acceleration gives...

suppose g(r) is a scalar function which is constant inside the volume 'v' but discontinuous at the boundaries of 'v'. The magnitude of discontinuity is given by constant 'M' then can we write the following expression \int\nablag(r)dv=M\int\hat{n}\delta(r-rs)dv=M\hat{n}\intd\deltav where...

Hi Forum! I have got a question about the induced scalar potential. I will present the problem from beginning. Lets say we have a Poisson's equation in form: \epsilon \nabla^2 \phi = -4\pi \varrho(r,t) where \epsilon is the dielectric constant. By use of the Fourier transform...

Hello, I have very complicated expressions containing scalar products like a1*b1 + a2*b2 + a3*b3 In order to reduce the complexity, I would like to establish a set of rules like rule={a1*b1 + a2*b2 + a3*b3 -> pAB, ...} in order to replace each time the scalar product by an...

What is the general strategy in solving vector equations involving grad and the scalar product? In particular, I want to express \Lambda in terms from \mathbf U \cdot \nabla\Lambda = \Phi but it looks impossible, unless there is some vector identity I can use. Thanks in advance.

If i have the mgf of X and the mgf of Y where X~N(mx,vx) and Y~N(my,vy) and X and Y are independent , then if i want to show that aX +bY ~ N(amx+bmy , a^2vx+b^2vy) how would i do this - need to be able to do the convolutions way and the mgf's way, for the mgfs way is it just, mgf(ax+by) =...

"Fun" Magnetic Scalar Potential Problem Homework Statement An infinite cylindrical shell of radius b is placed inside a constant field B which points along the upwards z-axis. A second cylindrical shell of radius a<b is placed inside the first cylindrical shell, and the volume from b>r>a...

On page 35 of Jackson's Classical Electrodynamics, he calculates the Laplacian of a scalar potential due to a continuous charge distribution. In the expression for the potential, the operand of the Laplacian is \frac{1}{|r-r'|}, where r is the the point where the potential is to be...

Hi folks, If I have a Lie algebra \mathfrak{g} with an invariant (under the adjoint action ad of the Lie algebra) scalar product, what are the conditions that this scalar product is also invariant under the adjoint action Ad of the group? For instance, the Killing form is invariant under...

Coulomb Law and Vectors - How do you find a scalar answer from the vector form?? Two small metal spheres carry equal charges q. They are located at positions r1 = (1,1,0) nm and r2 = (0,0,0) nm and feel a repulsive force of magnitude (mod) F = 0.05 N How much charge is on each sphere...

What do people mean when they say that mass renormalization of scalar field theories confronts us with a fine tuning problem. It's said the divergence in the mass of a scalar field is quadartic, rather than logarithmic, this poses a fine tuning problem. Why and how, and what does that mean...

Homework Statement This is not a home work, I actually make this problem up and work on it. I want to verify whether I am correct in the step and I need help to solve the final integration. The question is: Given a plastic circular ring radius = a with line charge density glued on...

Suppose I have the scalar field f in the xy-plane and that it is smooth. Its total derivative is given the normal way, i.e. df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy and the gradient of f is given the normal way as well. I read in a paper that, due to the...

For the following scalar field: \psi(x,y,z) = (y-1)z2 Find grad \psi Here is my attempt at: Multiplying out brackets: yz2 - z2 Therefore grad \psi = 0+Z2 J -2ZK Is this correct??

This is exact copy from Griffiths Introduction to Electrodynamics 3rd edition page 421. This is regarding to information travel in space. In time varying situation, E depend not only on V, but on A also.

Homework Statement i have to find the scalar and vector projection of a=i-j+k and b=2i-j-2k and i got: Vector proj = (1/3)(i-j+k) = i/3 + j/3 + k/3 scalar proj = (1/9)(2i-j-2k) = 2i/9 - j/9 - 2k/9 is this correct?

Homework Statement Is it possible to use the triple scalar product to solve anything greater than a 3x3 matrix? Homework Equations Ax + By + Cz + D = 0 The Attempt at a Solution In terms of planes, the triple scalar product can be used to determine if the NORMALS of the planes...

This is a conceptual problem that I'm sure is pretty common. How can kinetic energy (1/2mv^2) be a scalar quantity when it includes a vector quantity like velocity?

Homework Statement When we're given an equation in form r = r0 + sa + tb, how do we convert it to scalar form Ax + By + Cz + D = 0? I've been having trouble with plane form, but I can do it fine when its given in 2- or 3-D form.

Homework Statement A uniform line charge of -4π x 8.85 pCm^-1 is situated between the points (-5,0) and (-2,0) m and another such line of positive charge between (2,0) and (5,0) m. A) Find the electric scalar potential V at (1,0) m. B) Find the electric field intensity E at the same...

I would really appreciate the help, I've been trying to figure this out for the last three hours no joke. Homework Statement Write the scalar equation the line given the normal vector [3,1] and point (2,4) Homework Equations R=[X0,Y0]+ T[M1,M2] The Attempt at a Solution...

scalar functions :( First of all I'm sorry for posting new thread about for this simple topic. I know scalars are quantities that are fully described by a magnitude or numerical values. For example i setx related scalar function and named it f(x) suppose that f(x)=5 and how about if...

what can be defined by the following equation? im new to calculus, and I'm totally lost now :(

For example, the right-handed sneutrino. It can decay into both (s)leptons and anti-(s)leptons, so it is also the anti-particle of itself. I wonder how it looks like mathematically. If it is the same as normal scalar field, we can still distinguish its anti-particle (the complex conjugate)...

Hi, So if we have the Lagrange density for a massless scalar field: L=\sqrt{-g}\left(-\frac{1}{2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi-\frac{(n-2)}{4(n-1)} R\phi^2\right) Then under a conformal transformation g_{\mu\nu}=\omega^{-2}\tilde{g_{\mu\nu}} , then the Ricci sclar goes to...

Sometimes we need to calculate the evolution of the scalar field \phi with the equation of motion \frac{\partial^2 \phi}{\partial t^2}+3H\frac{\partial \phi}{\partial t}+m_\phi^2 \phi = 0. And we can get the field \phi=Ae^{im_\phi t} where A is the amplitude of the scalar field (damped by...

Hey guys, does any of you know where I could find the Feynman rules for scalar QCD? If they where colour ordered, even better! Cheers, earth2

Hi all :) can anybody help me out in understanding scalar function and vector function? the difference between them

The effective action Γ[ϕ] for a scalar field theory is a functional of an auxiliary field ϕ(x). Both Γ and ϕ are defined in terms of the generating functional for connected graphs W[J] as W[J] + \Gamma[\phi] = \int d^dx J \phi , \quad \frac{\delta}{\delta J(x)} W[J] = \phi(x) Show - \int...

Homework Statement This is what we are given in the assignment: Recall a definition of scalar product on complex numbers. Let A = [[3,1],[1,2]]. Prove that the product as defined by: * => dot product u * v := uT * A * conjugate(v) ( = Sum from i,j=1 to 2; uiAijconjugate(vj) )...

I have a problem where part of the solution involves taking the Curl of the partial derivative of a scalar. If A is a scalar function, then wouldn't taking the partial derivative of A with respect to time "t" just give another scalar function?

Homework Statement The vector -1.90A has a magnitude of 59.1 m and points in the positive x direction. Calculate the x component of the vector A. Calculate the magnitude of the vector A. Homework Equations 3. The Attempt at a Solution I understand vectors but having a...

Homework Statement Draw the vector C = 1.5A -3B (Mastering Physics problem) A is 4.5 and B is 1.0 The Attempt at a Solution I've tried it 4 times and still can't do it. I've looked at some sites but I guess I just don't understand it. I've heard of the head to tail method, or something...

Is it possible to explain, in one or two paragraphs, what the scalar curvature, R, is as it applies to General Relativity (the Einstein Field Equation, specifically?). This needs to be understandable to a high school AP-C physics student. Signed, Me - the high school AP-C physics student...

Basic question on scalar filed theory that is getting on my nerves. Say that we have the langrangian density of the free scalar (not hermitian i.e. "complex") field L=-1/2 (\partial_{\mu} \phi \partial^{\mu} \phi^* + m^2 \phi \phi^*) Thus the equations of motion are (\partial_{\mu}...

Homework Statement If \phi depends on a single position only, \phi=\phi(x,y,z) Can I say that: \oint{\frac{\partial\phi}{\partial{x}}dx=\oint{d\phi}=[\phi]_{a}^{a}=0 Provided that the point a lies on the closed path being integrated around? Homework Equations The Attempt at a Solution I...

Homework Statement Is this true or false? \int_V {\vec \nabla \Phi \bullet {\bf{E'}} \cdot {d^3}x} = \vec \nabla \Phi \bullet {\bf{E'}} - \int_V {\Phi \cdot \vec \nabla \bullet {\bf{E'}} \cdot {d^3}x}

Homework Statement Let's say A is a 7x7 matrix which is defined as [a b c 0 0 0 0; b a 0 d 0 0 0; c 0 a b e 0 0; 0 d b f 0 e 0; 0 0 d 0 f b g; 0 0 0 d b f h; 0 0 0 0 0 0 0] where semicolon (;) represent a new row and a space is a new column.Homework Equations If y = expm (A*t), where expm...

Hi, My question is. Can in principle, a Lagrangian density for some theory be a pseudo-scalar. Normally people say that the Lagrangian needs to be a scalar, but it case it is a pseudo-scalar it would also be a eigaen function of the parity operator. This topic could well be on the...

Hi I was reading a physics book and i came to the part where the started to explain vectors and scalars and i got really confuzzled(confused/puzzled) please help

Does anybody remember some reference to models where the Z and W particles are in massive susy multiplets of vector type? Such models should predict, besides the zino and wino, scalar partners for the Z and W, as well as new chiral fermion for each (probably the later should be able to...

Group Theory: Most general scalar potential out of 2 doublet irreps of S3. I'm taking a course on group theory in physics, but the teacher is really bad at making the bridge between the maths and the physics. As homework I have to do the exercise below. I think I know how to do it but I'm...

greetings in a scalar gradient why does the unit vector has appeared?scalar gradient only represent the change in that scalar quantity along x,y and z axis.then why unit vector along x, y and z comes in picture? advanced thanks.

hi, I do wonder if the Higgs boson is a quantum object because since it is the (only) particle with spin 0, then it should not behave like a wave(since the wave aspect is connected to the fact that it is spinning) and therefore not experience the uncertainty principle. Or am I wrong?

I was surprised that I have never had to do this in so long and forgot the basic way to factor out a scalar multiple when a matrix is raised to a certain power (for example -1 for inverse matrices). Basically, I just want some confirmation: (λT)^n= λ^n (T^n ) ∶ for λ ϵ F and Tϵ L(V)...

Hello all. Again, thank you for the help so far. Forgive the lack of tex in this post, it somehow was creating errors no matter what I tried. My question this time involves understanding the F and D terms in SUSY theories. From what I understood, they were introduced as auxiliary fields (EOM...

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...

Hello to all, Greetings! i know there are really great minds here in this forum, I just wanted to know if any of you have heard of these scalar energy pendants? are they safe? and what medical benefits do they give? I work in CT and MRI so i know a little bit of physics. from my...

This is a pretty elementary question but I had it on a quiz and it made me think... does a speedometer measure a scalar or vector quantity? I answered that it measures a vector quantity my rational being that it is the instantaneous speed in a forward direction, always. It doesn't matter if...