Scalar Definition and 777 Threads

Hi, Following my recent https://www.physicsforums.com/showthread.php?t=375638" with density matrix formulations of scattering theory, here's a question I faced on yesterday's particle physics exam. I did some mechanical computation, but I am not fully convinced of what I did (basically computed...

Is there any particular reason that scalar curvature is defined R = g^{ab}R_{ab} instead of R = R^{ab}R_{ab} ? Do both scalars share the property that they are zero if and only if every component of R^{a}_{bcd} is also zero?

Graphics of one variable functions are two dimensional lines. Graphics of two variable functions are three dimensional surfaces. Three variable functions cannot be plotted. But can I think of the usual 3D representations of vector and scalar fields as manners of visualizing a three variable...

Y=a+b because Y,aa+Y,bb=0

Homework Statement Classify each of the following quantities as scalar(s) or vector(v): Temperature Speed Acceleration Volume Work Area Mass Electric Field Velocity Displacement Force Homework Equations none The Attempt at a Solution Temperature - scalar Speed - scalar...

Homework Statement Show that u, v, w lie in the same plane in R3 if and only if u · (v × w) = 0. Homework Equations The Attempt at a Solution if u · (v × w) = 0, then u is orthogonal to vxw, and vxw is orthogonal to v and w. therefore, u must lie in the same plane...

Hi, I wonder if someone could help me. I'm trying to find the potential function,\phi, of the field: v = y2z3i + 2xyz3j + 3xy2 z2k So using v = \nabla\phi, I have found: \frac{\partial \phi}{\partial x} = y2z3x + F(y,z) \frac{\partial \phi}{\partial y} = y2z3x + G(x,z)...

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'm studying the properties of the energy momentum tensor for a scalar field (linked to the electromagnetic field and corresponding energy-momentum tensor) and now I'm facing the statement: "for a theory involving only scalar fields, the energy-momentum tensor is always symmetric". But I've...

I hope someone can explain this to me: In multiple textbooks I've seen it said that a single particle wave function (no spin) transforms as a Lorentz scalar. I.e. if we have a Lorentz transformation from an old frame to a new frame \overline{x}=\Lambda x (x is short for (t,x,y,z)) then...

Homework Statement Show that with d spatial dimensions the potential \phi due to a point charge q is given by \phi (r) = \frac{\Gamma(\frac{d}{2}-1)}{4\pi^{d/2}}\frac{q}{r^{d-2}} Homework Equations The Attempt at a Solution The electric field strength is known to be: E(r) =...

How do you find the scalar product of two non-orthogonal many particle states? For example <\leftarrow,\rightarrow|\uparrow,\downarrow> I wanted to express both as a 4-vector in the up/down basis, but this seems weird, since then a state |\uparrow\downarrow+\downarrow\uparrow> is like...

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

Homework Statement Hello all, thanks for reading... I was assigned to calculate feynman rules for the scalar QED theory via functional methods. The fields are a scalar complex field \phi, \phi^* and gauge field A_\mu, and the lagrangean is \mathfrak{L} = (D_\mu \phi)^* (D^\mu \phi) - m^2...

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 Homework Equations I think that I need to find the moment of the force F about the line BC first. Then, using that moment, find the "projection" of M_{BC} onto the X axis to find the answer. M_{BC}\sin \left(45^{o}\right) However, I am not getting anything...

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) =...

Hi everyone, I'm reading section 9.2 of Peskin and Schroeder, and have trouble understanding the origin of a term in the transition from equation 9.26 to 9.27. Specifically, equation 9.26 is \frac{1}{V^2}\sum_{m,l}e^{-(k_m\cdot x_1 + k_l\cdot x_2)}\left(\prod_{k_{n}^{0}>0}\int d \Re...

Ok I have seen the tensor double dot scalar product defined two ways and it all boils down to how the multiplication is defined. Does anyone know which is correct? I believe the first one is correct but I keep seeing the second one in various books on finite element methods. 1. \nabla \vec{u}...

Hi, I have a problem to find the meaning of a special partial differential: partial scalar partial vector. i.e. dF/dn where F is a scalar and n is a i.e. normal vector. This is a partial diff. n could be a vector consisting of partial differentials, (dT/dx,dT/dy) I have looked in...

Homework Statement A sphere of radius a has a charge density which varies with distance r from the center according to http://img14.imageshack.us/img14/9577/wangsnessproblem594.gif where A is a constant and http://img35.imageshack.us/img35/555/wangsnessproblem593.gif .[/URL] Find the...

Homework Statement Find the scalar product of the 2 vectors. Vector A is north of east at 70 degrees with a magnitude of 3.60m Vector B is south of west at 30 degrees with a magnitude of 2.40mHomework Equations ABcosxThe Attempt at a Solution I did dot product using the formula...

Hi Just wondering if someone can tell me if the following are scalar or vector quantities and why Current Potential Potential Difference Also, I'm wondering if we include plus/minus signs in calculations depending on the charge. Ex. would current be negative if it was a negative...

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...

Is work a scalar or a vector quantity and why?

The Kretschmann scalar (the full contraction of the Reimann tensor K = R_abcd R^abcd) is often used to identify singularities - i.e. for a Schwarzschild black hole, K \propto 1/r^6, so we have a singularity at r=0, but not at the Schwarzschild horizon). Clearly, as r->\infinity, K->0. Is K=0...

Homework Statement I am trying to prove that: \nabla \cdot (\psi\mathbf{A}) = \mathbf{A} \cdot\nabla\psi + \psi\nabla \cdot \mathbf{A} Where nabla is a scalar function and A is a vector field The Attempt at a Solution I tried expanding both the LHS and RHS, but I think I am getting...

Homework Statement If a and b are 4-vectors give the definition of the scalar product a.b and demonstrate its Lorentz invariance Homework Equations The Attempt at a Solution So (with 4-vectors double underlined!) a.b = a0b0-a1b1-a2b2-a3b3 a' = (a0*gamma - beta*gamma a1 ...

Find the scalar equation of the plane which passes through the line intersection of planes x+y+z-4=0 and y+z-2= 0 that goes through (2,4,7) and satisfies the conditions a) it is 2 units from the orgin b) it is 3 units from the point a(5,-3,7) I would really apprecaite if some toke me...

Homework Statement Given a tensor Mab, Prove that its trace is a scalar. Homework Equations The Attempt at a Solution To prove the trace is a scalar, I know I have to prove it doesn't transform under coordinate transformations. Now, we can transform M^a_b as follows...

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...

If force is always parallel to displacement and displacement is always in a straight line and doesn't change direction. Then the displacement is equal to distance right? Distance is a scalar quantity. Does this mean that force parallel to displacement or distance as it would be is a scalar...

Homework Statement Hi there - I'm wondering about how you can actually show the existence of a scalar potential for an irrotational vector field E - if \nabla \times E = 0 everywhere, then how does one show there exists a scalar potential \phi(x) such that E=- \nabla \phi ? The Attempt at...

Hi this is the question that I am unsure about... Find and then sketch the level curves of the scalar field T(x,y) = (2x+y)/(x^2 -y^2) for; T = -1 T = -0.5 T = 0 T = 0.5 T = 1 I am unsure about these answers which I got by subbing each of the values into T(x,y) 1) T = -1 After...

I have a conservative force given in three vector components as normal. Each component is a function of x, y and z. I need to find the scalar potential. I am a bit confused about this because of the force's complexity. I know the V = (integral) F.dx, for a 1 dimensional problem, but i...

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...

http://img520.imageshack.us/img520/9580/56788025.th.jpg See the problem above. I can do all of the problem, barring the last part. I have found r and r.r: http://img520.imageshack.us/img520/1590/29349935.jpg How does this allow me to find the minimum and maximum distance...

I have been searching through the literature and popular textbooks for this simple answer. I know that in the absence of soures, i.e. matter fields the Ricci scalar is zero. This is synonymous with saying that the Ricci scalar vanishes in vacuum and that the resulting space is flat. However...

In Ray d'Inverno's book on general relativity, he defines the volume element in a way which makes it a scalar density of weight -1, meaning it transforms with the inverse of the Jacobian. Every other source I have looked at seems to say it should transform with the Jacobian, making it a scalar...

The temperature in an auditorium is given by T = x2 + y2 - z. A mosquito located at (1,1,2) in the auditorium desires to fly in such a direction that it will get warm as soon as possible. In what direction must it fly? I know that the gradient of T will point to the direction where the...

Homework Statement the displacement vector A has scalr omponents of Ax= 80.0 m and Ay= 60.0 m. the displacement vector B has a scalr component Bx= 60.0 m and a magnitude of B=75.0m. The displacement vecto C has a magnitude of C= 100.0 m and is directed at an angle of 36.9 degrees above the +...

To any teachers or students, either instructing or taking, a Calculus-based Physics I course: I tutor a calculus-based general physics course in kinematics, and similar topics, and, I recently had a student approach me about his inability to grasp the scalar/dot product, in vector operations...

Homework Statement Imagine a spatially 2d world. The electromagnetic field could be richer here, because you could add to the Lagrangian L an additional term (known as the Chern-Simons Lagrangian) L_{CS} = \epsilon_{0}\frac{\kappa}{2}\epsilon^{\alpha \beta...

what are the differences between scalar and vector quantities? why do we use */-in specifying direction of any scalar quantity

A force F of 6 units acts in the direction 30 degrees west of north. An object is constrained to move north-westerly, that is, 45 degrees west of north. (a) Sketch the force vector roughly to scale on a set of axes that has the positive y axis pointing north, and write F using exact values...

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...

Euclidean norm is defined usually as|v|2= g(v,v), where g is a nondegenerate, positive definite, symmetric bilinear form. But how can make it backwards? What properties must norm have that g(v,w) = (|v+w|2 - |v|2 - |w|2)/2 be a positive definite, symmetric bilinear form?

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