Scalar Definition and 777 Threads

Homework Statement I'm confused about the difference between the following two statements: \mathbf{V_1}\mathbf{V_2}=V_1V_2\cosh (\phi) and \mathbf{V_1}\mathbf{V_2}=\gamma c^2 Where \gamma is the Lorentz factor of the relative speed between the two vectors. Both vectors are time-like. The...

Hey again, I have a question on a couple of things related to feynman diagrams but also the relativistic scalar propagator term. First of all, this interaction: The cross represents a self-interaction via the mass and characterised by the term: -im^2, is this just some initial state...

Homework Statement If M is a square matrix, prove: (A, MB) = (adj(M)A, B) where (A, MB) denotes the scalar product of the matrices and adj() is the adjoint (hermitian adjoint, transpose of complex conjugate, M-dagger, whatever you want to call it!) Homework Equations adj(M)=M(transpose of...

Why is there no meson made up by only up and down quarks but even under parity? Is there something that forbids its existence? The pions are all axial (pseudoscalar) mesons. As we go higher in energy, there are such "flavour-pure" mesons. Is this a consequence of the almost-unbroken isospin...

hi we know that our universe is homogenous and isotropic in large scale. the metric describe these conditions is FRW metric. In FRW, we have constant,k, that represent the surveture of space. it can be 1,0,-1. but the the Einstan Eq, Ricci scalar is obtained as function of time! and this...

Homework Statement Hi I a attempting to derive the expression for the conserved Noether charge for a free complex scalar field. The question I have to complete is: " show, by using the mode expansions for the free complex scalar field, that the conserved Noether charge (corresponding to complex...

Why Work Is Scalar Quantity ?? I'm wondering that Why is work a scalar quantity ? Since it is the product of the force and displacement which are both vector?

Homework Statement Suppose that a,b,c are nonparallel nonzero vectors, and that ( a \times b) \cdot c = 0 . Show that c is expressible as a linear combination of a and b. Avoid geometric arguments (that is, try to stick to vector algebra and symbols in the proof).Homework Equations The Attempt...

Double contraction of curvature tensor --> Ricci scalar times metric I'm trying to follow the derivation of the Einstein tensor through double contraction of the covariant derivative of the Bianchi identity. (Carroll presentation.) Only one step in this derivation still puzzles me. What I...

I know that physically, they describe relationships whereby, for instance a vector field, for each point in three dimensional space (a "vector"), we have a "vector" which has a direction or magnitude. Now I once asked what the difference between a vector field and a vector function is and the...

Hello! I seem to have a problem with spherical coordinates (they don't like me sadly) and I will try to explain it here. I need to calculate a scalar product of two vectors \vec{x},\vec{y} from real 3d Euclidean space. If we make the standard coordinate change to spherical coordinates we can...

[SIZE="4"]we already know that the scalar component of the Centripetal ( Radial ) Acceleration vector is always negative because it's ALWAYS directed to the opposite direction of its unit vector ( toward the center of the circle ) , and this is satisfying to me and to the formula . however ...

Homework Statement Homework Equations Definitely related to the divergence theorem (we're working on it): The Attempt at a Solution I'm a bit confused about multiplying a scalar field f into those integrals on the RHS, and I'm not sure if they can be taken out or not. If they can be, I...

Someones like teachers in my country says energy is vector and scalar . Is that true ? Anyone can prov that ?

Of the 3 vectors, does it matter what order I cross / dot them? <a \times b> \bullet c =? <a \times c> \bullet b

How can i divide elements of an array into a scalar. I mean, i have read my data file into a matrix in FORTRAN which this matrix is 1*3414. Then, I want that each elements of this matrix is divided to (24480*2). I will be so grateful if you guide me the appropriate function. Thanks a lot

Hi all, I'm a part III student and taking the QFT course. The following seems "trivial" but when I went and asked the lecturer, the comment was that they too hate such nitty gritty details! The problem is page 12 of Tong's notes: http://www.damtp.cam.ac.uk/user/tong/qft/one.pdf All...

Here's the link that I read for Laplacian- http://hyperphysics.phy-astr.gsu.edu/hbase/lapl.html It looks as if the laplacian is scalar but the point is we know that ∇x∇xA= ∇(∇.A) - ∇2A This means that laplacian should be vector in nature which contradicts what was given in the link...

Hello everyone, Does everything in the universe have potential energy? I know there are two main form's of energy that are showen every day... Motion KE and potential energy and I believe all physical object's have PE and some are in KE even if they lose that motion they will return back to PE...

Homework Statement From the inequality |a.b| <= |a||b| prove the triangle inequality: |a+b| <= |a| + |b| Homework Equations a.b = |a|b| cos theta The Attempt at a Solution Making a triangle where side c = a+b. Don't know how to approach the question. Thanks.

Homework Statement I need to prove both of these (in exercise 11) http://postimage.org/image/x7shxv11f/ Homework Equations The dot product The Attempt at a Solution

Homework Statement If the magnitude of the sum of two vectors is less than the magnitude of either vector, then: -the vectors must be parallel and in the same direction -the scalar product of the vectors must be negative -none of these -the scalar product of the vectors must be...

u and v are contained in V Lets say the scalar multiplication is defined as: ex. ku=k^2 u or ku = (0,ku2) u=(u1,u2) does this mean that this is also the same for different scalar m? mu=m^2 u or mu = (0,mu2) u=(u1,u2) and does this mean the same for any vector v kv=k^2 v or...

u and v are contained in V Lets say the scalar multiplication is defined as: ex. ku=k^2 u or ku = (0,ku2) u=(u1,u2) does this mean that this is also the same for different scalar m? mu=m^2 u or mu = (0,mu2) u=(u1,u2) and does this mean the same for any...

Homework Statement Express the 5.2-kN force F as a vector in terms of the unit vectors i, j, and k. Determine the scalar projections of F onto the x-axis and onto the line OA. I have attached an image of the problem. Homework Equations Fx = Fcos(θ) Fy = Fcos(θ) Fz = Fcos(θ)...

Brian Powell [bapowell] has a new paper out - Scalar runnings and a test of slow roll from CMB distortions, http://arxiv.org/abs/1209.2024. This is interesting and challenges some of the more radical ideas that are currently popular. Very nice, Brian!

Identify each of the quantities below as Vector or Scalar. Speed of a train. (Vector) Volume of a cube. (Scalar) Acceleration of a rocket. (Vector) Mass of a pint of milk. (Scalar) Velocity of a train. (Vector) Force of gravity. (Scalar) I put my answers in parentheses but I am not...

Hello! I am preparing for an exam, I didn't really had much time for, and it would be nice of you if you could help me! Homework Statement Draw a figure, so that the following is true: (AC - AB) * AB = 0 2. The attempt at a solution Since I had to miss some classes, I don't really have...

Homework Statement In the problem, the electric scalar and vector potentials are, \phi=0, \vec{A}=A_0 e^{i(k_1 x-2k_2y-wt)}\vec{u_y} I have to find E, B and S. Then, I have to calculate \phi ' that satisfies div\vec{A}+\frac{\partial \phi '}{\partial t}=0 Then calculate E and B...

Can anyone clarify the concepts of zero vector and zero scalar? -Devanand T

I have the vector: {\bf{u}}(x,y) = \frac{{x{\bf{i}} + y{\bf{j}}}}{{{x^2} + {y^2}}} Where: x = a\cos t y = a\sin t I know I need to use the equation \int\limits_0^{2\pi } {{\bf{u}} \cdot d{\bf{r}}} And the answer is \int\limits_0^{2\pi } {} ((a\cos t/{a^2})( - a\sin t) +...

In this expression the junk on the left is a scalar. The stuff before the integral is another scalar. The integral is a time-like curve between x1 and x2 and at imagine fgf(x1) is a lower left corner of the rectangle and fgf(x2) is the upper right corner and x2-x1 is the length of the base of...

Homework Statement Find vector and scalar equations that passes through point P(3,7,-1) and is perpindicular to the line of intersection of 2 planes. P1:x-y-2z+3=0 P2: 3x-2y+z+5=0 So initially i started by finding the line between the two planes. N1 Does Not Equal N2 so they are not...

Which is the mass dimension of a scalar filed in 2 dimensions? In 4 dim I know that a scalar field has mass dimension 1, by imposing that the action has dim 0: S=\int d^4 x \partial_{\mu} A \partial^{\mu} A where \left[S\right]=0 \left[d^4 x \right] =-4 \left[ \partial_{\mu} \right]=1...

It's impossible that the higgs boson was the only scalar boson in nature. Could quantum-nonlocality be mediated by scalar boson or connected with scalar field? How do you discount or refute this?

Homework Statement I have the following task: In quantum free scalar field theory find commutators of creation and anihilation operators with total four-momentum operator, starting with commutators for fields and canonical momenta. Show that vacuum energy is zero. Homework Equations...

I'm having trouble fully understanding what electrical potential means. If there are two point charges of opposite signs and a point charge somewhere around them, we simply add the two voltages separately? Not as a vector sum? Also the concept of negative potential, does this mean that the...

Homework Statement We have a matrix Anxn (different than the identity matrix I) and a scalar λ=1. We want to check if λ is an eigenvalue of A. Homework Equations As we know, in order for λ to be an eigenvalue of A, there has to be a non-zero vector v, such that Av=λv The Attempt at a Solution...

Homework Statement Find the Scalar Equation of a Plane containing the points P(1,1,-1) Q(0,1,1) Homework Equations ax + by+ cz = d The Attempt at a Solution PQ = [-1,0,2]T [x,y,z]T = [1,1,-1] + s[-1,0,2]T + t[a,b,c]T ^ This is the vector equation.

If you Lorentz transform a scalar: U^{-1}(\Lambda)\phi(x)U(\Lambda)=\phi(\Lambda^{-1}x) If you now perform another Lorentz transform, would it it look like this: U^{-1}(\Lambda')U^{-1}(\Lambda)\phi(x)U(\Lambda)U(\Lambda')=\phi(\Lambda'^{-1}\Lambda^{-1}x) ? But isn't this wrong...

Need to find the Ricci scalar curvature of this metric: ds2 = e2a(z)(dx2 + dy2) + dz2 − e2b(z)dt2I tried to find the solution, but failed to pass the calculation of Riemann curvature tensor: <The Christoffel connection> Here a'(z) denotes the first derivative of a(z) respect to z...

Homework Statement Need to find the Ricci scalar curvature of this metric: ds2 = e2a(z)(dx2 + dy2) + dz2 − e2b(z)dt2 Homework Equations The Attempt at a Solution I tried to find the solution, but failed to pass the calculation of Riemann curvature tensor: <The Christoffel...

the potential difference between b and a is defined as follows: V(b) - V(a) = -∫E \bulletdl the integral is taken from a to b. so the potential of a positive charge, with infinity as reference, is V(r) - V(infinity) = V(r) = -∫E \bulletdl the integral is from infinity to r...

I'm trying to prove the conformal invariance (under g_{\mu\nu}\to\omega^2 g_{\mu\nu}) of \bar{\Box}{\bar{\phi}}+\frac{1}{4}\frac{n-2}{n-1}\bar{R}\bar{\phi} I've found that this equation is invariant upto a quantity proportional to...

In Physics it seems quantities are either Scalars or Vectors (let's not get into tensors, but if there are other types, please tell me). Vectors I understand reasonably well. Scalars, however, I'm not so sure about: Consider the Scalar quantity of Temperature. There is absolute zero, but...

In the Einstein tensor equation for general relativity, why are there two terms for curvature: specifically the curvature tensor and the curvature scalar multiplied by the metric tensor?

Hi, I'm trying to find a general expression for the scalar triple product for 3 vectors in a simultaneous configuration, that depends only on the inter-vector angles, A1, A2 and A3. I have expressed this quantity in terms of the spherical polar coordinates of the vectors (the length being...

-3i-j+5k = t (root34/102 (11i-13j+4k))-s(-j-k)+r(2i+2j+k) how do i write this eqn as 3 scalar equations and a system of three linear eqns for the three parameters r,s, and t. PLEASE HELP...

Homework Statement I understand the premise of Noether's theorem, and I've read over it in as many online lectures as I can find as well as in An Introduction to Quantum Field Theory; Peskin, Schroeder but I can't seem to figure out how to actually calculate it. I feel like I'm missing a...

We know that work is the dot product between force and displacement .. so dot product always gives scalar (horizontal projection etc) hence work is a scalar quantity? I want the reason behind it... we always do work in specific direction.. suppose a man in appliying force at the angle...