Recent content by Petr Mugver

Hi all, for job reasons I have come across LCCA, and I have started documenting myself reading this ebook that I found googling: Fuller-Petersen, LCCA. Now, I'm new to the topic, and I have a few questions: 1) Is it just about calculating all the costs of two projects, maybe taking inflation...

Yes, it sounds so obvious. I feel stupid now... :)

Uhm, please don't let me write the formula, but when you take the derivative with respect to t of the momentum dM/dv, don't you get extra terms due to f(t) and df(t)/dt?

Suppose I have a mechanical system with l + m degrees of freedom and an associated lagrangian L(\alpha,\beta,\dot{\alpha},\dot{\beta},t) where \alpha\in\mathbb{R}^l and \beta\in\mathbb{R}^m. Now suppose I have a known \mathbb{R}^l-valued function f(t) and define a new lagrangian...

Thanks to you, I also learned a lot thinking about theese things.

(1) + (3): It is equivalent because I showed that if instead of L(p) you use any other M(p) (for example the one you said, M(p) = L(p)M, with M in the little group) then when you calculate D_{\sigma\sigma'}(M^{-1}(\Lambda p)\Lambda M(p)) you get a different matrix (because D is a faithful...

This is one of the mistakes. Instead, write: \frac{\partial L}{\partial x_i}=\sum_j \frac{\partial L}{\partial q_j}\frac{\partial q_j}{\partial x_i}+\sum_j \frac{\partial L}{\partial \dot{q}_j}\frac{\partial \dot{q}_j}{\partial x_i} You fergot the second piece. Remember...

I strongly suggest you to study the Dirac's formalism of bras and kets, it makes all theese relations much clearer. Anyway, if U_n is complete and orthonormal, you must have, for every f belonging to the space: f=\sum_nU_n(U_n,f) or, in the x-representation f(x)=\sum_n U_n(x)\int...

Divide the x-y curve in small rectangles of base dx and height x^2. Now revolve each of theese rectangles around x=-1, obtaining a cylindrical shell of internal radius \pi (1+x)^2 and external radius \pi (i + x + dx)^2. The base area of this shell is dA(x) = \pi (1+x+dx)^2 - \pi (1+x)^2 =...

QuArK21343, can you give an example of a system whose energy, linear and angular momentum are conserved in one inertial system, but not in a different inertial system?

Ok I think I've got point (2). Call \Omega\in\mathbb{R}^4 one of the disjoint subsets of space-time, such that every two points p,q\in\Omega can be connected by a proper ortochronous homogeneous Lorentz transformation (POHLT). Every such \Omega is good for what follows, except the trivial one...

(1) I think the answer is yes: given a W belonging to the little group associated to a certain k, then choose p = k \Lambda = L(k)WL^{-1}(k) Note that L(k) belongs to the little group, and so does \Lambda, so L^{-1}(\Lambda p)\Lambda L(p)= L^{-1}(k)L(k)WL^{-1}(k)L(k)=W (2) I have to think it...

Following the philosophy of the previous post, a vector field is a vector function that behaves properly under, for example, rotations. So if R is a rotation a vecor field v(x) must satisfy v(Rx) = Rv(x)

L'L is symmetric positive definite, so it can be diagonalized with an orthogonal matrix M (that is, M'L'LM = D where M^-1 = M' and D is diagonal with positive eigenvalues). So: L'L = U'U MDM' = U'U D = M'U'UM = (UM)'(UM) so, just put UM = E U = EM' where E is the diagonal matrix whose...

I'm not sure about this, but I think that, for mathematicians, fields and functions are the same thing: f(x,y,z) is a scalar field, (f(x,y,z), g(x,y,z), h(x,y,z)) is a vector field etc. For physician a field is not just a general function, but a function that behaves properly under certain...