Recent content by FrederikPhysics

Thank you for your answer. If i understand your post the statement of invariance is a statement of the form of an equation independent of variables. But then is not every equation involving only the gauge field Aμ and coordinates invariant under gauge transformations since the gauge...

The Lagrange function generating these Yang-Mills equations are gauge invariant L=L', but as mentioned the Yang-Mills equations themselves transform according to the adjoint representation (DμFμν)'=UDμFμνU† which does not seem invariant to me, still people say that the are invariant under gauge...

Hey. When talking about invariance of a function f under some transformation T we mean that T(f)=f. But what is meant by invariance of an equation f=0? As far as I can see it makes sense to call an equation invariant when the transformed equation T(f)=T(0) is equivalent to the original equation...

Hello, I am looking for some nontrivial metric on ℝ^2 invariant under the coordinate transformations defined by the 2x2 matrix [1 a12(θ)] [a21(θ) 1], where aik is some real function of θ. In the same way that the Minkowski metric on ℝ^2 is invariant under Lorentz transformations. Does...

I am wondering about the minimum possible uncertainty (standard deviation) in an electron's position (Δx). How precise can one know the electron's whereabouts without creating other sorts of particles and phenomenons. I know of the localization energy interpretation of the energy uncertainty...

Okay, so one might say: Let ##T=\frac{1}{2}m\dot{\textbf{r}}\cdot\dot{\textbf{r}}## be the kinetic energy of a one particle system, ##\textbf{r}## the position vector in some frame and q a set of generalized coordinates. ##q_{k}## is called a translation coordinate when there exists a vector...

For a system consisting of one particle with mass m one writes T=½m(dr/dt2+r2 dθ/dt2+r2sin2θ dφ/dt2) in spherical coordinates, θ being the polar angle and φ the azimutal angle, that makes T=T(r, θ, dr/dt, dθ/dt, dφ/dt).

I am currently reading Goldstein's Classical mechanics and come on to this problem. Let q1,q2,...,qn be generalized coordinates of a holonomic system and T its kinetic energy. qk correspondes to a translation of the entire system and qj a rotation of the entire system around some axis, then...