Recent content by Heisenberg1993

Let "T" be the generator. Then the group element is g=eiαT, where α is the parameter. The existence of the "i" already makes the exponential imaginary. If we make the generator pure imaginary, this will in fact require α to be pure imaginary.

That's exactly my question, why it doesn't look like which (R or R2)?

Why is i that two cones connected at their vertices is not a manifold? I know that it has to do with the intersection point, but I don't know why. At that point, the manifold should look like R or R2?

I was reading some lecture notes on super-symmetry (http://people.sissa.it/~bertmat/lect2.pdf, second page). It is stated that ". In order for all rotation and boost parameters to be real, one must take all the Ji and Ki to be imaginary". I didn't understand the link between the two. What does...

Thank you all for your interesting ideas :smile:

I've attached the relevant sections. Please read them and clarify the misunderstanding Thanks

Hello NascentOxygen Indeed the book is discussing a different situation. It is discussing the motion of a single wheel, not one that is related to another by the gears of the bike. If you have the book, extended 8th edition, please read it on page 279.

In Chapter 11, section 11-4, subsection friction and rolling, it is stated that the static frictional force is along the same direction as the direction of motion because the point of contact of the wheel with the floor is moving in the opposite direction. Then, in the next subsection, the same...

Hi! It is stated in V. Mukhanov's book "Physical foundations of Cosmology" the following (page 44, after equation 2.25): "In contrast, for the dust dominated universe, where ηmax=2π, the event horizon exists only during the contraction phase when η>π." could someone please explain why is this...

So in a sense we don't need the second condition to show that A is real, just the fact that we used the transpose of the matrix is enough. If the m,atrix was complex, then we should have used the complex adjoint of it, right?

Thanks for the reply concerning the first question, in A. Zee's book "Quantum Field Theory in a nutshell", it is stated that "any orthogonal matrix can be written as O=eA. from the conditions that OTO=1 and det(O)=1, we can infer that A is real and anti-symmetric." From the first condition, I...

1- How can infer from the determinant of the matrix if the latter is real or complex? 2- Can we have tensors in an N-dimensional space with indices bigger than N?