Recent content by Rabindranath

How would the theory look if gravitational mass was not equal to inertial mass?

Thanks for pointing out the missing information. The basis in question is such that the full ##\mathfrak{o}(m+n-x,m+n-x) \equiv \mathfrak{o}(d,d)## metric representative has the block off-diagonal form $$\eta = \begin{pmatrix} 0 & I_d \\ I_d & 0 \end{pmatrix}$$ (where the block ##I_d## is the...

So, as far as I understand, ##\wedge^2(x)## would be the algebra of bivectors ##u \wedge v##, for ##u## and ##v## of dimension ##x##. Does this sound like a meaningful statement?

Your four points basically sum up my questions perfectly. I assume that the integers in question double as names for algebraic structures, and that e.g. ##8## and ##\bar{8}## would be two different structures corresponding to ##x = 8##. Would this make sense?

Let's say I want to study subalgebras of the indefinite orthogonal algebra ##\mathfrak{o}(m,n)## (corresponding to the group ##O(m,n)##, with ##m## and ##n## being some positive integers), and am told that it can be decomposed into the direct sum $$\mathfrak{o}(m,n) = \mathfrak{o}(m-x,n-x)...

Thanks for your reply. I do believe, however, that I do account for the fact (correct me if I'm wrong). From the definition of the Christoffel symbol ##\Gamma^\lambda_{\mu\nu} = \frac{1}{2} g^{\sigma\lambda} \{ \partial_\mu g_{\nu\sigma} + \partial_\nu g_{\mu\sigma} - \partial_\sigma g_{\nu\mu}...

Given a Weyl transformation of the metric ##g_{\mu\nu} \rightarrow g'_{\mu\nu} = e^{\Omega(x)} g_{\mu\nu}##, I'm trying to find the corresponding connection ##\Gamma'^{\lambda}_{\mu\nu}##, and from that ##-## via the Riemann tensor ##R'^{\lambda}_{\mu\nu\kappa}## ##-## the Ricci tensor...

1. The problem statement I want to write the angular momentum operator ##L## for a 2-dimensional harmonic oscillator, in terms of its ladder operators, ##a_x##, ##a_y##, ##a_x^\dagger## & ##a_y^\dagger##, and then prove that this commutes with its Hamiltonian. The Attempt at a Solution I get...

Rather ##z \mapsto \left|\left<z_0 |z \right>\right|^2## if I use your example. That is, going back to my example again, for some arbitrarily chosen fixed element ##\left|\psi\right>## in the Banach space ##B_\phi##, I'm interested in the map ## \left|\phi\right> \mapsto...

I want to prove Cauchy–Schwarz' inequality, in Dirac notation, ##\left<\psi\middle|\psi\right> \left<\phi\middle|\phi\right> \geq \left|\left<\psi\middle|\phi\right>\right|^2##, using the Lagrange multiplier method, minimizing ##\left|\left<\psi\middle|\phi\right>\right|^2## subject to the...