Recent content by Irigi

This is a misunderstanding. My matter satisfies Tμν;ν = 0. I was arguing that this condition is not enough to prevent creation of matter from nothing if (some particular form of) exotic matter is present, I never said I would like to violate energy/momentum conservation. I am interested in...

Thank you very much for your reply! I see, I wasn't aware of this. I can intuitively understand why DEC implies causality conservation. But does DEC violation automatically mean causality violation? Is there some theoretical example of classical matter that preserves causality and breaks the...

Hello everybody. I would like to kindly ask your help with a hypothetical hairy question about which I think a lot recently. It is known fact, that it is not possible to construct a wormhole without exotic mass that violates the weak energy condition. It is also known that many quantum fields...

OK, you are right then, there might be a problem. Can you give me some link on this topic, please? Is the problem already in Dirac's equation without radiative corrections? How does QED fix it? Thanks.

This doesn't seem correct. If we squeeze the atom to size x, we also know that Δx ≈ x and from uncertainty principle Δp ≈ p ≈ ℏ/x. Since Ekin ~ p2 ~ x-2, it grows faster that Coulombic potential -1/x around x = 0, so the kinetic term ougweights the potential one. That's why there should always...

Thank you! It seems to me that ansatz (**) works, very nice. Btw. did you mean \psi_n(x,t) = e^{-i\epsilon_n t} e^{-ie\chi(x,t)} u_{\epsilon_n}(x)\;\;? (\chi is function of both time and space, right?) Btw. these functions \psi_n(x,t) are no longer eigenfunctions of Hamiltonian, since...

Yes, sorry. I think it should be obvious, that if Hamiltonian H=\frac{p^2}{2m}+\varphi(r) has eigenvalues \varepsilon_n, Hamiltonian related by gauge transformation H'=\frac{p^2}{2m}+\varphi(r) - \frac{1}{c}\chi'(t) will have eigenvalues \varepsilon_n'=\varepsilon_n - \frac{1}{c}\chi'(t)...

OK, but this is still not so easy. For example if I choose \chi=f(t), Hamiltonian H=\frac{p^2}{2m}+\varphi tranformes into H'=\frac{p^2}{2m}+\varphi - f'(t). Since Hamiltonian commutes with time, H=U^\dagger H' U=H'\;is not true and the eigenvalues get changed! I showed above that only by a...

Btw. when we do the gauge transformation A'=A+\nabla \chi,\; \varphi'=\varphi-\frac{1}{c}\frac{\partial\chi}{\partial t}, \; \Psi'=U\Psi=\exp\left(\frac{ie}{c\hbar}\right)\Psi\;,operator related to every measurable quantity (for example Hamiltonian)...

I think you can't simply take classical H_0 in arbitrary gauge and make it a quantum Hamiltonian \hat{H}_0. The rule "take classical Hamiltonian and change classical quantities for QM operators" is not an exact procedure (because of the ordering problem). I think that H_0, A, \phi has to be...

Just to summarize my previous post - it seems to me that the problem is probably not in Born's rule, but in the procedure of finding "stationary states" for time-dependent Hamiltonians. We have such procedure if the Hamiltonian is time independent (finding its eigensystem and adding the...

Something is clearly not OK here, you cannot have space dependent eigenvalues. Inspired by http://iopscience.iop.org/0305-4470/20/3/023", I did some calculations. I do not have the general answer, but here are some hints: Transformation \chi(r,t)=\chi(r): Here, it is pretty simple. I start with...

I found article on gauge-invariant perturbation theory. It probably does not directly answer your questions, but it might be interesting reading. http://prd.aps.org/abstract/PRD/v20/i12/p3095_1