Recent content by protonsarecool

Actually I made a mistake in that line. ## -\bra{1}\ket{\eta} = (-1)^2 \bra{1}\eta\ket{1} ##, so that line of reasoning didn't actually work. But now the picture is clear, and consistent with your quote of Shankar: ## -\eta = - \eta \bra{1}\ket{1} = \bra{1} \eta \ket{1} = - \bra{1}\ket{1} \eta =...

I've thought about my post #8 some more, and Altland&Simons treatment of fermionic coherent states is consistent with other textbooks, and the annihilation operators do have to anti-commute with the Grassmann eigenvalues. See for example Eduardo Fradkin "Field Theories of Condensed Matter...

It's in the book he is citing, Altland & Simons "Condensed Matter Field Theory". On p. 160, they start by defining a fermionic coherent state by requiring that it is an eigenstate of the annihilation operators, just as in the bosonic case. $$ a_i \ket{\eta} = \eta_i \ket{\eta} $$ Then they...

It is a common strategy in physics. As we look into very short times t << 1, higher powers of t will give much smaller corrections and are thus neglected. The dominating contributions close to the limit t -> 0 come from the lowest powers of t, which is in this case the quadratic term. Also look...

Yes, <c|w><w|c> = |<c|w>|^2 is a real number.

The 2-form you have written down is just the Berry curvature, which happens in this context to be also the first Chern form. Forms like this do pop up a lot in the context of topological insulators, and i guess skyrmions as well. The 1-form you are writing would look like a Berry connection (of...

To come back to the original question, here is another very recent calculation regarding meta-stability of our universe: Scale-invariant instantons and the complete lifetime of the standard model Anders Andreassen, William Frost, and Matthew D. Schwartz Phys. Rev. D 97, 056006 – Published 12...

Thermal quantum field theory describes quantum systems in thermal equilibrium, while you are describing a non-equilibrium situation. You will probably need Keldysh field theory to model anything like this. But i don't know if your specific question has been studied before.

Right, i have no idea how i could see any such diagrams in the OP. Guess i was tired. OP, please forget that i said anything.

Take a photon-photon-electron vertex. You could have the time-ordering such that: electron spontaneously is destroyed/annihilated and 2 photons "come out" electron and photon interact and 1 photon comes out Even as a virtual process (ie. at least one internal line coming out of the vertex)...

Classically, moving charges produce magnetic fields, sure. But notice that even then, a classical moving electron does not change momentum by "producing" a magnetic field (which is just the Lorentz transformed electric field anyway). The quantum version of this is slightly more complicated, in...

I don't think it is a good habit to think of Feynman diagrams in terms of actually "happening" dynamical processes. They are just useful shortcuts in a perturbative expansion of time-ordered correlation functions. One should first learn enough foundations of QFT (either in the functional...

To answer your google question, it is called the Cartesian product. As fresh said, it is just the set of ordered tuples.

You can use the covariant derivative in the Dirac equation and treat it as a "single particle" equation with coupling to a classical EM field. If you solve eg. the hydrogen problem this way, you get several relativistic corrections that you would not get out of using the Schroedinger equation...

Yes. More specifically, Susskind et al. conjecture that quantum entanglement and Einstein-Rosen bridges (ie. wormholes) are really the same ("ER=EPR"), and from that somehow follows that QM=GR. https://en.wikipedia.org/wiki/ER%3DEPR https://arxiv.org/abs/1708.03040