Recent content by DrFaustus

schieghoven -> Seems like you'll have to study Glimm&Jaffe a bit more before being able to meaningfully disagree on QFT discussions :) Don't take it personally or be offended, it's just so big and technical as a subject that, for *physicists*, it's hardly worth the effort of studying properly...

I really wish people and books would stop "teaching" and "explaining" QFT by ONLY talking about Fock space. Not even for free theories it is the be all and end all of QFT (just think about thermal states... they do *not* live in Fock space), let alone for interacting theories where you're thrown...

AxiomOfChoice -> Your argument above does not hold. If A-B=0 it does not follow that A=B=0, but only A=B. Also, consider the 1D free Hamiltonian, which is simply -\partial_x^2, and have it act on a e^{ipx}. You have a "real" Hermitian operator acting on a complex function giving you a real...

Before giving you my suggestions I need to ask you what are you looking for in the books. Very simply, physicists' books can give mathematicians headaches. So my question is if you're looking to learn some physics like a physicist would or if you want to know the physics but prefer some...

george.jones -> Good observation, the second term comes from the geodesic condition indeed. arkajad -> That's precisely what I'd like to understand better. I know it's a derivative wrt p^\alpha, which is why I think the full equation should be covariant. Could you give me some more details or...

The first term is manifestly covariant because f is a scalar and for scalar quantities the covariant derivative coincides with the usual partial derivative...

orentago -> Now I get it where your confusion is! When integrating by parts you always assume (because it's convenient) that the relevant quantities decay to zero at infinity. Or in this case, that the "surface term" vanishes. Remember that when integrating by parts the term "outside the...

tom.stoer -> Because it is :) What I'm really referring here to is the rigorous (mathematical) construction of interacting fields. But even at a formal level, you cannot extend the harmonic oscillator analogy to an interacting field. Write down the interacting equations of motion, just like you...

orentago -> Your first line seems completely wrong (typos?), but the last equality in the first line would seem what you need. Move the \nabla_x acting on the commutator to the field by partial integration, you pick a minus and a \nabla_x^2 \phi(x). Then evaluate the commutator, you get a delta...

AxiomOfChoice -> The reason why you *want* a self-adjoint Hamiltonian (and not only Hermitian...) is that for s.a. operators you can spectrally decomose them and define functions of those operators, not so much that the eigenvalues are real. For instance, say the eigenvalues of some operator are...

The connection between harmonic oscillators and quantum fields only holds for free fields, independently on whether it is a scalar, spinor or gauge field. And the reason is more mathematical than physical, meaning that you can see that the Lagrangian of a free field is really a collection of...

tom.stoer -> QFT is full of mathematical problems, but this one most definitely is not one of them. Field operators depend on a continuous parameter, the spacetime coordinates, and taking derivatives with respect to one really is just what one would expect it to be. At least if we are talking...

The "proof" of the above "rule" can be found in any calculus book. The derivative wrt x is a partial one so it does not act on B(y). In other words, B(y) is treated as a constant when it comes to partial differentiation wrt x. Expand the commutator and see the magic unveil... All the hints...

It's the collisionless Boltzmann equation: p^\mu \frac{\partial f}{\partial x^\mu} - \Gamma_{\alpha \beta}^\gamma p^\alpha p^\beta \frac{\partial f}{\partial p^\gamma} = 0 The first term is manifestly covariant, and so should be the second one. As for the Christoffel symbol, Wald states...

Hi everyone, have a question about covariant, coordinate independent quantities in GR. Reading Kolb and Turner's book The Early Universe one can find the Boltzmann equation in a GR setting. Now, one of the terms in that equation is - \Gamma_{\alpha \beta}^\gamma p^\alpha p^\beta...