Recent content by Haorong Wu

Hi, Paul Colby. Then, after the interaction, what should I do next? Should I accept that the EM fields now violate the Lorenz gauge conditions, or should I throw away the temporal and the longitudinal components to restore the gauge conditions, or should I resort to the Ward identities to...

Hi, @DelajaSchuppers. Thank you for your answer. I am not familiar with the UniPhiEd theory. I understand the continuity equation is broken in the finite time interaction. Then, do we lose the privilege to choose the gauge, even before the interaction starts? For example, if the interaction...

Suppose we choose the Lorenz gauge conditions for an EM field, ##\partial_\mu A^\mu=0##. The EOMs for the field are given by ##\Box A^\mu=J^\mu##, with ##\partial_\mu J^\mu=0##. If the interaction time is ranged from ##-\infty## to ##t##, ##A^\mu## satisfy the Lorenz gauge, because ##A^\mu(x) =...

Very sorry for the confusion. In my manuscript last year, I typed ",i.e." in LaTeX. However, in the proofs, I notice that they are all replaced by "-i.e.," by the editor, as in the following figure. Therefore, in my recent manuscript, I typed "---i.e.," in LaTeX. However, in the proofs, they...

Last year, I submitted a manuscript to PRD. I noticed that all ",i.e.," are modified into "-i.e.," by the editor. Therefore, in my recent manuscript, I typed "---i.e.," in LaTeX. However, all the "-i.e.," are modified again into "-i.e.," by the editor. I could not distinguish the difference...

Hi, @Ibix, and @PeterDonis. I am recently interested in boosting a scalar field, so I found this paper, Relativistic Hall Effect. I am sorry it is not open-access, so I am not sure whether you can access it or not. The mode functions, Eq. (9), are a little complicated as the authors use the...

Suppose we can boost from a frame ##S## to another frame ##S'## by using a Lorentz transformation ##\Lambda##. Also, ##\phi(x^\mu;\omega,\mathbf k)## is a mode function of a scalar field in frame ##S##. Then, how do we express this mode function in frame ##S'##? Here is my attempt. First, the...

In Peskin's textbook, the coupling factor is given by a constant in the interacting field theory. The scattering matrix ##S## is given by the time-evolution operator, ##\exp(-iHt)##, in the limit of very large t, i.e., ##t\rightarrow \infty##, as expressed in Eq. (4.71). In my mind, the...

@PeterDonis , from the image in the book, it appears that ##\mathbf r## is not the relative position vector. I may solve the problem. Denote ##\mathbf x=\mathbf r-\mathbf R##. Then, ##\nabla_{\mathbf R}\psi_n(\mathbf r-\mathbf R)=(\frac \partial {\partial R^1}\psi_n(\mathbf r-\mathbf...

In studying the Aharonov-Bohm effect, a model of an electron confined in a box is used, for example, on page 353 of Modern Quantum Mechanics by Sakurai et al. The box makes one turn along a closed loop surrounding a magnetic flux line. In the derivation, there will be an integration involving...

Thanks, @renormalize. I mistakenly thought the integral value was somehow related to the integration in the equation.

In the book, quantum fields in curved space, when calculating the vacuum energy divergence for scalar fields, it reads: I could get the answer by letting ##k=m\tan t ## and using the properties of Beta functions and Gamma functions, but I still do not understand what it means by saying "with...

Thanks, @Demystifier, @PeterDonis, @Sagittarius A-Star. Below is my attempt to understand this question. In the exponential, ##e^{-i\omega x^0}## of a mode function, the factor ##\omega## before the time coordinate ##x^0## had better be (or at least be related to) the frequency (energy)...

I am reading a paper, A Pedagogical Review of Black Holes, Hawking Radiation and the Information Paradox. On page 17, it reads that and I am not convinced that the two sets of coordinates are associated with different observers. I think the coordinate systems are independent of observers...

Thanks, @Philip Koeck and @pasmith. I will try to demonstrate the first expression. Suppose ##F(\omega)## is the Fourier transform of ##f(Q)##, i.e., ##f(Q)=(2\pi)^{-1/2} \int d\omega F(\omega) e^{-i\omega Q}##. Then the integral \begin{align} &~~\lim_{r\rightarrow \infty} \int_0^\infty dQ f(Q)...