Comment by pseudo-goldstone on Gauge invariance of Faddeev-Popov determinant...
@Leonard sorry yes you're absolutely right. I've actually made a larger error in the Taylor expansion I wrote. For example, if your gauge group has a Lie Algebra structure then the new metric is given...
View ArticleComment by pseudo-goldstone on How to tell if a theory is "local"?
I don't disagree with you but this doesn't really answer the question. What you've said is already what I had in mind, the question is if you were to give me a $J_{ij}$ which were severely more...
View ArticleComment by pseudo-goldstone on Equivalence Principle in Newtonian Physics vs...
Moreover Newtonian physics never satisfies the equivalence principle for a simpler reason. Just imagine your observer has a laser pointer. In Newtonian physics the trajectory of the laser light will...
View ArticleComment by pseudo-goldstone on Confusion regarding the Susskind-Uglum conjecture
Indeed that's all there is to it! There are several places in the literature that make reference to the claim, for example, appendix A of this paper: arxiv.org/pdf/1506.02669.pdf. They show there that...
View ArticleComment by pseudo-goldstone on Conjugate momenta in Radial Quantization
If I'm thinking about a path integral, that's valid when I do the path integral over the entire spacetime, but if I am doing a path integral over a disc, say, for state preparation, then the radial...
View ArticleComment by pseudo-goldstone on Question on Majorana Path Integral
@asdf, I'm not sure I'm totally clear on your confusion, but if I've interpreted things correctly I think you might be making a (reasonable) mistake regarding the notation for the path integral. A...
View ArticleComment by pseudo-goldstone on Difference between stationary states,...
I would only add that "stationary states" are a different concept from bound and scattering states. A stationary state is just another word for an eigenstate of the Hamiltonian. In particular, every...
View ArticleComment by pseudo-goldstone on How to Choose which space to work in for...
Yes it's both. In the position basis, the Hamiltonian is $H = -\frac{\hbar^2}{2m}\partial_x^2$ whereas in the momentum basis it is simply $H = \frac{p^2}{2m}$, where $p$ is a real number corresponding...
View ArticleAnswer by pseudo-goldstone for Decoupling of ghost fields in axial-gauge QCD
I believe that the answer to your question lies in thinking about the whole path integral, rather than just the Lagrangian of QCD. The purpose of using the Faddeev-Popov prescription is not necessarily...
View ArticleAnswer by pseudo-goldstone for Can massless particle have effective mass?
As has been mentioned in the comments a few times, the Higgs mechanism may be what you're looking for. Here's an example:Suppose we have the following Lagrangian density:$$\mathcal{L} =...
View ArticleQuestion on Eq. 7.40 of "Conformal Field Theory" by Di Francesco et. al
I am trying to understand the second line of (7.40), which I've written below.$$\begin{align}\langle \alpha|\alpha\rangle &= c_\alpha h^{n(\alpha)}[1 + O(1/h)]\\\langle \alpha | \beta \rangle...
View ArticleHow to tell if a theory is "local"?
Suppose I have a collection of $N$ quantum systems, which I would like to think of as lattice sites. If you tell me that these $N$ sites have some particular embeddings $\vec{x}_i$ in $\mathbb{R}^d$,...
View ArticleProof that $-\partial^2 G(x, y) = \delta(x-y)$ for free field propagator
I recently realized that there is a slightly pedantic issue when one normally proves that the equations of motion acting on the free field propagator gives a delta function which I have become confused...
View ArticleAnswer by pseudo-goldstone for A free parameter when switching from $\phi$ to...
It should be fine as long as you put the right normalization in $\pi$. If one takes $$\pi(x) = i\sqrt{\frac{m_x}{2}} (a_x^\dagger - a_x)$$then everything works out.In general, you can always add a...
View ArticleAnswer by pseudo-goldstone for Why is it that we cannot detect any...
I'm not sure if this is quite the answer you're looking for but these are my thoughts on the question.In my understanding, the answer to your question, in principle, is nothing! However, in practice it...
View ArticleAnswer by pseudo-goldstone for Entropy in chaos dynamics
In the context of quantum chaos and eigenstate thermalization, I believe this review has many of the answers you are looking for: https://arxiv.org/abs/1509.06411
View ArticleAnswer by pseudo-goldstone for Renormalization in quantum field theory by...
Does this work (that is, are all the regularized integrals associated with Feynman diagrams actually finite in this scheme) or is there some problem I'm not seeing?At least perturbatively (which is the...
View ArticleComment by pseudo-goldstone on What can we say about the eigendecomposition...
$\Gamma_{m, n}$ has eigenvalue $0$ if $m\neq n$, but if $m = n$, then $\mathcal{N}(\Gamma_{n,n}) = |1\rangle \langle 1|$, and by linearity there are no eigenoperators which span the diagonal basis...
View ArticleComment by pseudo-goldstone on Question on Eq. 7.40 of "Conformal Field...
Yeah I agree it seems like the behavior you said, I'm not sure how one would even get to the result they have? But agreed that it doesn't affect the result of their analysis.
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