I am new to research and I have yet to internalize the concept of journals and their utility in archiving scientific literature.
Almost all the papers I have read recently are from this website called arxiv. Arxiv calls itself to be a preprint archive. Anyone can upload a PDF file to the reposit...
the other paper does specify that the path of a sting is specifically arbitrary
that paper never even mentions why stings are to be added
"Wolfgang Smith (born 1930) is a mathematician, physicist, philosopher of science, metaphysician, Roman Catholic and member of the Traditionalist School. He has written extensively in the field of differential geometry, as a critic of scientism and as a proponent of a new interpretation of quantum mechanics that draws heavily from medieval ontology and realism."
I'm curious, how frequently on StackExchange do you get people who seemed to have learned a whole lot of fancy words, but don't seem to understand basic concepts, and then they get super argumentative...
(this question is simpler than its length implies.
I did this on purpose to provide a nice complete development for future readers)
The setup
Suppose we have a two-level quantum system with Hamiltonian
$$H/\hbar = -\frac{\Omega}{2} \left[ I(t)\sigma_x + Q(t) \sigma_y \right] \, .$$
Now suppos...
@BenNiehoff For real, physicists do have a tendency to use fancy words. My QM prof keeps calling the Dirac delta a distribution, but then he uses it like a function and on test functions that are not even test functions
@ACuriousMind Oh, did your bounty expire? I was thinking of looking into that one, but I was busy last week and I'm not sure if I'd come up with a more definitive answer than Polchinski and Figueroa-O'Farrill anyway :P
I am working with Wiener path integrals, which have the basic case $$\int_{\mathcal{C}(x,t;0,0)} d_W[x(\tau)] = \frac{1}{\sqrt{4 \pi D t}} \exp \left( - \frac{x^2}{4 \pi D t} \right) $$
@ACuriousMind Well, the relation is that if I put a particle at $(0,0)$ and let it diffuse, it's probability distribution at time $t$ is $$\frac{1}{\sqrt{4 \pi D t}} \exp \left( - \frac{x^2}{4 D t} \right) \, . $$
The probability that a path goes through a set of "gates" at those times is $$\int dx_1 \cdots dx_N \frac{1}{\sqrt{4 \pi D \epsilon}^N} \exp \left( - \frac{1}{4 D \epsilon} \sum_{i=1}^N \left( x_i - x_{i-1} \right)^2 \right) \, . $$
@TheDarkSide If you really care about it - some of us have written to him directly expressing hope that he will come back, though to my knowledge he hasn't replied to any such contacts. Still, if done respectfully and once, it's something to consider.
He even makes a great point about the JNF coming from isolating the most invertible and most zero-ness of any map, though the image and null space not being disjoint means you have to modify your notion of zero-ness to nilpotency
The last few terms don't really help - since each $x_i$ is coupled to both $x_{i-1}$ and $x_{i+1}$, every change you make there will propagate through the entire sum, so to speak
The problem with the $x_{N+1}$ appearing is that this has no real nice interpretation anymore. In the $x_{N+1} = 0$ case, you can just write the integral as $\int_{\mathbb{R}^N} \exp(x^T A x)\mathrm{d}x$.
So, I have this guy I was trying to help on PhysicsForums...he has started going on about jet bundles and Gribov ambiguities, but doesn't seem to understand that the Levi-Cività connection and gauge connections are basically the same type of object
@DanielSank If you compare your formula with the once you just asked me about, you find that the $J_i$ are $2 A_{i,N+1}x_{N+1}$ for $i = 1\dots N$, which, come to think of it, is just $-2 \delta_{i,N} x_{N+1}$.
@DanielSank Well, it's almost a tautology - the propagator is the Green's function for $\nabla^2$, and taking the integral with the Green's function is the inverse operator to the operator it's the Green's function for by definition
I'm not sure I understand what you mean by that. It's the additional factor you get when you complete the square in the Gaußian, I don't have a good interpretation for it
(this question is simpler than its length implies.
I did this on purpose to provide a nice complete development for future readers)
The setup
Suppose we have a two-level quantum system with Hamiltonian
$$H/\hbar = -\frac{\Omega}{2} \left[ I(t)\sigma_x + Q(t) \sigma_y \right] \, .$$
Now suppos...
