@lucabtz Nice work :) Not nitpricking much, but I would point out that there are weakly coupled bulk gravitational theories which do not have an usual Fock space representation. For example quantum gravity on dS space. For example see the intro to this relatively recent work.

But whatever you wrote is correct because obviously you are not discussing general quantum gravity in that context. I think it is not much well known and I myself came to know recently, so pointed it out...

Hello Everyone....

@DIRAC1930 If you want complicated theoretical math and real world applications you should go into fluid mechanics

@Slereah Fluid mechanics has complicated theoretical math? What's the most ``theoretical treatment" of fluid mechanics that you have seen?

I don't go into it much but I know they certainly do

Lots of analysis there

Hmm...I myself have seen some cool group theoretical applications to fluid dynamics as in here for example. But I thought that these dont fall into mainstream fluid dynamics...

Even deriving a Lagrangian description is so difficult because the equations("of motion") are 1st order ones

One of the application of kinematic groups I've seen is fluid dynamics

oh

Why is this the definition of $O(n,n,\mathbb{R})$ given in most treatments of T duality in string theory? I thought that the matrix which is preserved is $\text{diag}(-1,-1,...,-1;1,1,..,1)$ where there are $n$ number of $-1$s and $n$ number of $+1$s?

Now it becomes perfect results for perfectly elastic head-on collision between Earth and ball (when ball was dropped from the building) which look outside the Earth frame then convert into Earth frame. Results

@DIRAC1930 Theoretical physics is extremely broad. It's not like you have to restrict to those areas which are at this moment detached from experiments

There is not just QFT and QG

Consider e.g. theoretical condensed matter physics

Now, the reason why I joined the room:

I need to borrow your strength, fellows. Once again, I need to walk down the path of the quantum world and believe me, I'd rather just reject it at once! Leave me to my beloved classical - Hilbert space free - world, for God's sake!

@SirCrackpot echoes from multiverse

@Sanjana nice to know

thanks

@SirCrackpot i think @DIRAC1930 does not want to realize this

@Sanjana I don't know much about t duality but the two preserved matrices are related by a simple change of basis so the definitions are equivalent

@naturallyInconsistent echoes but no meows

@SirCrackpot mew mew mew .... mew mew mew ... mew mew mew...

QUACK

SQCRACK

CRACK

And that's also something I wanted to say ever since I became a crackpot

cant find the will to actually do something today

i have to hand in the thesis on friday

@lucabtz welcome to my life

Imagine going from the marvels of GR to quantum phase transitions

i have all these little problems that need to fit together and i dont know which one to tackle and which one to leave for future work

i mean my advisor said we are going to write a paper on this work so soon i will have to deal with all of those

@lucabtz that's wonderful

Not all theses become papers

yeah i am happy about it

there has been some interesting results even though i feel like most stuff can be found already somewhere in the litterature

but sure there is a somewhat different perspective on it

Ive been rushing my friend's thesis. She did all the work, but she doesn't know LaTeX like miao miao does.

In the def of principal fiber bundles here, is the fiber preserving property of the group action enclosed in property b)?

@fqq oh, right. Thanks

@SirCrackpot P E G

calling the base manifold E isnt the best idea since usually E is the total space of vector bundles

@lucabtz I agree

@lucabtz are you just commenting on the notation or is that an answer? :P

@SirCrackpot i feel thats the reason the author called the base space E

@SirCrackpot anyhow it looks like so

Sure enough b) encloses G-equivariance

even though when they write $\psi_a: \pi^{-1}(U) \to \pi^{-1}(U)$ it seems like they are already supposing $\psi$ is fibre preserving

Although those are not the fibers I see why you say that

@SirCrackpot right they are not

idk

So rather than "enclosed" I would say it is understood

@lucabtz still there would be some kind of assumption in that direction as a generic action might map you well outside of your neighborhood $U$, so I think your idea is right and it's just implied

@SirCrackpot yeah G-manifold morphisms are G-equivariant maps if im not mistaken

@SirCrackpot yeah im not really sure with that

Where is ACM?! We're talking about Trautman now

Who by the way I learned is a physicist and not a mathematician as I thought

@SirCrackpot in the past few days i havent seen ACM, just some messages yesterday

I know, and my GPS tracker is not communicating either

No wait, that was classified

@DIRAC1930 real world physics can be interesting too. e.g. standard model and GR. u need not study hypothetical models to have interesting math

@SirCrackpot u will love it this time. quantum world has the best rides.

I loved GR because I understand Riemannian geometry

Until I devote to hardcore functional analysis I will pretend to despise QM

@SirCrackpot i should do the same

@lucabtz devote to FA or pretend to despise QM

@SirCrackpot devote to FA

what do you use in latex in between the domain and codomain of a function like $f: A \longrightarrow B$, I kinda like \longrightarrow, but ive seen \to used sometimes too. what is your preference?

@Slereah My interests are really only really in QM/QFT but in the latter, moreso low energy/ medium energy phenomenon and not so much stattering stuff so all the low hanging fruit has already been picked. And all the stuff in the former is either interesting but difficult to get funded in, or not so interesting mathematically (even for my not so high level)

@DIRAC1930 in QM there are plently of interesting mathematical problems

for low energy QFT I mean we dont really know much about it

there are plenty of open problems

@lucabtz By low energy QFT I meant cond matter

@DIRAC1930 i mean also there there is still a lot to do

many interesting theories

which apply to reality too

also for some reason you dont like QCD, but we basically know nothing about QCD

I feel so out of place in cond-mat departments. Even brilliant cond mat theorists haven't heard of a positron so the language barrier is quite large. And then their fundamental aim is often technological applications and not finding from QM/QFT/stat-mech macroscopic laws of the universe

at low energy

@DIRAC1930 i doubt they dont know about positrons tbf

By QCD at low energy, is this in the realm of why a proton at low energies exist?

of course its not about fundamental laws if its condensed matter though

@DIRAC1930 i mean yeah also, confinement is a millenium prize problem

@lucabtz Their language is more so using the terminology of holes however this is very different. They have no need for positrons

But look at this list en.wikipedia.org/wiki/List_of_quasiparticles

It is completely different world

@DIRAC1930 i mean holes and positrons are not the same thing, this isnt a terminology problem its just two different concepts. they dont speak about positrons because ordinary matter is made of electrons not positrons

Exactly

@DIRAC1930 i mean i know about quasiparticles, i took some condensed matter

i think its fun and you get the connection to reality you seek

I wish I found it more interesting

I did used to find it interesting

Learning QFT has ruined my life

@DIRAC1930 do u also want to have a physics career

I'm not sure anymore

I would like to research physics for my life

oh

then u hav to pick stuff based on funding, yeah

But I would rather work on something every 5 years and not publish it

if u just like learning physics, then u can read whatever u find interesting but u probably wont be able to contribute to physics in that life path

@ACuriousMind have you ever though that you could change your username to become a superhero?

ACuriousMan

You could also be like Chainsaw Man "Save me ACM"

@SirCrackpot you can change yours to CrackpotMan

@SirCrackpot lol

But please do not act like him when you save someone

@lucabtz feel responsible, for this is my villain origin

@DIRAC1930 wait

Ideally I would do 2 PhD's, one in quantum optics and one on the boundary between cond-mat and hep-th

I know that feel

@DIRAC1930 most people don't even finish their PhD, I think getting 2 is a bit of a stretch

It's not like getting two degrees

inside a human, there exists a large ecosystem of smaller living beings

why does the cosmic web resemble the human neuron system?

is that a well accepted view

?

@SirCrackpot I agree

@KellanHeerdegen im hearing this for the first time

oh

I believe the web shape is a common shape because of strength and connectivity

shoot I gtg

there is the integrated information theory of consciousness en.m.wikipedia.org/wiki/Integrated_information_theory

maybe one can apply it to the cosmic web

but this is all speculative

Hello?

This isn't a question, but theoretically if we could go faster than light we could go back in time, but if we went back to earth it would be normal, so even if we could go faster than light we could only see the past, not experience it.

Also, the movie Interstellar is a work of art.

@lucabtz I prefer the long arrow when equations are not inline

I use \to only when I'm feeling lazy in the chat

Otherwise \rightarrow (which as far as I can tell displays the same as \to)

Just that \to is the one I use for limits (this is my personal preference though)

$\to$

it works. i had been using rightarrow. thanks

$\rightarrow$

@SirCrackpot but then I would take away the possibility that I'm not a man of flesh and blood :O

Can somebody have a look at something I asked a few days ago here?

Your questions are research level and it is difficult for the general populace to help you...

@naturallyInconsistent Umm...is it? But they are just finding near-horizon geometry in a different way...just basic calculus...I hope maybe it is not that difficult this time :)

maybe, but someone needs to first understand what even the question is. We usually integrate over the entire configuration, so why is it only integrated over angular variables?

@ACuriousMind AI confirmed

That's why you hate chat GPT, you feel replaced

And now save me, ACM

Maybe a bit above

helloo

@SirCrackpot yes

"As the volume of a d-dimensional sphere of radius R is $S_d R^d / d$" what is $S_d$?

Wikipedia page getting something bit different.

Nevermind.

@Mad The pure constant that is the hypersurface area of a unit-radius sphere in $d$ dimensions.

Very wierd human mind, very wierd.

@ACuriousMind so G-manifold isomorphisms are not G-equivariant but also fiber preserving

@SirCrackpot I mean I don't know how the text defined "G-manifold" but the second diagram that should commute in (b) is clearly the condition of fiber-preservation

Do the classical Maxwells equations get modified in the limit of distances of the order of light years as an example?

i.e. $e$ changes with energy scales due to renormalization group arguments, does this effect the classical laws at that energy scale

@lucabtz because internet providers suck I currently only have irregular internet access; my presence will continue to be spotty for a few days

@ACuriousMind that can't be happening in Germany

You liar AI

@DIRAC1930 Large distances = low energy limit, and we already are taking all the low energy limit behaviour into exact account in Maxwell's.

Aren't the classical Maxwell's equations formulated at a length scale in and of themselves though?

i.e. the classical Maxwell equations (discovered at a length scale $L_1$) are then quantized, and then taking the limit is returning back to the classical Maxwell equations at a length scale $L_1$

Maybe the vacuum Maxwell equations at most become Maxwell's equations in matter depending on the situation at long distance scales, but on short distanced QED takes over

Can two different photons interfere with each other just like how EM waves interfere?

Also in a region of constructive interference of two identical EM waves are the number of photons being doubled since the superposed amplitude is 2x initial amplitude and hence energy being increased 4times..where are these extra photons coming from?

@Arjun from where the destructive interference zeroed them out.

@Arjun photons of the same type can; their behaviour is why we have classical EM waves

@naturallyInconsistent In this video (m.youtube.com/…) at about 4min 55sec Barton zwiebach says two different photons can't interfere with each other..because say if they destructively interfere from two photons we go to zero photons..why can't we apply the argument that these photons are showing up somewhere where photons constructively interfere?

Id instead point out that what Zwiebach is probably saying is that the interference pattern is coming from one photon interfering with itself and so the probability distribution is already of the interference pattern form, so 2-photon interference is not needed to describe that.

bleb

it seems like open quantum systems is not as big a research area as i would expect it to be. is this a wrong impression?

@naturallyInconsistent but did he not say that two photon interference is not possible due to energy conservation violation?That is what has confused me a bit

@SirCrackpot the problem is not technical, it's bureaucratic, so it's very German actually :P

And also if it happens where and when does it happen? And what exactly does it mean for two photons to interfere?

And in what situations should one use it and in what situations should one not use it to describe what's happening

suppose i have an initial density operator $\rho_0$. Suppose I want to describe the dynamics of this system. So, I cook up a dynamics relation. Upon first thought, you want $\rho_0$ to be a density operator at every point in time (so the evolution operator needs to be trace-preserving and completely positive for all $t$ in the evolution interval). Is this condition really necessary?

@Arjun it is way past time to sneepppuu so i'll watch it tmr

@it's okay..sleep tight meow..purrrr purrr purrr

@Arjun oh, it is a known thing that at extremely high temperatures, 2-photon interference at least via pair production ought to alter the famous Planck's blackbody radiation. It is just that we have yet to achieve temperatures that high enough.

purrr purrr

I see

@SillyGoose are you saying that you are open to the possibility of your density operator being invalid for some finite short stretches of time?

@naturallyInconsistent yes i was wondering about this possibility

@SillyGoose what is the point of entertaining this possibility?

@SillyGoose $$\mathrm{Tr}(H^\dagger \rho H) = \mathrm{Tr}(H^\dagger H \rho) = \mathrm{Tr}(I \rho) = \mathrm{Tr}(\rho)$$

Unitarity preserves the trace

as it is done (roughly) in say QFT to my understanding. virtual particles don't follow all the expected rules, but so long as your initial and final state is "physical" it seems okay

@naturallyInconsistent well there is more freedom in defining what your dynamics relation is

(and what Slereah said.)

I should maybe explicitly say that I am considering the evolution of a privileged and open quantum system

so evolution will not be unitary

o

Well if your system isn't unitary why expect the trace to be preserved

@SillyGoose but that ought to immediately take you outside of physics.

Particles can just disappear if your system is open

hm okay maybe then to simplify the situation let's suppose trace is still preserved, but i would like to be open to the evolution being not necessarily completely positive for all time

@naturallyInconsistent why so

Like, there are plenty of statistical thermodynamics stuff that become undetermined the moment we lose quasistaticity, so that the thermodynamic functions are only defined for the initial equilibrium state and final equilibrium state; the path in between is non-well-defined. However, if you are talking about a density operator, that should always be well-defined

well so how is this generalization of evolution as I have described above different (in theme/concept) than allowing for virtual particles in the dynamics of QFT? (I do not really know anything about virtual particles, so perhaps I misunderstand the reason for introducing them and so on)

@SillyGoose Something like Einstein's argument as to why all conservation laws should be local. Feynman lectures included it. Prior to SR, it was perfectly fine for conservation laws to only be global, as in, stuff disappear here and pop up instantaneously somewhere else, or pop up eventually in time. But with SR, the time ordering is no longer sacrosanct, and so the conservation laws are forced to become local.

@SillyGoose Technically, the unitary time evolution operator and the S matrix still exist for finite times. It is just that we have no computational tools to get at them analytically. It is just a complication coming from our mathematical failures that the quantities that we can calculate are only well-defined in the infinite time limit, with lots of fake virtual particles appearing in the middle of the perturbation calculations.

okay so you're saying virtual particles are a mathematical convenience that happens to give pretty good answers, and it would be perhaps a different (or perhaps an interpretation on the other end of the spectrum) to see virtual particles as genuine parts of a system's evolution?

@SillyGoose there are many posts on P.SE that assert the fundamental truth, that virtual particles are perturbation theory fiction.

hi

i found the point a , can someone help me solving the b, pls

i solved point a with this

is correct?

@Pizza correct

b is 41.6s

What's the term used to describe a fuel's energy to waste ratio

if such a term exists, and also I'm guessing it's dependent on numerous conditions

if I have two fuel types (for combustion, let's say) $A$ and $B$ where $A$ produces the same exothermic energy as $B$ but far more "waste", is this possible?

I need to learn chem >_<

It's because in the derivation of efficiency for a diesel engine we have $W = Q_h - Q_c$ for some reason i'm trying to figure out

nvm I got it

@naturallyInconsistent How did you find b? Pls

@ACuriousMind hope you go back soon, i may need some algbro-geometric to complex-geometric translations

@SirCrackpot yeah i do the same, except i always use the long arrow even in inline math

hi I guess that people visiting this chat to promote their question on stackexchange are seen as annoying and unpolite, right?

i dont know

whats your question

it is crazy that this simple Schroedinger equation knows about conformal field theory

oh, nothing quantum. it's just plain old boring springs and masses...

there must be a dumb error somewhere or something I can't see

@l4teLearner the coordinates you pick seem clever

also i would expect those configurations to be stable too

@l4teLearner not boring, its an interesting problem

it's from Fasano, Marmi Analytical Mechanics

I must have done a dumb computation problem somewhere or a mistake in the modeling

anyways, thanks for having had a look. cheers

> Fasano, Marmi

Do we have another Italian user? :)

right! they wrote an english version, by the way

Me and @SirCrackpot are also Italian

ciao :) nice to meet you guys. a presto