The h Bar

6:02 AM

hmm does anyone remember the tool which lets you write in octave but it computes as numpy or something along those lines?

Slereah

12:59 PM

Someday I hope to do a derivation of like circuit laws from string theory

to make the dumbest possible derivation

I'm not sure how one does the drude model using strings, but hopefully there is a way

although I guess I can have the field of the nuclei as a background $B$-field maybe

and only consider electron motion

Semiclassical

3:01 PM

@slearah derive Snell's law from QFT

bolbteppa

3:13 PM

@Semiclassical you joke but even in classical form that isn't done until nearly 300 pages into book 8 of L&L

Semiclassical

yeah, it's not entirely a joke. it's hard lifting to just do it rigorously in classical field theory

which i suppose goes to how 'classical' a sharp change in index of refraction is

Slereah

I mean you can't even do it properly with basic field theory I assume

It's like a step function so I'm guessing there is some kind of distribution stuff involved

the conductor can be modeled as a target space with infinitely many lines removes along a lattice and with the basic Coulombian $B$-fields generated from that I guess

and then you model the electrons as all the worldsheets going through it

Is there a description of the Kalb Ramond field that's not like string theory proper

Like if you consider a charged cosmic string in an EM field maybe

bolbteppa

3:43 PM

It's macroscopic em so you're using averaged em fields, all that's basically ignored :p

Slereah

@bolbteppa You are not considering the spirit of thing I intend, I believe

Is there a mapping from basic EM fields to a corresponding Kalb-Ramond field?

If you considered a "classical" charged string as some limit of a string of charged point particles, it would move through an EM field as if moving via some kind of $2$-transport

What would that corresponding $B$-field look like from the perspective of the EM field

Actually you know who talks about charged classical strings

It's Barbashov!

I really need to give Barbashov a full read

He's the only sane person who ever wrote about string theory

bolbteppa

Yeah there's just a ton of stuff in the last two chapters

Slereah

I think the $B$-field he gives is $(16.25)$

$$S = -T \int \int d^2 u \sqrt{g} + q \int \int d^2 u x'_\mu \dot{x}_\nu F^{\mu\nu}$$

bolbteppa

That's just a usual em field

Slereah

Makes sense I suppose

More Anonymous

3:52 PM

@bolbteppa But its obviously predicted by the multiverse of string theory :P

Slereah

If you have to build a $2$-form out of the EM potential, the EM tensor is a logical choice

Slereah

4:05 PM

Barbashov also gives a bunch of references for it

Let's see

the reference being... himself

mathnet.ru/links/d8b91d6d36663bfcfa4003de8fa84e49/tmf3148.pdf

hm

link.springer.com/article/10.1007/BF01036330

a less soviet option

bolbteppa

What's going on there...

Slereah

He also shows the equivalence between the $B$-field version and the plain old "a bunch of point particles" version, too

which is nice

if you integrate out the spatial part of the string you end up with the usual $A$-field

Well, two of them, actually

One for each end of the string

bolbteppa

I don't know if there's any $B$ stuff there

Slereah

I don't think people talked about $B$-fields back then

bolbteppa

Equation (3) really looks shocking

Slereah

4:12 PM

But there's a string with an $U(1)$ gauge interaction term that depends on a $2$-form

I am willing to consider that maybe this is related to the $B$-field in some manner

It's hard because I don't think there are books in between Barbashov and Deligne

bolbteppa

I think this is just a usual em field, the $B$'s really are their own beast, maybe a $B$ is the better thing to do here?

Slereah

I mean I guess that it's like, this doesn't describe everything a $B$-field can be

But I think that if you have a classical EM field, then this is your $2$-connection for a string

it describes how a string moves in that field

it's the simplest version of a $2$-connection

I may have to ask a PSE question to check tho

bolbteppa

Yeah it's just a usual em field they even reference L&L above equation 18 about it

The weird thing is the 'velocity' they use, which is also used in the string, it involves $x'$ in the velocity...

It's how they set up the string action at the start of their book

Slereah

I'll need to read Barbashov in more details I think

there's a bunch of other papers if you want although they're all at least originally in Russian

Not sure if they're all translated

bolbteppa

One thing they do in their book which other's don't is using Green's theorem when you deal with the boundary terms in the eom

Slereah

4:26 PM

a lot of books don't bother to do much about the classical string

which is too bad because I think having to learn about strings and their quantization at the same time is a bit much

Slereah

4:37 PM

but it would be nice to have something less messy than Barbashov

Slereah

4:49 PM

I mean I guess I did learn about the classical string in acoustics, but that string was a bit too classical

Does the bridge of a guitar qualify as a D-brane?

thank you Barbashov

ACuriousMind

@Slereah we're not really "quantizing the theory of the classical string" even if it may look that way

otherwise you'd have to call QFT "quantizing the theory of the classical particle", which is...unhelpful at best

Slereah

@ACuriousMind I know

But still

ACuriousMind

understanding how a classical particle works won't help you understand QFT, understanding how a classical string works won't help you understand string theory

Slereah

It is a very good idea to do it first

bolbteppa

It's just a hard book it really is

Slereah

4:56 PM

Well I mean

ACuriousMind

also you should've done the classical string in some mechanics course :P

Slereah

Barbashov isn't abstract, but it's complicated

Everything is fairly plain math but there is a lot of it

@ACuriousMind Well as I said, I did

But I only majored in acoustic guitars, we didn't do electric guitars

So I don't know about strings in an EM field

also I don't play guitar that fast

So we didn't do relativistic strings

IIRC we just treated strings as a series of point particles linked by springs

in the Limit

ACuriousMind

I'm not sure why you think this would be useful. The Polyakov action does not involve EM fields and the classical solutions to the equations of motion don't have any special meaning in string theory

Slereah

idk, I think it's interesting

ACuriousMind

well, I'm just explaining why I think it's perfectly understandable why string theorists don't do this

it's certainly interesting as an application of classical physics, but I wouldn't expect to find that in a string theory book :P

bolbteppa

5:02 PM

Yeah I've never seen this EM field stuff they're doing, I can't believe 5.3 of that paper it's as close to normal em as I've ever seen strings get, it looks great

Slereah

Also I am like 100% sure that whatever this is has some string theory application somewhere on nlab

Although that is a low bar certainly

bolbteppa

What is 'the general Cauchy Problem for a free Relativistic String'

Slereah

I don't know anything more than the title would imply

Couldn't find any other image of Barbashov, so in his honor I made this

Thank u Barbashov

Soviet anthem plays

looking for him on google, that guy's a ghost except for his papers

maybe I'd have more luck in cyrillic

ah yes, more results if I look for Б. М. Барбашов

full name Boris Barbashov

photo.jinr.ru/image/1980118110/1980-181.tif

Hm, I guess the chat won't display a TIF image

B.M.Barbashov, D.Jebert (GDR), M.K.Volkov, A.V.Efremov.

Барбашов, Борис Михайлович

Барбашов Борис Михайлович (род. 26 апреля 1930) — советский и российский физик, специалист в области квантовой теории поля, теории струн. В 1952 году окончил физический факультет МГУ. С 1952 г. работал в ОИЯИ. В 1960 году получил ученую степень доктора физико-математических наук. Является автором многочисленных статей и книг по ядерной физике. == Примечания == == Литература == Барбашов Б. М., Нестеренко В. В. Модель релятивистской струны в физике адронов. — Москва: Энергоатомиздат, 1987. — 176 с. == Ссылки == Борис Михайлович Барбашов Борис Михайлович Барбашов

He even has russian wikipedia fame

jinrmag-jinr-ru.translate.goog/win/2015/23/…

"And imagine - complete darkness in the classroom, there is a kerosene lamp on the teacher's desk, a little light on a magazine or a book, and everyone else somehow has to study and learn. It was in such conditions that I studied in the 4th grade: first in one school, then in another - what is called on wheels."

Solid education

bolbteppa

5:51 PM

The intro says they were doing this back in 1965 before strings even existed...

Slereah

Back then they had to do string theory with actual pieces of string provided by the soviet union

It was a harsher time

bolbteppa

The posters on the wall in that picture are hilarious

Slereah

I think you're using the word "posters" a bit willy nilly here

that's like a newspaper clipping with Lenin on it

bolbteppa

You never know, they may have come up with it in 1965 given the other things they apparently did on that side of the iron curtain

Slereah

"There was no central heating in Moscow, we came home from school, made a fire in the stove, dined on what our parents had left, and unwashed sat on the sofa and fell asleep. This is the fate of many children of the war."

Reminds me of when my grampa tells WWII stories

I mean "string theory" is a very broad term

you don't need to worry at all about a unified theory or even QCD to work on a relativistic string

I guess that the pomeron/regge trajectory intersected with the relativistic string at some point and it became string theory

I wonder if in 3 months, if I google Barbashov, the log of this page will come up as the main biographical source on Barbashov

english-language one, anyway

B. M. Barbashov seems to be short for Boris Mihajlovic Barbashov

Take note, future person finding this page on google

Also if you look at his interview translated by google, there's a word sometimes translated as "donut" and sometimes as "bagel", and it's actually this :

Бараночное изделие

Бараночное изделие — традиционный русский обварной хлебный продукт пониженной влажности в форме кольца или овала, как правило, длительного хранения, предлагаемый как закуска к чаю, которую берут руками (снэк, hors-d’œuvre). Основные виды: баранки, сушки, бублики, в каждом из видов существует множество сортов — простые, с маком, с тмином, сдобные, ванильные, солёные и другие. Общее всех этих видов — тонкая глянцевая поджаристая поверхность, образующаяся благодаря ошпариванию изделий перед выпечкой и предохраняющая продукт от проникновения плесени при длительном хранении. По технологии приготовления...

Love me some baranochnoe with my cup of coffee

arxiv.org/pdf/hep-th/9410024.pdf

Heizenberg

PM 2Ring

8:05 PM

@Slereah A Barbashov quartet.

Slereah

This is what the h-bar looked like in the 60's

rb3652

9:20 PM

Hi @Slereah, sorry to ping. I have a question.

imbAF

Hi, I have a question regarding entropy. If entropy always increase or is equal to zero (in an isolated system), then how does the total entropy of a system that undergoes a reversible cycle is zero? if the system undergoes a rev cycle, that means that it goes from state A to B in a rev way and entropy increases, and then when it goes fomr B to A it increases again, then how it's the entropy zero?

Slereah

9:53 PM

Know who else talks about n-connections

link.springer.com/article/10.1007/BF01889624

"It is proved that the generalization is compatible with space-time locality only if the gauge group is $U(1)$"

I guess that's why you don't see a lot of non-Abelian higher gauge

Slereah

10:13 PM

"In a spacetime of dimension $n$, the magnetic monopole is another extended object whose history has dimension $n - p - 2$, dual to that of the electric pole"

does that mean that the electric pole has dimension... p+2?

seems strange

DIRAC1930

11:14 PM

Does having $U(1)$ gauge invariance just mean that $\mathcal{L}$ is invariant under transformations $\Psi \rightarrow e^{\imath \theta(X)}\Psi$?

Slereah

Well it's a U(1) gauge on a string, so I'm less sure how that works out

DIRAC1930

Sorry I was asking a question about simple regular electrodynamics lol

Slereah

Oh then yes, basically

Well, the action is invariant

the Lagrangian can still vary

DIRAC1930

What happens if I have a different representation of $U(1)$?

Slereah

Up to a total derivative

Same principle applies I guess

Like if you had two charged particles, and they transformed as $(\phi, \psi) \to (e^{ia(x)}\phi, e^{ia(x)}\psi)$

They should probably still leave the action invariant

DIRAC1930

11:18 PM

Okay

ACuriousMind

@DIRAC1930 if you want to formulate this in terms of representation theory, gauge symmetry under a group $G$ means that you have non-trivial representations $\rho_\psi$ at least for some fields $\psi$ and everything is invariant under $\psi\mapsto \rho_\psi(g(x))\psi$ (plus a slightly different transformation of the gauge field)

Slereah

IIRC if you have a different rep that might change the connection slightly

DIRAC1930

Is $g(x)$ in this case an element of $G$?

ACuriousMind

yes, $g$ is a smooth $G$-valued function

Slereah

but it's easy enough to see for U(1) because I think it only has one irrep?

Everything else is just direct sums

DIRAC1930

11:21 PM

So if I had $\psi \rightarrow \rho_\psi(g(x))\psi$, how would I relate those fields back to the regular fields?

ACuriousMind

in terms of the algebra, you have $\psi\mapsto\mathrm{e}^{\mathrm{i}\rho_\psi(\theta(x))}\psi$ (abuse of notation - $\rho_\psi$ is now the representation of the algebra_)

DIRAC1930

Oh so $\psi \rightarrow \rho_\psi(g(x))\psi$ is the infinitesimal transformation?

ACuriousMind

for $\mathrm{U}(1)$, all representations are of the form $\mathrm{e}^{\mathrm{i}n\theta(x)}$ for $n\in\mathbb{Z}$ and $\theta$ just an $\mathbb{R}$-valued function

DIRAC1930

What do you mean by $R$-valued function?

Slereah

oh is it a winding number thing

ACuriousMind

11:23 PM

typed the wrong \mathxx command, sorry :P

DIRAC1930

What about when you had $G$ valued functions though

ACuriousMind

well, U(1) is a terrible example for that because you can't really tell it and its algebra apart :P

Slereah

@ACuriousMind can't you

one's a circle and one's a line!

DIRAC1930

Do fields transform from one representation to another through $\psi \rightarrow \psi'= S\psi S^{-1}$?

ACuriousMind

@Slereah I mean that the "exponential map" is just the identity modulo $2\pi$

Slereah

11:25 PM

well yes, that's what a circle is

If you were modulo 1m you'd just be a pair of legs

ACuriousMind

@DIRAC1930 what do you mean?

for every symmetry group, every field transforms in a fixed representation

what's $S$ supposed to be there?

DIRAC1930

Well for example are $\mathbf{E}$ and $\mathbf{B}$ chosen to satisfy maxwells equations

Do they transform under a particular representation of U(1)?

ACuriousMind

$E$ and $B$ are not the "fields" in the Lagrangian formulation of EM

DIRAC1930

Okay ignore that

ACuriousMind

(and since they are gauge-invariant, they transform in the trivial representation)

DIRAC1930

11:28 PM

But if I had a Dirac spinor field, I do a similarity transformation through $S$ to the other representations right?

And the transformations will also change right?

ACuriousMind

I really don't know what you mean

what "other representations"?

where does this $S$ come from?

DIRAC1930

Well we have the Dirac representation, the Majorana representation

etc

ACuriousMind

well, those are representations of the Lorentz group

that has nothing to do with any U(1) representations

DIRAC1930

I was using it as an example

Let me say it differently

If I have U(1) gauge invariance, I can have a field that transforms through $\psi \rightarrow \rho_\psi(g(x)) \psi$, or I can have a different field that transforms through $ F\rightarrow \rho_F(g(x)) F$

How do I relate $F$ and $\psi$?

ACuriousMind

why do you want to "relate" them?

if they're two different fields, there is no relation between them

DIRAC1930

11:32 PM

So I get the same answer when I do computations

ACuriousMind

...why would you get the same answer for different fields?

DIRAC1930

But then saying electromagnetism is a $U(1)$ gauge theory isn't enough to describe really anything

ACuriousMind

you really need to give a bit more context here

I can't tell what the setting here is supposed to be

DIRAC1930

Electromagnetism

Or any gauge field

ACuriousMind

if you have pure electromagnetism, there is only a single field, the gauge potential $A$

the gauge field is special because it doesn't transform in any linear representation, but as $A\mapsto A + \mathrm{d}\theta(x)$ in terms of the algebra-valued function $\theta$

DIRAC1930

11:34 PM

Okay, so we define which representation of $U(1)$ it transforms under?

ACuriousMind

again, the gauge field is special and that's not a U(1) representation in the proper sense of the word

any other fields $\psi_i$ will have an ordinary linear representation $\rho_i$ associated with them such that they transform as $\psi_i\mapsto \rho_i(\mathrm{e}^{\mathrm{i}\theta(x)})\psi_i$

DIRAC1930

What's an ordinary linear representation?

ACuriousMind

just a "representation" in the sense of the mathematical definition of the word

DIRAC1930

How do we define which $\rho_i$ we use?

ACuriousMind

I used "ordinary linear" as a contrast to the "weird" thing the gauge field does

@DIRAC1930 we just...do

DIRAC1930

11:38 PM

So its convention?

ACuriousMind

part of giving a definition of a specific theory is saying what representations your fields transform under

DIRAC1930

e.g. the Gellmann matricies?

ACuriousMind

@DIRAC1930 no, different choices will give you different physical theories, in general

DIRAC1930

Ah okay that's interesting

ACuriousMind

the physical meaning of choosing the representation is saying what charges the associated particle has uinder the gauge symmetry

DIRAC1930

11:39 PM

So really we should be saying the $SU(3)$ Gellmann representation gauge group?

ACuriousMind

e.g. choosing the trivial representation under the EM U(1) means the field/particle has no electric charge

choosing $n=1$ means it has 1 unit of fundamental charge, etc.

DIRAC1930

What about $n=3$?

ACuriousMind

...can you wager a guess? :P

DIRAC1930

4 units of fundamental charge

lol

ACuriousMind

exactly :P

DIRAC1930

11:40 PM

Why isn't this taught properly

its very annoying

ACuriousMind

for SU(n) representations, it's not quite so simple because the representations aren't all 1-dimensional labeled with a single number

but fundamental particles usually tend to come only in their fundamental or adjoint representations (think "red, blue, green" or "blue-antired, red-antigreen, etc." for SU(3))

DIRAC1930

Ah yes, so is the adjoint representation a very specific representation?

Wait are these all irreps?

ACuriousMind

well, it's always the representation you'll associate with the gauge bosons

again, U(1) is a terrible example for that because its adojint representation is the trivial representation, i.e. the photon is uncharged

DIRAC1930

So we can do a similarity transformation between different representations of the irrep?

ACuriousMind

I don't know what a "representation of an irrep" is

DIRAC1930

11:43 PM

Is that what the difference between Dirac and Marojana fermions are?

ACuriousMind

irrep means irreducible representation

DIRAC1930

By that I mean $A = S B S^{-1}$ for an irrep B

ACuriousMind

that's just a change of basis

DIRAC1930

Yes thats what I mean

Is the basis determined just through convention?

ACuriousMind

yes, that's how linear algebra works - any basis is just as good as any other

you can do most of the math without ever picking a basis if you try hard enough

but usually picking a basis and doing concrete matrix algebra is easier in actual applications

DIRAC1930

11:46 PM

But there are too many terms to contend with

Slereah

yes, yes there are

SU(3) is pretty bad

DIRAC1930

Unless you're using a computer

Slereah

Imagine people using E(8)

ACuriousMind

in what case are there too many terms to contend with?

DIRAC1930

Well I mean just multiplying $3\times 3$ matrices is too much work for me

Slereah

11:48 PM

It's easy enough

ACuriousMind

oh

Slereah

Although some entries can get wide

ACuriousMind

well, better train that, then :P

Slereah

do they teach you the method at school

DIRAC1930

I make too many little mistakes

And everything just gets messed up

ACuriousMind

11:48 PM

matrix multiplication shouldn't be hard, it should just be tedious

Slereah

of putting the first matrix on the left

and the second matrix on the upper right

DIRAC1930

It's not hard, its just I make a little multiplication error that I don't spot and it messes everything up

Slereah

it is the easiest method to do it imo

DIRAC1930

I just use an online calculator

It takes way less time

ACuriousMind

hunting the trivial math error is an extremely common phenomenon when doing physics calculations by hand

Slereah

11:50 PM

watch out for sign errors, factors of 2 and of pi

DIRAC1930

Do I change basis from the Dirac representation of a spinor to the Majorana representation via $D = S M S^{-1}$?

ACuriousMind

yes and no

formally, the Dirac representation is a representation on a complex vector space and the Majorana representation is a representation on a real vector space

they are not isomorphic, so there's no change of basis to turn one into the other

DIRAC1930

Interesting

So what's the point in Majorana fermions if they aren't isomorphic to actual fermions?

ACuriousMind

however, the Majorana representation "sits inside" the Dirac representations as a subspace and the common way to show that is to pick a basis for the Dirac representation in which all the $\gamma$-matrices are real so you can forget about the complex part

@DIRAC1930 they're not isomorphic to Dirac fermions, that doesn't mean they're not fermions

DIRAC1930

Isn't everything that anti commutes a fermion though?

ACuriousMind

11:52 PM

sure

Slereah

I will say no to be a contrarian

ACuriousMind

there are three different kinds of spin-1/2 fermions - Dirac, Majorana and Weyl

DIRAC1930

Interesting

ACuriousMind

@Slereah ah, sure, let's also bring a discussion about spin-statistics into this!

DIRAC1930

I thought you could go from Dirac to weyl via a change in basis

Slereah

11:53 PM

@ACuriousMind ghost fields and supersymmetry!

ACuriousMind

@DIRAC1930 no, both Weyl and Majorana fermions are "half" a Dirac fermion, but in different ways

Slereah

Dirac fermions are just two Weyl fermions in a trenchcoat anyway

DIRAC1930

Are they 2 component spinors?

Okay

Why are there 3 different irreps of the spin 1/2 rep?

ACuriousMind

Majoranas are the "real part" of a Dirac fermion, they are 4d real valued. Weyl fermions are the left- or right-handed part of a Dirac fermion, they are 2d complex valued (assuming four spacetime dimensions)

@DIRAC1930 again, "representation of a representation" is not a thing

DIRAC1930

Okay sorry

Slereah

11:55 PM

what you have is that you have two irreps corresponding to spin 1/2

DIRAC1930

I don't know the correct terminology

Slereah

The left and right representation

DIRAC1930

Why does spin 1/2 have three different irreps