The h Bar

@vzn Tarantino remakes every 70's exploitation film that has existed, with a Hollywood tinge to it. Cronenberg makes cerebral horror movies. I don't see any grounds to compare them.

vzn

6:05 PM

@BalarkaSen "artistic" sex + violence? film noir?

Balarka Sen

Only a superficial viewing of either of the director's work could produce such a question

bolbteppa

The only bad movie I think he made was Jackie Brown tbh

Balarka Sen

@vzn Cronenberg is absolutely not film noir.

If you think it's all about sex and violence I don't have a good response for you

vzn

@BalarkaSen dead ringers seems rather noir to me.

Balarka Sen

It's psychological horror

not a thriller or a crime film, where noirs are usually seen

Have you seen anything other by Cronenberg? Just one film out of the blue might be misrepresentative of the man's work

Dead Ringers is about the generic sexual horror present in every person of the male gender. It's a quite interesting idea.

Cronenberg is greatly influenced by Freud's works on sexuality. Most of his horrors are of the sexual kind.

vzn

6:13 PM

have seen a few of his movies. am not saying he is typically noir. reading wikipedia, ofc the authority, noir as a genre has slippery elements. en.wikipedia.org/wiki/Film_noir

Balarka Sen

Eg, They Came from Within (his first movie, btw). The Videodrome has all kinds of sexual symbolicism in it

vzn

@BalarkaSen lol suicide is not a crime? :P

ACuriousMind

@vzn Jurisdictions actually differ about that.

vzn

@ACuriousMind lol something to quibble about

Balarka Sen

That's a legal issue. But just because there's a suicide or a murder in a movie doesn't mean it's a crime thriller. C'mon son.

ACuriousMind

6:16 PM

However, in most Western countries, suicide itself is legal, though assisting suicide is often a crime.

Balarka Sen

I think a lot of people mistake a lot of Lynch films as crime thrillers

bolbteppa

Any takers
$$\frac{\partial L}{\partial \dot{x}_{\mu}} = - \frac{1}{2 \pi \alpha'} \dfrac{(\dot{x} \cdot x') \dot{x}^{\mu} - x'^2 \dot{x}^{\mu}}{\sqrt{(\dot{x} \cdot x')^2 - x'^2 \dot{x}^2}} $$
$$\frac{\partial^2 L}{\partial \dot{x}_{\mu} \partial \dot{x}_{\nu}} = ?$$

vzn

@BalarkaSen so youre a film critic expert now? there is substantial literary debate on the noir genre. it seems rather easy to make the case dead ringers is noirish or probably other movies by cronenberg, or that hes influenced by the style etc.

Balarka Sen

@vzn I am not a film critic. I am rebuking your shallow thought that just because a movie has a suicide then it's a "crime thriller" :P I don't need to be a movie anything to say that

If you want to be happy with calling Dead Ringers noir, go ahead. Whatever that makes you happy I guess!

bolbteppa

The eigenvalues of that Hessian are the constraints of NG

vzn

6:19 PM

huh, 3s with google always turns up something interesting

> David Cronenberg's Videodrome isn't just a classic sci-fi horror, but also a brilliant noir thriller. denofgeek.com/movies/videodrome/36391/…

Balarka Sen

The director himself would probably deny that label

ACuriousMind

@BalarkaSen Don't you know about death of the author? ;)

vzn

@BalarkaSen maybe hes not as hung up on labels as you are.

Balarka Sen

@ACuriousMind I do

@vzn I like my labels to be consistent.

vzn

@BalarkaSen right, a mathematician vs hollywood. some contrast there eh? (whats that about "shallow thinking"?) :P

Balarka Sen

6:22 PM

Like I said, a lot of Lynch movies are called "crime thrillers". I never understood that

@vzn Cronenberg is not from the Hollywood

vzn

@BalarkaSen lol

Balarka Sen

He's an independent Canadian filmmaker, which is why he is good

Hollywood can only produce camp

vzn

@ACuriousMind afaik its largely illegal all over the world. but illegal in that paradoxical sense. eg "not prosecuted" etc

@BalarkaSen have you ever heard of the term "distribution"?

Balarka Sen

Perhaps. I am not as fluent on my terminology as wikipedia readers

Slereah

@bolbteppa Nambu?

vzn

6:29 PM

← utterly shameless, reads wikipedia regularly o_O

Balarka Sen

Somehow I dont doubt that

:P

vzn

@BalarkaSen :P

Balarka Sen

Ok I gotta go now. I am done with dinner and I need to get some work done

vzn

thx for the engaging film commentary/ analysis/ criticism

Slereah

>film analysis

>not even a topological space

vzn

6:31 PM

BaSe has a topological space... between his ears :P

Phase

Something something Hausdorff

That's literally the only thing stuck in my head from existing here

Slereah

this is Hausdorff

Balarka Sen

but is it normal?

Phase

Oh actually I lied

I have also had the name "Sobolev" drilled into my retina

bolbteppa

Wait, so $L = m \sqrt{\dot{x}^{\mu} \dot{x}_{\mu}}$ has conjugate momentum $p^{\mu} = \frac{\partial L}{\partial \dot{x}_{\mu}} = \frac{m \dot{x}^{\mu}}{\sqrt{\dot{x}}^2}$ and a hessian of $\dfrac{\partial L}{\partial \dot{x}_{\nu} \partial \dot{x}_{\mu}} = \frac{m g^{\mu \nu}}{\sqrt{\dot{x}^{\mu} \dot{x}_{\mu}}} - \dfrac{m \dot{x}^{\mu} \dot{x}^{\nu}}{(\dot{x}^{\mu} \dot{x}_{\mu})^{3/2}}$ with $\dot{x}_{\mu}$ as the eigenvector of the $0$ eigenvalue

$\dfrac{\partial L}{\partial \dot{x}_{\nu} \partial \dot{x}_{\mu}}(\dot{x}_{\mu}) = [\frac{m g^{\mu \nu}}{\sqrt{\dot{x}^{\mu} \dot{x}_{\mu}}} - \dfrac{m \dot{x}^{\mu} \dot{x}^{\nu}}{(\dot{x}^{\mu} \dot{x}_{\mu})^{3/2}}](\dot{x}_{\mu}) = \frac{m \dot{x}^{\nu}}{\sqrt{\dot{x}^{\mu} \dot{x}_{\mu}}} - \frac{m \dot{x}^{\nu}}{\sqrt{\dot{x}^{\mu} \dot{x}_{\mu}}} = 0$ so why is $p^2 - m^2 = 0$ the constraint

Slereah

6:36 PM

I dunno

vzn

full dislosure, helping BaSe with his own argument, the title of that web page was: Videodrome: how Cronenberg subverts the noir thriller genre... as in that quote, "great artists first learn the rules, so they can break them"...

Balarka Sen

I don't buy it. If it makes you happy, feel free to believe it.

vzn

@BalarkaSen lol back already? hes probably said something about noir in an interview somewhere. might be amusing to google sometime.

Phase

jeez you two move past the sexual tension and kiss already

vzn

ewww

Balarka Sen

6:40 PM

@vzn I don't want to google it.

vzn

(Balarka is a male name right?) :P

Balarka Sen

What makes you think I am a heterosexual male?

Anonymous

@Phase murder/mutilation?

Anonymous

@BalarkaSen No one thinks that

Anonymous

That's highly unlikely

ACuriousMind

6:41 PM

@Blue ...that's an odd response to "kiss already".

Balarka Sen

@ACuriousMind LMAO

vzn

@BalarkaSen freudian slip? nobody said you were straight... actually phase implied exactly the "contrary"

bolbteppa

Great, so the eigenvectors of the NG Hessian are $\dot{X}$ and $X'$ which means you still have to play with functions of these to find your constraints

ACuriousMind

Note to self: Never make out with @Blue.

Phase

@ACuriousMind you coulda warned me ealier

now I'm missing a hand and an eyeball

ACuriousMind

6:42 PM

@Phase Warned you about what?

Oh.

Balarka Sen

@vzn Then what do you say about Phase's suggestion?

Slereah

$$\frac{\partial L}{\partial \dot x^\mu} = m \frac{1}{\sqrt{\dot x^\mu \dot x_\mu}} x^\mu$$

Checks out so far

vzn

@BalarkaSen think youre the one that seems to contain all the tension, dont know how you normally release it, not sure can help you with that :P

Phase

<- it was actually just a vague implication not a suggestion @BalarkaSen

@vzn that sounds pretty gay idk if that was intentional

Balarka Sen

lololol

Anonymous

6:44 PM

@ACuriousMind Just keeping up with the category of movies being spoken about :P

vzn

← suddenly wondering "orientation" of who am surrounded by o_O

Phase

my sexuality is represented by a vector in Hilbert space

vzn

@Phase spin? :P

Slereah

$$\frac{\partial L}{\partial \dot x_\mu \partial \dot x_\nu} = m \left[ \frac{1}{\sqrt{\dot x^\mu \dot x^\mu}} g^{\mu\nu} + \frac{\partial}{\partial \dot x_\nu} \left( \frac{1}{\sqrt{\dot x^\mu \dot x_\mu}} \right ) x^\mu \right]$$

ACuriousMind

@Phase Probably a better representation than the 1d axis we normally work with :P

bolbteppa

6:46 PM

A Hilbert space full of ghosts... (burn)

ACuriousMind

Although the Hilbert space could be one dimensional.

Slereah

Lessee

Phase

@ACuriousMind It's actually a zero dimensional space there's no such thing as distinct sexualities

Slereah

@ACuriousMind The Hilbert space of the vacuum?

Phase

It's something the Russians invented back in the 60s

Tbh

I dont see what's wrong with sexuality being a 1 dimensional spectrum

The Kinsey scale works pretty well

Balarka Sen

6:47 PM

I sexually identify as a Cthulhu

Phase

hot

Balarka Sen

Bet you can't make that a 1-dimensional spectrum

:roasted:

Anonymous

Cthulhu looks cute

Phase

@BalarkaSen cthulu's are really just closeted gays

So you're a 6 on the scale

Slereah

@BalarkaSen There's only one operator for the 1d (projective) Hilbert space and it's the identity

$I |0\rangle = |0\rangle$

ACuriousMind

6:49 PM

@Phase Well, I'd argue that there should be at least an additional axis for strength of the sexuality - people vary wildly in the strengths of their desires, with those identifying as asexuals on one end of the scale.

Slereah

With a perfect spectrum of $1$

Phase

That's a good point actually

wait

vzn

@Blue lovecraft was very noir you know :P

Phase

how on earth would you define that

Balarka Sen

lovecraft was also very racist

Phase

6:50 PM

Sexual intensity is very situation, dynamic and mood dependent

ACuriousMind

@Phase And that's why good social science is hard ;)

Phase

@BalarkaSen did he hate the Noirs

Balarka Sen

yes

Slereah

$$\frac{\partial L}{\partial \dot x_\mu \partial \dot x_\nu} = m \left[ \frac{1}{\sqrt{\dot x^\mu \dot x^\mu}} g^{\mu\nu} + \frac{\partial}{\partial \dot x_\nu} \left( \dot x^\mu \dot x_\mu \right )^{-1/2} x^\mu \right]$$

vzn

@ACuriousMind you guys ought to write a paper on that. or at least a blog. but be careful about citing it in here :P

Slereah

6:51 PM

$$\frac{\partial L}{\partial \dot x_\mu \partial \dot x_\nu} = m \left[ \frac{1}{\sqrt{\dot x^\mu \dot x^\mu}} g^{\mu\nu} -\left( \dot x^\mu \dot x_\mu \right )^{-3/2} x^\nu x^\mu \right]$$

Yeah it checks out

Balarka Sen

Not all of us write blogposts on the internet all day. We have a life.

That is to say, chatting in here

:P

vzn

@BalarkaSen right. you guys chat :P

Slereah

$$\frac{\partial L}{\partial \dot x_\mu \partial \dot x_\nu} = \frac{m}{\sqrt{\dot x^\mu \dot x_\mu}} \left[ g^{\mu\nu} - \frac{\dot x^\nu \dot x^\mu}{\dot x^\mu \dot x_\mu} \right]$$

Anonymous

amazon.com/Funko-POP-Literature-Lovecraft-Cthulhu/dp/B00P1NXFEE

Anonymous

Awesome

Balarka Sen

6:54 PM

@Phase Lovecraft literally has a story where someone wakes up with the horrific realization that one of his ancestors may have had African descent.

vzn

@Phase hey youre in india right? maybe "closer" to BaSe than anyone in here? o_O

Slereah

Basically $$\frac{\partial L}{\partial \dot x_\mu \partial \dot x_\nu} = \frac{m}{p} \left[ g^{\mu\nu} - \frac{p^\nu p^\mu}{p} \right]$$

Phase

Im not indian

Anonymous

@vzn he's Brit

Phase

why on earth would you think that

Balarka Sen

6:55 PM

Phase is from Br8on m8

oi oi

Phase

Im a saudi prince actually

vzn

@BalarkaSen might now have to go read lovecraft graphic novel lyring around for yrs for 1st time

Anonymous

@Phase I doubt you'd be on this site in that case :P

Balarka Sen

I only recently read a few of Lovecraft's works

Slereah

Wait

@bolbteppa

ACuriousMind

6:56 PM

@Blue Depends on where he is in the order of succession :P

Balarka Sen

I don't dislike it

Slereah

I think I see your error

vzn

@Phase there are so many darned indians in here its hard to keep track. ps your profile pg followed from chat is 404, strange... was it Phase or Blue in india?

bolbteppa

There's no error in what I posted

Balarka Sen

I am not an Indian

Anonymous

6:56 PM

Me neither

Slereah

When you apply the eigenvector, you assume that $\dot x^\mu \dot x_\mu = 1$

Which is only true with the constraint

Phase

@vzn the chat logs your profile with the thumbnail when you first join

But I've deleted my account a few times since then

so the link it has for my profile is outdated

or something like that

vzn

← still reeling from the numerous months of jee dialogue in here

Phase

Blue is indian

Balarka is spanish

Balarka Sen

cultural appropriation @vzn

@Phase Thank you. I love Spain

Phase

6:58 PM

muoy bien

vzn

coulda sworn BaSe at least lives in india? hmmm

Balarka Sen

@Phase spaget

Wait, that's an Italian meme

Phase

Jesus

Balarka Sen

rip

Phase

Your european knowledge is worse than my indian knowledge

bolbteppa

6:59 PM

There's no error, what I did was show $\dot{x}_{\mu}$ was an eigenvector of the Hessian with eigenvalue $0$, which indicated the presence of constraints and you can't invert the Lagrangian to find the Hamiltonian, but that doesn't tell you what the constraint is, you need to search for it apparently, and the real issue is doing this same dance for Nambu-Goto, showing $\dot{x}$ and $x'$ are two 0 eigenvalue constraints, indicating two constraints you again must search for apparently :(

Phase

@vzn Balarka is on the run from @0celo7 because of his communist views and 0celo7's homicidal tendencies so he has a fake indian identity

Anonymous

@Phase If anything, he's Russian

vzn

@#%& lol geez busted

in Mathesians, Aug 26 '14 at 15:21, by Balarka Sen

It's horrible in this part of India

Phase

that's part of the fake identity thing

0celo7 has hundreds of guns he's doing it for his own safety

Slereah

@bolbteppa But why do you have $\dot x^\mu \dot x^\nu \dot x_\mu \to \dot x^\nu$

vzn

7:01 PM

oh so hes like a spy? interesting 007 is my favorite

Balarka Sen

@Phase What is this fantastic meme?

I want to watch it

I wanna know more

Phase

@vzn have you seen Austin Powers?

It's like british 007

Slereah

that is not generally true for any velocity

(or any parametrization, even)

vzn

you guys are only this )( far away from a hit movie script right here

Phase

@BalarkaSen it's called playing PUBG with a man who is so addicted that he would even go without the glory of heroin for it

Balarka Sen

7:02 PM

It's not a movie script. It's an anime script

Phase

heroin > pubg anyday, any rational person knows that

bolbteppa

@Slereah that is over $(\dot{x}^2)^{3/2}$ so the $3$ becomes $1$ and it all goes to 0

Balarka Sen

this is the next DBZ

the next Naruto m8

vzn

@Phase luvd it... liked carrell + anne hathway in maxwell smart, check it out

Phase

@BalarkaSen I put an ironic naruto filter on my profile pic on FB

it has spanish on it and I have no idea what it says

Slereah

7:03 PM

Hm, true

Balarka Sen

@Phase Is that like vaporwave filter but with spanish instead of japanese

Phase

bolbteppa

I don't want to work out the NG Hessian but I do :(

Phase

can any spaniards translate

I'm curious what it says

I think the top says "my namma jeff"

but idk what the rest says

Balarka Sen

@Phase Fuck yeah this is great

Phase

7:05 PM

Naruto is a strange beast

the fanbase is perplexing

@BalarkaSen real physics shit

Balarka Sen

r/iamverysmart material

also "Is that how they run in Japan?" lmao

Anonymous

@Phase It just says "My name is Naruto but you can call me Nuto because I lost the ar when I saw you". That must be some meme (?)

Phase

I dont understand

a better version would be

CooperCape

@BalarkaSen Ahhhh yes thanks goddamn iodoform (soz for v. late reply had a piano lesson)

Phase

"My name is Naruto but you can call me Naro because I busted my nut when I saw you"

CooperCape

7:09 PM

Also that conversation from like 18:40 was class jus' sayin' was a great toilet read.

Anonymous

Piano is old fashioned. Get a drum

CooperCape

:c

Need it for ma music a level

I think doing a music a level while only playing drums would be hard af

Balarka Sen

@Cooper Don't you have anything better to do than reading h bar transcript when pooping?

CooperCape

Literally nah

Balarka Sen

Pathetic

CooperCape

7:10 PM

<3

what do you do on the toilet then?

Phase

@CooperCape stop shitposting

Anonymous

Are we now gonna discuss our poop time reads?

CooperCape

Actually scrap that i don't wanna know

Balarka Sen

I want to say "I just concentrate on dropping that log bro" but that is maybe too vulgar

Slereah

@bolbteppa arxiv.org/pdf/1702.07598.pdf

^this might be relevant

CooperCape

7:11 PM

How much concentration does it require?

Slereah

Not sure tho

Seems unpleasant

Phase

@BalarkaSen gotta make sure not to fall over in the street

CooperCape

I just let my body do the work.

Slereah

Oh wait

They don't actually cover Nambu

bolbteppa

That's pretty formal, it probably explains the logic of it somewhere

CooperCape

7:13 PM

I hate how my laptops off button is next to the volume.

Slereah

nvm

CooperCape

Or I hate my coordination idk

bolbteppa

The only person brave enough in the world to attempt to calculate this stupid Hessian seems to be in

4

A: How to find the rank of the matrix $\frac{\partial ^2\mathcal{L}}{\partial \dot{X^\mu} \partial \dot{X^\nu} }$ for the Nambu-Goto string Lagrangian?

I) In this alternative answer we resolve the singular Hessian $H_{\mu\nu}$ of the Nambu-Goto string action by introducing two auxiliary variables from the onset, thereby indirectly showing that the Hessian $H_{\mu\nu}$ must have co-rank 2. The target space metric has $(-,+,\ldots,+)$ sign convent...

Slereah

I can see why the constraint, tho

The momentum should be conserved and this is only true if the constraint is applied

Although... I guess you could have other constraints

By taking parametrizations that aren't proper time

I don't think that's necessarily the constraint

bolbteppa

Hmm

Slereah

7:16 PM

just the most common one

and it does collapse the phase space to the proper subspace

although all constraints should certainly have the momentum be properly inside the light cone, but I don't know how to prove it from this alone yeah

But if you take the parametrization $\tau \to 2 \tau$ then $p^2 \to p^2 / 4$

Balarka Sen

Grmpf I didn't get much work done today

Slereah

$p^2 -4m^2 = 0$ is also a proper constraint

bolbteppa

So Sherk just says by reparametrization invariance you can set some things equal to some things making the NG equations really easy, and these magically turn out to be the constraints later on, and there's some link between reparametrization invariance and constraints I don't get yet, and then there's this Hessian argument about non-invertibility which is the most general approach I think, but now it's not actually giving the constraints, you still need to search for them

Balarka Sen

I think I will spend the rest of the night writing more of the dynamics notes

bolbteppa

This just says they exist and the number of them which is something and what they should be functions of

Most string books just say 'look, these things are constraints magically!' which is fine but come on

Slereah

7:19 PM

The Hessian is due to the "proper" form of the Lagrangian equation

bolbteppa

Pages 12 and 13 here arxiv.org/pdf/1010.2062.pdf explain why the Hessian arises unavoidably very nicely and babylike

Slereah

Where you find out that $$\ddot x \frac{\partial L}{\partial \dot x^\mu\partial \dot x^\nu} = F(\dot x, x)$$

bolbteppa

Yeah

Slereah

Which means you can get the acceleration uniquely only if you can invert the Hessian

bolbteppa

Yeah that's what those pages say

Slereah

7:22 PM

reparametrization invariance basically mean that you can make the velocity anything you want

Since $\tau \to f(\tau)$ means $\dot x \to f' \dot x$

Hence you need to fix the parametrization

bolbteppa

So that's fine, computing the Hessian is supposed to give you that $\dot{x}^{\mu}$ and $x'^{\mu}$ are eigenvectors of eigenvalue 0 in NG, and you get 2, maybe Dirac constraint theory says you then need to form functions of these eigenvectors to find the actual constraints and there's no choice but to search for them

Slereah

which, from that formula, you can simply do by picking an origin point and a constraint on the velocity

bolbteppa

Hmm

That's interesting

Slereah

if you want more details than you'd ever want about constraints you can try Henneaux

bolbteppa

Regge wrote an old book on constraints which vaguely looks dumbed down enough for a physicist compared to Henneaux

Slereah

7:28 PM

I don't really know the general trick to collapse the phase space, though

there's a whole theory on the phase space manifold and the gauge and whatever but I don't know how it works

Apparently you have to use regularity conditions

something about the rank of the Hessian and all that

Generally you're gonna need some formula $\phi(p, q) = 0$, but while $p^2 - m^2 = 0$ is obviously fine, I don't think $p^2 + m^2 = 0$ would be (given the same signature)

I'm not sure why though

Although that one might simply be a domain issue, since that would require complex values

But you can't have $p^2 = 0$ either

bolbteppa

Oh man

Pretty close

Seems to be an error but not too bad

Slereah

what is

bolbteppa

\begin{align}
\frac{\partial L}{\partial \dot{x}_{\mu}} &= - \frac{1}{2 \pi \alpha'} \dfrac{(\dot{x} \cdot x') \dot{x}^{\mu} - x'^2 \dot{x}^{\mu}}{\sqrt{(\dot{x} \cdot x')^2 - x'^2 \dot{x}^2}} \\
\frac{\partial^2 L}{\partial \dot{x}_{\nu} \partial \dot{x}_{\mu}} &= -\frac{1}{2 \pi \alpha'}\{ [(\dot{x} \cdot x') \dot{x}^{\mu} - x'^2 \dot{x}^{\mu}] \frac{\partial }{\partial \dot{x}_{\nu}} \dfrac{1}{\sqrt{(\dot{x} \cdot x')^2 - x'^2 \dot{x}^2}} + \\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{1}{\sqrt{(\dot{x} \cdot x')^2 - x'^2 \dot{x}^2}} \frac{\partial }{\partial \dot{x}_{\nu}} [(\dot{x} \cdot x') \…

Plugging $\dot{x}_{\nu}$ in should give 0, Hessian must have a mistake somewhere, but looks nice enough

Slereah

gee wizz

bolbteppa

7:49 PM

I don't see an error but there has to be one

Slereah

Hm, wait

Maybe my mistake is

I'm looking at primary constraints

Primary constraints don't have to obey the EoM

bolbteppa

Kiritsis' String book says this is all you have to do, that last thing should equal $0$ for $\dot{x}_{\mu}$ and $x'_{\mu}$

He just doesn't compute the Hessian, just says this is what happens

Slereah

it is trivial

bolbteppa

Yeah it's just taking derivatives

books.google.fr/…

also just says it

0celo7

@bolbteppa dear god

bolbteppa

7:59 PM

Find the error

This is ridiculous, look, the other 0 eigenvalue eigenvector almost works out

\begin{align}
\frac{\partial^2 L}{\partial \dot{x}_{\nu} \partial \dot{x}_{\mu}} (x'_{\nu}) &= [ -\frac{1}{2 \pi \alpha'}\{ \dfrac{-(\dot{x} \cdot x') x'^{\nu} + x'^2 \dot{x}^{\nu} + 2(\dot{x} \cdot x') \eta^{\mu \nu} - 2 x'^2 \eta^{\mu \nu}}{\sqrt{(\dot{x} \cdot x')^2 - x'^2 \dot{x}^2}} \} ](x'_{\nu}) \\
&= -\frac{1}{2 \pi \alpha'}\{ \dfrac{-(\dot{x} \cdot x') x'^{\nu}x'_{\nu} + x'^2 \dot{x}^{\nu}x'_{\nu} + 2(\dot{x} \cdot x') x'^{\mu} - 2 x'^2 x'^{\mu} }{\sqrt{(\dot{x} \cdot x')^2 - x'^2 \dot{x}^2}} \} \\

Slereah

Really I have no idea why we have the notion that $\dot x^2 < 0$ just from the Lagrangian

I don't see where the link between the tangent vector and mass comes from

What is the reason beyond "we know that it's the right one"

bolbteppa

What do you mean $\dot{x}^2 < 0$

In the SR action?

Slereah

I mean that the velocity is timelike

yes

PhiNotPi

New theory of everything: "Loop String Quantum Theory Gravity" (LSQTG), formed by alternating every-other word from the wikipedia articles on string theory and loop quantum gravity.

bolbteppa

$S = - m \int ds = - m \int \sqrt{g_{\mu \nu} \dot{x}^{\mu} \dot{x}^{\nu}} d \tau = - m \int \sqrt{\dot{x}^2} d \tau$ where $\dot{x}^2 > 0$ must hold right?

Slereah

8:09 PM

I suppose!

Could be zero though

bolbteppa

The metric there is $(1,-1,-1,-1)$ btw

Slereah

The worst metric :p

bolbteppa

If it's the bad one $(-1,1,1,1)$ then you need to say $\sqrt{-\dot{x}^2}$ to make it positive

Slereah

I am aware, yes

What prevents the velocity from being $0$ though, here

Well I guess that it can't be 0 everywhere and the tangent has constant norm

But the fact that I had to scrap arguments from like 3 different reasons is a bit unsatisfying :p

I guess that's why people use Nambu-Goto

Errr

Polyakov

Polyakov is best

bolbteppa

Ah

Basically, that action has to describe a particle of non-zero mass, which means $ds^2 = dt^2 - dx^2 - dy^2 - dz^2 > 0$

If $ds^2 = 0$ then you have light which is massless

In other words, the action is wrong, you need to add the einbein thing which comes from adding a constraint to ensure the action also describes massless particles

I never noticed that until I seen it in GSW tbh

Slereah

8:18 PM

I wonder what's the general constraint you can get from parametrization invariance

I think $$f'^2p^2 - m^2 = 0$$

there's probably other constraints you could apply but I think that's all the ones you can generate playing with the gauge

bolbteppa

Yeah my sense is there is some general reason why that's the constraint from parametrization invariance

I can't fix this second derivative :(

Slereah

I mean we have $p = m \dot x$ and $\dot x^2 > 0$

bolbteppa