The h Bar

0celo7

15:01

@ACuriousMind What kind of global structure are you looking for?

What kinds of features

ACuriousMind

Uh, I'm not looking for a particular structure. I just what to know if anyone has an idea how to dynamically determine it instead of treating it as an input.

0celo7

> dynamically determine it

From?

ACuriousMind

Some kind of action principle, ideally

0celo7

62

Q: What is known about the topological structure of spacetime?

General relativity says that spacetime is a Lorentzian 4-manifold $M$ whose metric satisfies Einstein's field equations. I have two questions: What topological restrictions do Einstein's equations put on the manifold. For instance, the existence of a Lorentz metric implies some topological th...

@ACuriousMind Wait, don't you need to know the manifold to do that?

18

Q: Global Properties of Spacetime Manifolds

When solving the Einstein field equations, $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$ for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, $g_{\mu\nu}$ which endows the manifold with some geometric structure. However, how can we deduce global prop...

general-relativity differential-geometry topology

Maybe you've seen these?

ACuriousMind

That's still not what I'm looking for. Those are about what spacetime generically is. I want to know how to select the specific manifold

@0celo7 For the usual way actions are written, yes.

0celo7

15:05

@ACuriousMind Usual?

There's an unusual way?

ACuriousMind

@0celo7 If I was convinced there is no way to do this, I would not be asking, would I?

0celo7

@ACuriousMind you might be trying to BTFO the GR folks

@ACuriousMind What "inputs" will you accept?

I don't have your answer, but I would like to know where you're coming from.

ACuriousMind

@0celo7 Also, again, this is not about GR specifically, this is basically about every field theory where stuff may depend on the concrete global structure, but the equations of motion only determine the local structure.

0celo7

@ACuriousMind that was a joke

bolbteppa

Another reference to $\psi (dz)^h$ books.google.ie/… and another arxiv.org/pdf/hep-th/0210015.pdf P8

ACuriousMind

15:11

@0celo7 Not sure. Something "reasonable".

0celo7

@ACuriousMind ...

What do you want for Christmas?

>Something reasonable

ACuriousMind

@0celo7 Dude, I said I might need to sit down and flesh this out but you keep asking me about it :P

0celo7

OK then, change topic!

The mapping onto extremals is nondegenerate for some small neighborhood around the initial data.

Is there some way to "extend" the Maupertuis principle to the $(q,t)$ space?

Maybe get a new manifold $M\times\mathbb{R}$ where $M$ is the configuration space.

ACuriousMind

How am I supposed to know? You're the one reading Arnold, I've never done anything with Maupertuis

@0celo7 That's what $(q,t)$-space is ;)

0celo7

Because you're smart and I need someone to bounce ideas off of.

@ACuriousMind Yes, of course. But then somehow...do something with it.

Slereah

15:15

So I have solved the radial part of the scalar field in that CTC spacetime

Except it is not in closed form yet

I still need to solve $\int \frac{\ln(\tanh(r))}{\sinh(r)} dr$

Fun!

Also I have yet to solve the angular/time part of the PDE

Which is the worst

Not even quite sure where to start

It's like $\psi_{tt} + \psi_{\phi\phi} - \coth(r) \psi_{\phi t} = k$

Danu

In case you guys are unaware

18

Q: Global Properties of Spacetime Manifolds

When solving the Einstein field equations, $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$ for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, $g_{\mu\nu}$ which endows the manifold with some geometric structure. However, how can we deduce global prop...

general-relativity differential-geometry topology

I bountied this question a long time ago

ACuriousMind

lol, would people please stop posting that? :D

Slereah

@Danu : And the answer is great :p

ACuriousMind

@Danu Slereah, 0celo7 and you now have all three posted that link within the last day here :P

0celo7

@ACuriousMind I have an issue: on the line, the various modes of a harmonic oscillator will always cross, not matter how small of a neighborhood you look at. But the modes are geodesics, so that violates the "geodesics don't cross" theorem.

bolbteppa

15:19

@Slereah I'm guessing convert tanh and stuff to exponentials for the integral, and for the pde it's a wave equation with some frills attached right?

0celo7

Hmm, I wonder if that theorem even works in 1 dimension.

obe

@0celo7 Arnold also has some books on dynamical systems lol.

0celo7

Or if there's even a guarantee that the CNN exists.

Danu

@ACuriousMind Well I get to

As the official sponsor

Slereah

Dunno

PDEs are never fun to solve

btw what are the general methods to check if a PDE's solutions are unique

I suspect pretty hard that they are not here

obe

15:22

@0celo7 did you mean this book?

Slereah

@ACuriousMind : Well as I told you

ACuriousMind

@0celo7 I don't think any of your tools work on the line because you need a curvature form, but all 2-forms on the line vanish.

0celo7

@obe no

Slereah

The Einstein equations don't say bopkis about topology

They are all local things

You need to add requirements on top to divine the topology of spacetime

0celo7

Ah! The geodesics on the line are all the same, they just have different velocity, right?

So that doesn't violate the CNN theorem. But I think in $(q,t)$ space none of the modes cross because the reach the same $q$ at different $t$. Hmm...

Slereah

15:25

$(\eta, \mathbb{R}^n)$ and $(\eta, \mathbb{T}^n)$ obey the same EFE

ACuriousMind

@Slereah Yes, I am aware that the EFE are local

Slereah

Well what do you want then

0celo7

Global!

Slereah

Global conditions on the manifold are pretty sparse

0celo7

The action is a global thing, I think that's what he wants.

Danu

15:26

@Slereah I think the obstructions to local existence and uniqueness are made explicit by Frobenius' theorem.

Slereah

Thx

obe

amazon.com/dp/0849384958/ref=rdr_ext_sb_ti_hist_2

Slereah

"Frobenius' original version of the theorem was stated in terms of Pfaffian systems"

The fuck is a pfaffian

"In the vector field formulation, the theorem states that a subbundle of the tangent bundle of a manifold is integrable (or involutive) if and only if it arises from a regular foliation."

Oh well obviously

0celo7

@Slereah cf. Lee or Straumann

Danu

Pfaffian form = one-form

Slereah

15:28

Oh

Danu

@Slereah Yup :)

Cf. Leeb's lecture notes, obviously

Slereah

that's a lot of fancy words for a dual vector

Straumann is a bit too focused on proving the existence and uniqueness

ACuriousMind

@Danu Careful, the Pfaffian of a matrix for example is unrelated to that

Slereah

I want to prove existence and non-uniqueness

Or maybe I don't

I don't know

0celo7

it's iff

Slereah

15:29

I highly suspect that I do

Danu

@ACuriousMind Pfaffian form

0celo7

so just prove it doesn't satisfy that, so it's nonunique

Danu

Anyways, I think this particular Frobenius' theorem is (in modern language, and appropriately generalized), a statement about equations concerning forms.

Slereah

"Cauchy Problem on Non-globally Hyperbolic Spacetimes" is a nice paper but it uses pretty simple methods

It's all cut and paste spacetimes

Danu

So I think it's safe to relate Pfaffian to form in this context

Slereah

15:31

Hm

I guess maybe I need to show whether or not that spacetime has a foliation first

(probably not)

I should look at the paper on the non foliation of Godel spacetime

I wish CTC studies involved more rock and roll and making out with my mum!

Isn't it a little weird that in Back to the Future, at the end, Biff is the McFly's servant?

Even though he almost raped mommy McFly

obe

@0celo7 Looking for advanced book on ODE's.

???

0celo7

how the fuck would I know

obe

You did ODE's this term?

Slereah

How would you know what you are looking for?

Maybe search your feelings

0celo7

Yeah, intro

Slereah

15:38

you know

Introspect

look inside your mind

See what you want

0celo7

hah

I should send that to Denzler

he may or may not appreciate it

bolbteppa

@Slereah Sorry you have to deal with that mixed derivative term before you can do anything to the pde, i.e. reduce it to normal form, and with a non-constant coefficient it will be different in different regions, a vague easy example is in section 1.6 of Strauss's PDE's

ACuriousMind

@Slereah It is. But I guess the narrative device of having the ending being a scene from the beginning with inverted roles was more important to the writers.

Slereah

there is also the weird thing that in the alternate timeline, Marty looks exactly like an old friend of Daddy McFly

bolbteppa

Also, papa McFly conquered Biff and took him as a trophy slave...

Slereah

15:41

This may raise some red flags

@bolbteppa The horror

bolbteppa

I don't think in the 1950's they knew such a word as r**e

Slereah

Let's look at Strauss, I suppose

Chapter 1 : Where PDEs come from

I assume it involves two PDEs loving each other very much

bolbteppa

A person loves a physical system so much they decide to treat it like a model to produce a baby pde

Slereah

Blah

0celo7

can i call putin "unstable"

Slereah

15:45

I wish they actually taught us how to solve differential equations in school

0celo7

what's a good word for him

Slereah

They sort of teach it for ODEs

But by the time it gets to PDEs they basically give up

bolbteppa

@Slereah in the Tikhonov/Budak 'collection of problems on mathematical physics' there are better examples of classifying pde's, similar to (harder than) yours in the first chapter

user54412

@Danu Not quite (as of the last data dump)

user54412

Bastian Treichler

15:53

@ACuriousMind if you have inputs for physics.stackexchange.com/questions/216388, I'm also reachable in the chat

user54412

@Danu I'm gonna use this plot to claim I'm nicer than you :p

Slereah

Hm

Bastian Treichler

@ACuriousMind regarding the Feynman diagrams question: as I understand it, these diagrams correspond to terms in the \lambda and J double expansion of the Z(J) term

Slereah

If I have a solution, can I check uniqueness just by throwing in $(f - f_{sol})$ into the PDE

ACuriousMind

@BastianTreichler Yes. But you set $J=0$ to get actual processes, and I'm quite sure the bubbles becoming particles vanish for that.

Bastian Treichler

15:57

so with "correct diagram" I mean a diagram that corresponds to a J^6 term up to lambda^2 order in this double expansion

ACuriousMind

Watching your questions, I think it might be very confusing to introduce the diagram language without deducing the LSZ formula that tells you you should only care about connected diagrams

Bastian Treichler

okay, maybe I have to change my question to factor out the non-connected diagrams:

Slereah

IIRC those diagrams evaluate to 0 in most theories

Bastian Treichler

this is a connected Feynman diagram corresponding to \lambda order 1 and J order 2, because there is one interaction and two "sources"

Slereah

If vacuum bubbles can radiate that is usually a bad sign

Abhijith S. Raj

16:00

Ball A is dropped from rest from a building of height H exactly as ball B is thrown up vertically from the ground. When they collide, A has twice the speed of B. If the collision occurs at a height h, what is h/H?

How to go about this problem? Should one first write down the equations for the positions of A and B?

Bastian Treichler

if time is flowing from left to right, this diagram is surely a correct interaction term of the scalar theory Zee's talking about

Slereah

I think that kind of thing happens in theories with unbounded Hamiltonians

David Z

Hi everyone! Time for a chat session

Bastian Treichler

but if time is flowing upwards, then the diagram is a "radiating vacuum bubble"

Slereah

Woo

Aniket

16:01

Yeahhh

Abhijith S. Raj

Ball A is dropped from rest from a building of height H exactly as ball B is thrown up vertically from the ground. When they collide, A has twice the speed of B. If the collision occurs at a height h, what is h/H?

How to go about this problem? Should one first write down the equations for the positions of A and B?

ACuriousMind

@AbhijithS.Raj We are not a homework help service.

Abhijith S. Raj

ok

Slereah

At least not for free!

ACuriousMind

@BastianTreichler Yes, then it's a 1-loop correction to the propagator

Aniket

16:02

Yes you should try to write down the equations. Nothing else is required.

Abhijith S. Raj

:(

David Z

well, it's okay to ask, at least in chat

but Abhijith, it is true, you'll learn more by trying it yourself for a while

Any topics anyone wants to focus on for the chat session?

Aniket

@AbhijithS.Raj Apply the free fall and kinematics equations.... and tell me what you get..

Slereah

So anyway

I got a new shelf

To put my science books in

And I still have room left

ACuriousMind

@BastianTreichler Yes. And purely kinematically, you see that it has to vanish because it doesn't respect energy and momentum conservation.

Bastian Treichler

16:04

@ACuriousMind and if time is flowing from bottom to top? if I'm asked to write all diagrams with $lambda^1 J^2$, what tells me that this diagram is only correct if time flows from left to right?

Slereah

This means I need to buy more science books

ACuriousMind

@BastianTreichler The diagram is "correct" both times. But in the end, as a contribution to the physical theory it matters only in the case where it's a correction to the propagator.

Most Feynman diagrams you can draw are just useless. It just is that way.

Sathyaram Ganapathy

@Abhijith S. Raj Hmmm I gave you some hints at your post..

Bastian Treichler

@ACuriousMind okay, so when drawing Feynman diagrams (to make calculations in perturbative QFT easier), we have to be careful to only consider diagrams that respect energy conservation?

0celo7

Chat ready for some math?

Slereah

16:07

No

I want physics dammit :V

0celo7

Aniket

@0celo7 Yes give it

0celo7

+10 for anyone who can prove the statement on the bottom.

Bastian Treichler

(because energy-momentum conservation is considered afterwards, when "translating" the diagram into the amplitude value)

0celo7

@BastianTreichler the Feynman noose

ACuriousMind

16:08

@BastianTreichler Yes. Formally, when you rewrite the integrations the integrals stand for, there are these delta-functions at the vertices which correspond to that

Slereah

Would you say an actual wormhole has topology (ℝ³ # T³) × ℝ

0celo7

actual worm hole has no topology, there's no such thing

Bastian Treichler

@ACuriousMind oh I see! the delta function "receives" 0 energy-momentum from the loop, so the outgoing particles have 0 energy-momentum and thus their term vanishes. correct?

ACuriousMind

@BastianTreichler Exactly

Bastian Treichler

@ACuriousMind when time goes horizontally, there's a different situation, because the incoming particle has already some non-zero energy-momentum

ACuriousMind

16:11

Exactly :)

Bastian Treichler

which can be passed to the outgoing particle, because the loop contributes nothing

great :)

thanks very much

ACuriousMind

@DavidZ Hm, not really. Do you have something?

David Z

nothing in particular

0celo7

@DavidZ See picture.

David Z

There are always recent meta posts to go over

Slereah

16:12

Hm

ACuriousMind

@0celo7 We're also not your personal theorem provers ;)

Bastian Treichler

@ACuriousMind if you want some rep, write it as an answer to my question.. if not, I'm gonna write it, just tell me

Slereah

Typing "find a Grøn, Ø" on Inspire Hep

Damn foreign authors :p

David Z

but I don't know that there's been any particular post we need to discuss the past couple weeks

ACuriousMind

Well

13

Q: Ultimately, what will the Physics Stack Exchange Become? Are there long term goals?

It was sometime back that I realized what we are synthesizing here (possibly) is an archive for an expert system. Put the Physics Stack Exchange together with an AI machine and you have a super-physicist. The same might be said of other Stack areas, knowledge bases. What will the stack eventuall...

discussion scope policy

would be the only one where discussion is possible

0celo7

16:13

My personal theorem provers

Aniket

Whats going on?

0celo7

See the above pictures.

@ACuriousMind You know you want to be :)

David Z

@ACuriousMind indeed, though I can't really think of anything that needs to be discussed with that one. It seems fairly resolved.

ACuriousMind

@BastianTreichler If you like, write it yourself. The thrill of getting rep declines after 20k ;)

David Z

There are also some old posts that we could go back over, in principle, but I wouldn't have anything new to add.

I keep meaning to prepare something for these chat sessions but I've been way too busy with work and stuff

Bastian Treichler

16:16

@ACuriousMind :D gonna do that

@ all what's the chat session for?

aren't we in chat session now?

yuggib

@BastianTreichler That seems to be a recurrent question...

Aniket

Many things happen here....

ACuriousMind

Does everything have to have a purpose?

David Z

@BastianTreichler yes, we are. The main point is just to get people into the chat room and to keep up some level of activity.

This room was very dead before we started having chat sessions.

ACuriousMind

That was years ago though, right?

David Z

16:19

The secondary purpose is to discuss issues relevant to the site, such as recent meta posts that have attracted a lot of attention, or big events in the world of physics that we might be interested in. But that takes some degree of planning, and I haven't had time for planning for a while.

@ACuriousMind yeah, that's true.

Aniket

@DavidZ How do you call it dead? There are many who scroll through the chats and search for learning material......

Rol

I like the name of the chat room, someone should get a cookie for it

user54412

@Aniket He means years ago.

David Z

@Aniket well, what exactly do you think I'm calling "dead"? ;-)

Aniket

@DavidZ Something that deals with RAW physics. ;-)

ACuriousMind

16:21

@Rol It's the asker of this meta question who came up with it, apparently

David Z

@Rol it's been long enough that I have no idea who suggested the name, but perhaps someone could find it by scrolling through old transcripts

oh, never mind me then

...now that I look at it, we never implemented Aarthi's suggestion of putting "physics" in the title

Ideas? I think we should do this, but do we want to go with "The h Bar: Physics Chat" or something else?

Bastian Treichler

@DavidZ looking forward to it.. will there be drumrolls when it starts? :)

David Z

when what starts?

ACuriousMind

@BastianTreichler The chat session started about half an hour ago ;)

user54412

@DavidZ I'm somewhat partial to leaving it as-is. Can one not search based on the description text?

ACuriousMind

16:24

@DavidZ Isn't the Physics in "General chat for Physics Stack Exchange" enough?

David Z

@ChrisWhite I'm not sure. I'll look into it before changing anything. cc@ACuriousMind

oh, apparently that does work now.

I suppose it didn't back in the old days.

ACuriousMind

Also, none of the other chatrooms with quirky names do that

user54412

I mean, look at the other rooms: The Whiteboard, The Frying Pan, The DMZ, Mos Eisley, ...

ACuriousMind

And mathematics is just...Mathematics.

Kinda sad

Bastian Treichler

@ACuriousMind oh ok :D

David Z

16:25

Mathematicians have no sense of fun :-P

ACuriousMind

They do know about $F_\text{un}$. It's unclear whether it exists, though.

David Z

haha

so I should say, mathematicians have not been able to demonstrate the existence of $F_\text{un}$

Bastian Treichler

Is there anyone who learned his/her physics using Zee's books, especially the two Nutshell books?

David Z

I've been a little curious about that myself

yuggib

@DavidZ They have demonstrated $F_{\mathrm{un}}$ do not exist in classical abstract algebra

but that hardly requires a proof :-D

David Z

16:30

that explains a lot

0celo7

@BastianTreichler I read his GR book cover to cover

His QFT one is garbage.

Bastian Treichler

@0celo7 but not the QFT one?

oh ok

0celo7

I have it.

Bastian Treichler

I'm currently reading them, and GR is so so so much easier to read and understand

chapter one of QFT, it's great to see all those achievements in such few pages, but to really understand it...?

@0celo7 what other QFT book would you recommend?

I mean are there better ones?

0celo7

@BastianTreichler I know virtually nothing about QFT

ACuriousMind

16:33

Ah, now that you're here @yuggib, might you have any input to my question about non-normal states?

Bastian Treichler

@0celo7 ok.. your statement about his QFT book being garbage, can you elaborate a bit?

Physics Meta

1

Q: Maybe anonymous users should not be allowed edits?

The suggested edit , erased the first line in my answer and replaced it with I think that gravity has an effect on any particle in our universe. Even the photons are attracted by the back holes (despite the fact that some physicists consider photons as having no mass !) But in quantic physic...

feature-request suggested-edits

Bastian Treichler

not sure if it's worth to continue reading..

0celo7

@BastianTreichler Uh, he never explains that Feynman diagrams don't correspond to reality.

Let's see what happens when we quote him

user54412

Interesting analysis: Measuring Metrics - A forty year longitudinal cross-validation of citations, downloads, and peer review in Astrophysics

2

ACuriousMind

16:35

::twitches::

0celo7

"The vacuum is a boiling sea of quantum fluctuations"

...nothing?

Bastian Treichler

yep :) fortunately I have been warned that chapter 1 is full of such statements..

0celo7

@BastianTreichler In that case, I guess the vacuum is a boiling sea of quantum fluctuations

ACuriousMind

@0celo7 Nononononononononononononononononononononononononononono

0celo7

there we go

Bastian Treichler

16:36

:)

but I thought that's just this "Motivation and Foundation" chapter, and that the "real thing" starts in chapter 2

yuggib

@ACuriousMind That is an interesting question indeed

Bastian Treichler

but that's the problem... if I need hours of parallel reading to understand a few pages of chapter one, how will it go when I get to chapter 2...

yuggib

but I have not further insight than the one given by moretti I am afraid (and I cannot understand the comment given by the other guy)

0celo7

people can we please focus on the important issue

ACuriousMind

@yuggib Yeah, no idea what Urgje wants to tell me, and the curved spacetime example is interesting, but I was hoping for some more generic statement about how they arise.

yuggib

16:42

@ACuriousMind The usual definition of normality I have seen involves either a state failing to be ultraweakly continuous (definition in nlab, that however seems representation dependent)

David Z

OK, well, if there's nothing in particular to discuss I should probably take off. I preemptively declare the chat session to be over in 18 minutes.

see everyone for the next one in two weeks!

yuggib

or when referring to a von Neumann algebra of a state that is not in the predual

ACuriousMind

@DavidZ See ya!

0celo7

@DavidZ Why is the mapping from initial data to extremals non-degererate!?!

yuggib

and since usually von Neumann algebras emerge as algebras of operators, i.e. when a representation is fixed, it really seem to be a concept that is meaningful only fixed a certain reference representation

Danu

16:44

@ChrisWhite You're not even wrong ;)

yuggib

and in QFT at least, representation-dependent definitions are unsatisfactory anyways... :-P

ACuriousMind

@yuggib So, from an abstract viewpoint, it's not really clear why the normal states should be singled out?

yuggib

As far as I know, no it is not clear

ACuriousMind

Because I keep finding the casual statements that those are the states corresponding to density matrices

yuggib

for example, you may imagine to have an evolution that kicks you out of normal states, even starting from these

indeed normal states are the only ones that can be represented as density matrices

ACuriousMind

16:50

@yuggib So, there are time evolutions possible that take a mixed state and produce something that is not a mixed state? That would indicate that the C*-algebra formalism is not only a different formalisation but a true generalization of quantum mechanics.

Danu

@BastianTreichler Zee's QFT book is extremely non-rigorous (to the point of being un-systematic), which kind of sucks.

yuggib

@ACuriousMind from a mathematical point of view, I am quite confident that this should be possible

obviously, it could not be easy to give an explicit form

but think of an "evolution" group $U(\cdot):\mathbb{R}\times\mathcal{L}(\mathscr{H})\to \mathcal{L}(\mathscr{H})$ that transforms bounded operators

Bastian Treichler

@Danu which QFT book would you recommend to learn from? I mean as "the first QFT book"?

0celo7

@ACuriousMind which stack should I put my extrmal question on

John Duffield

@bolbteppa : re if a child came to you and told you they wanted to study supersymmetry, what would you tell them? I'm not sure. I might say it's up to you to study what you want. But I might say don't waste your time, it's a hypothesis that's based on a lack of understanding of what an electron is. Study classical electromagnetism and QED instead.

0celo7

16:54

since you ppl don't seem to care

yuggib

in a way such that for some $t\in\mathbb{R}$, $U(t)\rho\notin \mathcal{L}^{1}(\mathscr{H})$ for any $\rho\in \mathcal{L}^{1}(\mathscr{H})$

Slereah

Danu

@BastianTreichler Schwartz' new book is pretty good

It's really really really long

Slereah

:D

Danu

But very explicit and clear, and because of its length it's also quite thorough.

yuggib

16:55

but $U(t)\rho\in \bigl(\mathcal{L}(\mathscr{H})\bigr)^*$

Danu

The only thing is the terrible abuse of indices he occasionally commits.

Bastian Treichler

@Danu ok thanks gonna check that one out

ACuriousMind

@0celo7 Hm, I guess either math or physics would be fine

@yuggib What's $\mathcal{L}^1(-)$?

yuggib

where $\mathcal{L}^1$ are the trace class operators, $(\mathcal{L})^*$ the dual of the bounded operators

ACuriousMind

Ah, okay

0celo7

16:56

@JohnDuffield QED says nothing about electron being a photon in a Dirac belt

yuggib

then you have an evolution that maps normal states (trace class) into non-normal ones (elements of the dual of the von Neumann algebra of bounded operators) that are not trace class

John Rennie

@Danu Has Schwartz written a QFT book?

I liked his GR book, so I might have a look.

Danu

@JohnRennie amazon.com/Quantum-Field-Theory-Standard-Model/dp/1107034736

It's my go-to reference now for "standard results"

ACuriousMind

@yuggib I see. I guess my question then becomes if it is at all physically meaningful to consider such evolutions

John Rennie

@Danu oops, Schwartz not Schutz

yuggib

16:59

@ACuriousMind On that question, I do not know an answer...

0celo7

isn't that the one @ACuriousMind said turned him off of GR for life?

Transcript for