The h Bar

I got sucked down a real rabbithole trying to make sense of how GB is related to BRST, there is something crazy there alright

Slereah

does it have spooky ghosts

IIRC GB is basically just the gauge condition written in QFT?

Like $\Box A |\Psi \rangle = 0$

Which I think is the $Q$ operator in BRST

Vaguely summarizing something I have been meaning to read up on

Gupta-Bleuler imposes the Lorentz gauge condition on the space of states, and the LG condition is related to gauge invariance of the action of course, and the LG condition being a scalar means it satisfies the Klein-Gordon equation, so that the space of states is invariant under time evolution. In the non-Abelian case,

trying to impose a scalar condition on the space of states will not satisfy KG and so the state space is not invariant under time evolution so we need a new symmetry to impose on the space of states to keep it invariant, and then the BRST current is like a Fourier transform of the Gupta-Bleuler conditions in the abelian case, and I'm lost...

Slereah

"Private conversation 1957"

Haag is a chatty fellow

Maybe one day I can put the hbar in a bibliography

12:27 AM

ooooof

something's not right there

Q: What explanations are there for this strong spike in the use of 'angular momentum' in the 1960s?

1:54 AM

0

A recent comment called my attention to the Google Ngram for 'angular momentum', which shows a very strong and rather sharp peak in the usage of the phrase shortly after 1960, followed by a steady decline with a loss of ~60% of the original frequency in today's usage. I find this extremely...

↑ extremely curious

@EmilioPisanty String theory angular momentum e.g. the Venenziano amplitude in dual models and the flurry of research trying to tie this to particle physics until QCD in the 1970's overtook this research and string theory waned, to be revived from a superstring perspective?

@bolbteppa and that's 20%-30% of the global usage of the phrase?

that'd be a lot of research in string theory

The Regge theory of complex angular momentum arose then and motivated it en.wikipedia.org/wiki/Regge_theory

My book says red light is deviated the least

But in previous section I read,it says” when minimum deviation happens (for i=e) light is paralllel to base

but in every photo of dispersion of light in prism red light is not parallel to base :/

2:06 AM

A similar strain would be that this Regge theory motivated (or was motivated by?) the research into axiomatic QFT from properties of the S matrix, with complex angular momentum underlying it in a big way apparently, too hard to make full sense of right now :p

In above picture (from Wikipedia) violet is parallel to base 🤔

@Fawad that is false in general

the angle between the red ray and the base depends on the initial incidence angle

that section of your book is likely describing a more restrictive geometry

the good thing is that you can just get a prism and check experimentally

@EmilioPisanty i will try today. I have prism

Should I do in sunlight or use white torch 🔦?

Cows

@BernardoMeurer @vzn @loocsieulb drive.google.com/file/d/1rKh9iqeIHOP1HZPZu2ab_zysY-d-drnv/…

I was just pitching my idea

in this pic

I will detail what happened next in later

was talking in front of +300 people give or take

coding a product with some (supernaturally awesome) senior programmer/analyst

I think the person i am coding with right now is a genius

vzn

nice man thx for sharing :)

Cows

2:17 AM

@vzn no worries anytime hehehe

loocsieulb

2:27 AM

@Cows awesome dude making the h bar proud :-)

5:18 AM

Is there any difference between $\phi$ and $\{\phi\}$?

where $\phi$ stands for null set

Anonymous

@Yashas There's a symbolic difference, isn't it? The latter is a set actually having an element $\phi$ (which doesn't make sense till you define $\phi$).

Anonymous

The former is the good old null set.

What's the cardinality of a null set?

Anonymous

0

$|\phi| = 0$? and $|\{\phi\}|$ is 1?

Anonymous

5:22 AM

@Yashas Right. But $\{\phi\}$ doesn't really have any meaning unless you define $\phi$ as something.

Anonymous

The equivalent notation for $\phi$ is $\{\}$ if you insist.

Anonymous

Not $\{\phi\}$ (that one doesn't mean anything in general)

Anonymous

Some people call it the set containing the empty set. But that is again a definition. You can define it anyway you want.

"The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers."

the cardinal number of the set of all natural numbers is infinity, right?

What does it mean to say that the cardinal number of a set is larger than the cardinal number of the set of all natural numbers?

Anonymous

There are different kinds of infinities. That's a common misconception. For example there exists no bijection from $\Bbb N$ to $\Bbb R$.

5:28 AM

If the number of elements in a set is logically less than the number of elements in the set of all natural numbers, then it is countable?

Anonymous

@Yashas Yeah, roughly that's it.

This definition is freaking me out. Why does the definition specifically mention the set of natural numbers?

because countable numbers is the set of natural numbers?

Anonymous

@Yashas Because you count using natural numbers. :)

Anonymous

Right.

Anonymous

If you're interested in this stuff read the first few chapters of one two three infinity by george gamow. That's an excellent book and provides good intuition.

5:33 AM

the set of all even numbers is countable because it is a subset of the set of all natural numbers?

Anonymous

Yup

Anonymous

Or rather:

Anonymous

You can define a bijection from one to the other

Anonymous

$y=2x$ ($x\in \Bbb N$ and $y\in M$ where $M$ is the set of even natural numbers).

"X is nonempty and for every ω-sequence of elements of X, there exist at least one element of X not included in it. That is, X is nonempty and there is no surjective function from the natural numbers to X."

where X is an uncountable set

What does the first sentence mean?

Why can't I have an infinite $\omega$ sequence of elements of X? Basically, all the elements of X written in order.

"1. The cardinality of X is neither finite nor equal to |N|
2. The set X has cardinality strictly greater than |N|"

doesn't 2 imply 1?

Wikipedia states them as two separate points

Anonymous

5:49 AM

@Yashas You can do that only if there exists a notion of "order" in a set.

Anonymous

Do you know the ZFC axioms?