Hermitian adjoint Puns

I am wondering if a property is true. Here is the link. A is an annihilation operator and n is an eigenket of a Hamiltonian, if it matters. It seems right but I don't know if they should swap places.

I'm gearing up for my Quals and need to make sure I understand the difference in case it gets asked. Would you guys agree with this distinction? An operator A is hermitian if <Au,v>=<u,Av> for all u,v in the domain of A. This doesn't necessarily mean A=A* as the domain of A* could be larger than the domain of A. So if A is hermitian and D[A]=D[A*] then A is self-adjoint Please correct me in even the smallest detail as I would much rather hear how wrong I am from you guys then from my qualifying committee

EDIT: formatting

Hey guys so I️ have an exam this week and I️ was wondering what happens if you take the hermitian or anti-hermitian of a matrix twice because it came up in a proof but I️ wasn’t sure how to go about it.

Also I’m sorry the weird symbols if you see them are just the letter “eye”

This review consists of two parts: an overview with marked spoilers and unmarked mild thematic spoilers to help potential readers decide if this work is right for them, and a more in-depth analysis, which contains unmarked moderate spoilers for Orthogonal.

#Overview

Tenet: Don't try to understand it, feel it.

Me: Oh come on, Nolan. That's just lazy, now. You call this sci-fi? You know you can't just slap some vague technobabble on it and call it a day, right? I hate how so much science fiction feels the need to dumb it down for the masses. What's the point of hiring renowned physicists to consult on your movies if you end up with scenes where your pilot has to have wormholes explained to him when he's literally in sight of the one he's about to fly through? I wish there was something out there that puts in some actual effort in the worldbuilding, something smart. Something that doesn't treat its audience like idiots. Such a shame, too. Inverted matter looks really cool.

Monkey's paw: *curls*

...

Well, the good news is, I found a story like that. The bad news is, having read it, I now feel like an idiot.

Welcome to the world(s) of Greg Egan, who puts the 'hard' in 'hard science fiction' in more ways than one.^1 He's the author of works such as Permutation City and Sqchild's Ladder, which are considered some of the hardest science fiction novels ever. But while those are set in more-or-less our world, Egan's most valuable contribution to the genre (at least, in my opinion), is his alternate universes, which run on different laws of physics from ours.

Orthogonal is a trilogy of novels (The Clockwork Rocket, The Eternal Flame, & The Arrows of Time; roughly 1100 pages total) set in one such universe. I chose it as my first Egan work to read largely because of its concept, which was just too intriguing for me to resist. From the blurb on the website:^2

>In Yalda’s universe, light has no universal speed and its creation generates energy.

>On Yalda’s world, plants make food by emitting their own light into the dark night sky.

>As a child Yalda witnesses one of a series of strange meteors, the Hurtlers, that are entering the planetary sys

I've been taking the time to self-teach myself a lot of stuff about quantum physics that I hadn't really understood and I've been going down a rabbit hole.

Thus far I have a much better understanding of wave functions, Plank constant and h bar, operators, the laplacian, shrodinger's equation, heisenberg uncertainty, spin, angular momentum, and total angular momentum as well as the hermitian matrix stuff for dirac and pauli matrices, and how ultimately the the dirac equation is derived from E2=M2C4 +P2C2 and momentum operators with the 4 component wave function and the expansion of the 4 component matrix. I've had to learn and relearn a lot of math to confirm how you get a lot of this stuff. (Can't say I understand Bra Ket stuff all that much, but I'm getting there)

I think I get it for the most part. My understanding has gotten a lot better.

Do I need to understand GR in full to understand QED with the addition of the dirac stuff? Or can I just know the famous equation and the general vibe of relativity and mass (rather, energy) bending spacetime such that things in an inertial reference frame travel along a new inertial spacetime geodesic without sensing any new force being applied or acceleration? Or is the rabbit hole that is GR really super important to understanding the math in QED.

I get the lagrangian = KE - PE

Looks like i need to understand what the dirac adjoints is, what gauge covariants or gauge covariance is, as well as electric field tensors and probably a bunch more, right?

My end goal is just to understand how they got to all that QED stuff right now so that hopefully all the other things become a bit easier to understand.

Does anyone have any suggestions of what to look into next?

Those are the subjects I'm going to have (with their syllabuses to give you a better idea on what we're going to have):

#Real and Complex Analysis

> 1. algebra and σ-algebra of sets. Measurable spaces. Measure, spaces with measure. Borel measure. Complete and regular measures. > 2. External measure. The problem of measure expansion. Caratheodory's condition. Constructions of Lebesgue measure. Characterization of measurable sets in the Lebesgue sense. > 3. Measurable functions. The space of simple functions. Theorem on approximation of measurable function by simple functions. > 4. Lebesgue integral and its properties. Relation of the Lebesgue integral to the Riemann integral. A theorem of convergence. Fatou's lemma. Lebesgue's convergence theorems. > 5. Productive measures. Tonelli's and Fubini's theorems. > 6. Functions with bounded variation. Absolutely continuous functions. Lebesgue's theorem of differentiability almost everywhere. > 7. Geometry and topology of the complex plane, Riemann sphere. Composite functions, continuity, elementary functions. > 8. Differentiation in the complex domain. Rules of differentiation. Cauchy-Riemann equations. Geometric interpretation of the complex derivative. > 9. Analytic functions (regular, holomorphic). Regularity of elementary functions. Conformal representation. > 10. Integration of complex functions. Curvilinear integrals of complex functions. > 11. Cauchy's integral theorem. Existence of a prime function. Cauchy's integral formula. Generalized Cauchy's formula. > 12. Expandability of an analytic function into a power series. Taylor and Laurant series. Zero points of an analytic function. Uniqueness theorem of analytic function. > 13. Cauchy's inequality. Integer functions. Liouville's theorem. Schwarz's lemma. > 14. Singular points. Residuum of a function. Determination of residues. Theorem on residues.

#Calculus of variations

> 1. Review of extremal problems of elementary analysis and basic concepts of functional analysis related to variational calculus. > 2. The simplest problem of variational calculus. Differential of a function. Necessary conditions for the existence of an extremum. Euler's equation. The case of many variables. Variational derivative. Invariability of Euler's equations. > 3. Generalizations of the simplest problem of variational calculus to the case of Banach and Hilbert spaces. > 4. parametric problems. Variational problems in param

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

Do your worst!

I'm surprised it hasn't decade.

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

It really does, I swear!

They’re on standbi

Buenosdillas

Pilot on me!!

PART II

https://en.wikipedia.org/wiki/Loschmidt%27s_paradox

Loschmidt's paradox, also known as the reversibility paradox, irreversibility paradox or Umkehreinwand,[1] is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics. This puts the time reversal symmetry of (almost) all known low-level fundamental physical processes at odds with any attempt to infer from them the second law of thermodynamics which describes the behaviour of macroscopic systems. Both of these are well-accepted principles in physics, with sound observational and theoretical support, yet they seem to be in conflict, hence the paradox.

The Big Bang

Another way of dealing with Loschmidt's paradox is to see the second law as an expression of a set of boundary conditions, in which our universe's time coordinate has a low-entropy starting point: the Big Bang. From this point of view, the arrow of time is determined entirely by the direction that leads away from the Big Bang, and a hypothetical universe with a maximum-entropy Big Bang would have no arrow of time. The theory of cosmic inflation tries to give reason why the early universe had such a low entropy.

https://en.wikipedia.org/wiki/CPT_symmetry

Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level.[[1

Dad jokes are supposed to be jokes you can tell a kid and they will understand it and find it funny.

This sub is mostly just NSFW puns now.

If it needs a NSFW tag it's not a dad joke. There should just be a NSFW puns subreddit for that.

Edit* I'm not replying any longer and turning off notifications but to all those that say "no one cares", there sure are a lot of you arguing about it. Maybe I'm wrong but you people don't need to be rude about it. If you really don't care, don't comment.

When I got home, they were still there.

I won't be doing that today!

[Removed]

You take away their little brooms

This morning, my 4 year old daughter.

Daughter: I'm hungry

Me: nerves building, smile widening

Me: Hi hungry, I'm dad.

She had no idea what was going on but I finally did it.

Thank you all for listening.

There hasn't been a post all year!

Why

It’s pronounced “Noel.”

After all his first name is No-vac

What, then, is Chinese rap?

Edit:

Notable mentions from the comments:

• Spanish/Swedish/Swiss/Serbian hits

• French/Finnish art

• Country/Canadian rap

• Chinese/Country/Canadian rock

• Turkish/Tunisian/Taiwanese rap

Those are the subjects I'm going to have (with their syllabuses to give you a better idea on what we're going to have):

#Real and Complex Analysis

> 1. algebra and σ-algebra of sets. Measurable spaces. Measure, spaces with measure. Borel measure. Complete and regular measures. > 2. External measure. The problem of measure expansion. Caratheodory's condition. Constructions of Lebesgue measure. Characterization of measurable sets in the Lebesgue sense. > 3. Measurable functions. The space of simple functions. Theorem on approximation of measurable function by simple functions. > 4. Lebesgue integral and its properties. Relation of the Lebesgue integral to the Riemann integral. A theorem of convergence. Fatou's lemma. Lebesgue's convergence theorems. > 5. Productive measures. Tonelli's and Fubini's theorems. > 6. Functions with bounded variation. Absolutely continuous functions. Lebesgue's theorem of differentiability almost everywhere. > 7. Geometry and topology of the complex plane, Riemann sphere. Composite functions, continuity, elementary functions. > 8. Differentiation in the complex domain. Rules of differentiation. Cauchy-Riemann equations. Geometric interpretation of the complex derivative. > 9. Analytic functions (regular, holomorphic). Regularity of elementary functions. Conformal representation. > 10. Integration of complex functions. Curvilinear integrals of complex functions. > 11. Cauchy's integral theorem. Existence of a prime function. Cauchy's integral formula. Generalized Cauchy's formula. > 12. Expandability of an analytic function into a power series. Taylor and Laurant series. Zero points of an analytic function. Uniqueness theorem of analytic function. > 13. Cauchy's inequality. Integer functions. Liouville's theorem. Schwarz's lemma. > 14. Singular points. Residuum of a function. Determination of residues. Theorem on residues.

#Calculus of variations

> 1. Review of extremal problems of elementary analysis and basic concepts of functional analysis related to variational calculus. > 2. The simplest problem of variational calculus. Differential of a function. Necessary conditions for the existence of an extremum. Euler's equation. The case of many variables. Variational derivative. Invariability of Euler's equations. > 3. Generalizations of the simplest problem of variational calculus to the case of Banach and Hilbert spaces. > 4. parametric problems. Variational problems in param

What did 0 say to 8 ?

" Nice Belt "

So What did 3 say to 8 ?

" Hey, you two stop making out "