Second Quantized Puns

In my Second Quantization seminar, it's been stressed that the whole thing is just a convenient mathematical trick to get rid of integrals and to automatically make sure the pauli principle is satisfied through operator algebra rules.

Electrons aren't annhiliated/created as they move from one energy state to another, but it's convenient to mathematically treat them as such.

My pop-science understanding of virtual particles makes me feel it's kind of the same case (it's easier to handle force using creation/annihilation of virtual particles mathematically.)

Background level for answers: BSc in chemistry, specializing in theoretical/quantum chemistry. Curious about quantum physics outside my training!

Let's say that you are interested in describing the statistical properties of a non-relativistic bosonic gas at low temperatures. Consider the following two options:

1. You propose a QFT level of description by introducing an action functional of a bosonic scalar field in imaginary time and compute field-path integrals to describe its statistical properties. This should allow you to study low-temperature behavior of the system such as condensation.
2. You propose just and ordinary many-body QM description of the system using first quantization. This can be done either with density matrices of the many-particle wave-functions ,or for example many-body path integrals in imaginary time of N particles. This also will allows you to describe statistical quantities of the same system.

I am aware that (1) is a more general description than (2), however I have difficulty with placing my finger on exactly where specifically the differences lie. Are there any phenomena where description (1) is more accurately than (2)?

Can someone tell best pedagogical books for studying second quantization. Thanks in advance

I am thinking of creating a set of reference pages at the end of my notebook containing all the foundational maths needed to be able to work in class.

My professor knows i have a terrible working memory and is fine with my keeping a reference on hand in his lectures to be able to work independently.

I already got the pre-req maths and got good grades... i just need reminders basically.

Sorry that this maybe a dumb question, but in the path integral formulation of QFT, it seems that no second quantization is needed(aka no field variable becoming a operator and forming algebra). Does that mean quantization is not required in QFT in path integral formalism?

https://physics.stackexchange.com/questions/455336/slater-determinant-in-second-quantization-using-the-creation-operators-help

Here's my question, I do not understand the answer, can someone explain it to me.

Just started taking a QFT class and have a little trouble understanding these notions.

Some people say that the first quantization is defining(?)

[x,p] = i

And the second is quantifying fields, i.e.

[φ(x), π(y)] = i δ(x-y)

While others say that the first quantization is the

[φ(x), π(y)] = i δ(x-y)

And the other being the introduction of creation and annihilation operators.

Can someone help me understand these concepts better?

Do your worst!

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 😂

We just launched a new open source Python library to help in optimizing Transformer model inference and prepare deployment in production.

It’s a follow up of a proof of concept shared on Reddit. Scripts have been converted to a Python library (Apache 2 license) to be used in any NLP project, and documentation has been reworked. We also added direct TensorRT support, which provides another boost in performance compared to the ORT+TRT backend. It will usually provide you with 5X faster inference compared to vanilla Pytorch, and up to 10X in specific cases. On a RTX 3090, perf_analyzer reports over 2800 inferences per second throughput!

Want to try it 👉 https://github.com/ELS-RD/transformer-deploy

The README includes some benchmarks on small, base and large transformer architectures to give you an idea of how large the benefit can be.

To learn more about the whole process you can also check this article showing how this open source library can beat some commercial product from Hugging Face company.

Why this Python library?

Basically, most tutorials on how to deploy in production a transformer model tell you to take FastAPI and put Pytorch inside. There are many reasons why it’s a bad idea, first of all, the inference performance is very low.

On the other side of the spectrum, there is Nvidia demos (here or there) showing us how to build manually a full Transformer graph (operator by operator) in TensorRT to get best performance from their hardware. It’s out of reach for many NLP practitioners and it’s time consuming to debug/maintain/adapt to a slightly different architecture (I tried). Plus, there is a secret: the very optimized model only works for specific sequence lengths and batch sizes. Truth is that, so far (and it will improve soon), it’s mainly for MLPerf benchmark (the one used to compare DL hardware), marketing content, and very specialized engineers.

The usual way to perform model optimization before deployment is to automatically convert your existing Pytorch / Tensorflow model to

From a solid-state theory point of view---what is the intuition behind second quantization? I've seen a lot of math, but I don't have much intuition for the idea. Is it just a convenient way of writing the Hamiltonian and states of a many-particle system in terms of the excitations that result from the way the particles interact, as opposed to the particles themselves?

I meant gematria.

I don't know where else to ask, so I am wondering if anyone here can give me some input.

How common is it for an 8 letter word to render to the same number, 87, in both Hebrew and English alphabets?

This word is a shadow-name I received, I just started to look into the numbers associated with it and made this interesting discovery.

Also, it happens that 8 + 7 = 15 = 10 + 5

(10 Yod) (5 He)

So 10 + 5 = 15 , the sum of Yod and He. This is the first force, masculine, notice its addition.

Out of which produces:

15

1 + 5 = 6 - 1 = 5

(6 Vau) (5 He)

The first part here is an addition (masculine) of the sum of Yod and He broken into (feminine, dissolution) its basic units (numerals, quantized, material in nature) so it is a mixture of both forces. Feminine in essence, masculine in execution. The last section is pure feminine, being a subtraction. In this way we have the divine duad encoded into the arithmetic.

________________________________

Yod He Vau He = YHVH

The first part of the name produces the second.. Same as the metaphysics of creation.

Here 8 represents eternity, infinite, and a complete process. 7 represents the entirety of the occult forces, Spiritual Man. 10 is the 'perfect number' representing God and Man, the whole, 1 and 0. 5 represents Man incarnate. 1 represents Source, The All, God. 1 + 5 = 6, where 6 is the number of the physical Form of Man, also the Trinity plus its Physical aspects.

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That distinction had carried over even after they had been demilitarized. However the Manticep Corp. were built, artifice did not simply extend down to their tissues and weaponry. Their minds were built. Desirable neural engrams were lifted from selected donors, then layered, modified, and cobbled seamlessly. The killing engrams, the single-minded pursuit of an objective without the drawback of myopic obsession. That gift lingered in all Landsmarine, abstract, indelible, and intrinsic to their sapience. No human could have invented such a code.

Korwin slept. But he was also awake. Even in the pod, with his bodily processes slowed and chilled he could repossess some awareness. Or he could let the hours roll past. Selera’s pod was to his right. Hendricks and Calvin’s to his left. Opposing the port in front of his head, he could see through the window. Like looking from within a well it clutched a disk of the night sky. The edge of the black-and-yellow planet poked into view. The rest was a speckled black.

Out there was beyond any gravity well, any spin-pull. No objectives, no obstacles, no ideals. Not even life or death. It simply was, baffling and unjustified.

Sometimes he allowed the pod’s systems to put him back to sleep. It was like blinking. The closing of the curtains, then the unveiling, and a day would pass. In moments like this he felt a kind of completion, usually reserved for when their senses confirmed the death of a target or the execution of an objective. The solidity of the floor, the untameable dark, the deafening silence—things that gave him satisfaction without purpose or meaning. There would be more. He would find them. And then he would dream.

The heavens deigned to respond with a flash in the night sky, attenuated through the Silentium’s window and again through the hibernation pod’s port. It was as ephemeral as a comet. Good portents. A promise of luck in the hunt. A sign of the goal at the end of the journey.

If he was a superstitious man.

His heart began to beat faster. The pod tried to arrest his functions, but his levels were spiking. So many cycles so delicately reduced to a near standstill by hibernation technology began to go awry. Faint red warnings flashed across the screen to his side.

When I started using Ableton, I did not know any keyboard shortcuts other than those common between most softwares (command + c for copy, command + s for save, etc.) After using Ableton for 10 years, these are the shortcuts that have saved me WEEKS of time one second at a time. Most of these are for arrangement view and I'm surely forgetting a few but here's my list of shortcuts I use every single project:

F9 (Record)

command + T (New audio track)

command + shift + T (New MIDI track)

With one or more tracks selected: command + G (Group tracks. You can group multiple groups in 10+)

With part of an audio or MIDI clip selected: command + D (Duplicate by highlighted length.)

With two or more MIDI or audio clips selected: command + J (Join/ consolidate)

Select any amount of time on the timeline: shift + delete (delete bars/ time from session)

With any single point in the session selected: command + i (add silence/ bars to session)

When editing MIDI: shift + command + U (quantization options menu)

When editing MIDI: command + U (quantize selected notes using current settings)

For Ableton 11: option + command + U (Show take lanes)

A (Toggle automation mode)

M (Toggle musical keyboard - turns the letters of your keyboard into a playable piano, also the first key to hit when automation mode won't toggle. Used to use this when I was just working with laptop.)

Please post any other regularly used shortcuts you can think of! This is not to flex how many obscure keyboard shortcuts you know. Only keyboard shortcuts that save time regularly please.

"Every time you can avoid going to the top menus, you are saving yourself time and carpal tunnel."

-Compducer

Pilot on me!!

I've heard about the quantization of spacetime, and I'm confused on whether spacetime really is quantized, as I've seen various accounts. The evidence for it is provided here:

"the evidence suggests that popular approaches are flawed. Correct formulation of the atoms of space and time is a prerequisite to formulating Quantum gravity, the holy grail of modern physics.

Current theories mostly depend on Planck scale structure, the smallest distance allowed in quantum physics. However if there were such small scale structure there should be anomalies in light from distant sources that have been excluded by experiment. I believe we can exclude Planck scale structure on the based that discrimination of such small distances would require energies much higher than have ever been observed, the Planck Energy.

A second major stumbling block, in my view, is the lack of understanding of the vacuum, or zero point energy (ZPE) of space. The popular view is that there are intrinsically random fluctuations in the vacuum accounting for energy in the order of 185 GeV/cm^3, which as Wheeler remarked, is an energy density only marginally less than that matter. If instead we postulate that the vacuum energy is ordinary energy measured to be zero because it is uniform and the lowest energy we can measure relative to then the obvious solution is that space and time are quantized by spacetime intervals exhibited by well understood quanta of ordinary energy. A third stumbling block in my view is that the universe is a continuum of fixed dimension. Quantum mechanics places no limit on the numbers of dimensions required to represent a quantum system. We can always consider a more complex systems having more dimensions without limit. The evidence is that these dimension are constructed locally within a quantum mechanical systems and do not obey any large scale a prriori extent on our world. General relativity shows space and time bends in on itself such that space and time is bounded within a hypersphere having a radius of the time since the apparent big bang times light speed. No dimensions extend forever.

Is this true? Are there explanations? Also, if electrons and quarks are quantized, doesn't this make them pixelated? What about gravity? More links in comments as I couldn't fit them all

I'm reviewing for my electronic structure theory exam, and as I look over the various quantum chemical models, I can't help but feel...

All these "quantum fields" are basically just mathematical tools/abstractions to allow us to handle N-body issues. The author of my book himself seems to highly imply this notion too (Surján Péter: Introduction to Second Quantized Formalism).

I've not studied QFT yet, so I'm wondering. Is QFT using a similar idea to HF to simplify dealing with multiple particles?

I'd trying to construct some calculations of loop corrections to EM fields in resonators, and I think it's critical to the effect I'm trying to analyze that the photons are manifestly in the various modes of the resonator, so I've got a second-quantization based approach to start. What I'd like to do is then couple that to some kind of typical loop-correction like via electrons. Has anybody heard of a calculation like that? I would really love some references.

Thanks for any help!