Good literature needed (QFT topics)

[raracon]

Summary:: Trying to find good books so that I can continue writing my paper about the vacuum

Hello fellow physics enthusiasts,
I require your support to find good and scientific literature about:
Lamb Shift
Vacuumpolarisation
Zero point energy

It can be a long source too, so don't be afraid to drop a 700 page source too :)

P.S I am still writing my work about the vacuum etc. . I just wasn't able to find a reliable source which discusses these topics in a scientific type of way

 

[strangerep]

To go into detail on any of those topics requires strong proficiency in QFT. Which QFT textbooks have you studied (i.e., worked through thoroughly) so far?

 

[raracon]

Welp, I am still in high school, so I don't really have access to textbooks and stuff. I just worked through what I could find on the Internet. Thing is tho that we are supposed to write a 15page paper on those things (plus casimir effect) and I couldn't really find any good sources (other that Wikipedia) that really bring the concept of I.e lambshift and vacuum or fluctuations together.

 

[strangerep]

Welp, I am still in high school, [...] we are supposed to write a 15page paper on those things (plus casimir effect) [...]

OMG. Those subjects are normally taught at 4th yr university or postgrad level. At high school level, you'll probably just get handwaving popsci articles that talk in terms of "virtual particles popping in and out of the vacuum" (which is actually a load of misleading garbage).

If I'm being too pessimistic, perhaps others here can be more helpful.

Edit: you could perhaps try the following Insights articles by Arnold Neumaier:

Virtual Particles
Misconceptions about Virtual Particles

but these might still be too advanced for high school level.

 

[raracon]

Yeah, well the seminars in Germany are wild. I do know tho that the idea of particles just appearing and dissappearing and their change of the energy of the vacuum is covered by the Heisenberg uncertainty principle is not quite right.

I am stuck with theese problems:
1. I can't quite grasp why lambshift is so important to the vacuum.
2. How do I explain the relation of the lambshift to the vacuum fluctuations or how do I explain vacuum fluctuations with the lamb shift?

 

[vanhees71]

Well, forget these handwaving explanations with "virtual particles" and "vacuum fluctuations". It's of course hard to study the real thing, which is quantum field theory, for which you need quite some pretty abstract math, but one can also try to explain the issues without these pretty bad popular-science narratives.

First of all relativistic quantum field theory tells us that the vacuum is indeed the vacuum, i.e., it's really nothing. It doesn't move at all, it looks everywhere and at any time and in any direction the same. Also nothing fluctuates at all. It's just a state, where nothing at all is present (or more precisely all there is, is space and time or rather "spacetime" of special relativity).

Now, as soon as you put something in this empty spacetime its no longer the vacuum, because you put something there, and what's very important to remember is that whenever you want to observe something in fact you must put something in there, i.e., as soon as you want to observe the vacuum, you destroy it in the sense that you must put something you probe it with there (including also a measurement device, which is even a macroscopic object consisting of zillions of atoms and molecules).

Now quantum field theory is so complicated that we are not able to solve it exactly but we have some powerful math to solve it approximately in a formalism called "perturbation theory". All we can describe really exactly in this formalism are non-interacting particles, and that's why we are starting with them. Let's concentrate on electromagnetism and thus quantum electrodynamics, which describes charged particles and the electromagnetic field. Of course charged particles interact via the electromagnetic field and that's why we can observe the particles and the electromagnetic field. E.g., we perceive the electromagnetic field as light, because an electromagnetic wave hits the retina in our eyes and this leads to a signal due to the photoelectric effect.

But now, since we cannot solve the full complicated system of interacting charged particles and the electromagnetic field exactly we start with a fictitious system consisting of non-interacting charged particles and the free electromagnetic field and try to take into account the interactions in perturbative way. The idea behind this is that the strength of interactions between elementary particles like an electron is pretty weak. The coupling constant, quantizing this strength is the finestructure constant $e^2/(4 \pi \epsilon_0 \hbar c) \simeq 1/137$, which is a pretty small value, and the hope is that we can describe the interacting particles and fields by calculating observable quantities as a power series in $e$ (or $\alpha$ for that matter).

In the 1950 Feynman found an ingenious way to depict these complicated pertrubations in terms of his famous Feynman diagrams, which look as if they would depict scattering processes, and to some extent they indeed do this, and that's why you can draw them also in pop-sci textbooks. The only problem is that they have to be understood in a quite delicate way, as particles and fields get a pretty specific meaning in the realm of quantum theory. What these diagrams really stand for are mathematical formulae which help you calculate all kinds of observable quantities like scattering cross sections, which tell you to which extent two particles (e.g., to electrons) are scattered in all possible ways allowed by the natural laws (conservation of charge, momentum, energy, angular momentum, etc.). That's what the formalism of quantum field theory provides to you and thus also the Feynman diagrams which are just a very clever notation for the corresponding formulas. So one possibility is that the electrons just get scattered on each other, so that after the scattering is over you again find two electrons. It can also happen that in addition to the electrons you also emit some radiation, and the quanta of the radiation are the photons. So you can emit one or more photons in addition to the electrons. Another possibility is that you create some photons and also some electron-positron pairs in addition and so on. What the Feynman diagrams tell you is the probability for each of these possilbe precesses to happen in a given way with all the particles in the final state with given momementa and energies.

Now there are also diagrams with loops. E.g., consider just one electron. Just a single electron line depicts a non-interacting electron. But now you can also have a contribution still having only electron lines as external lines but with some other lines building loops. These are called self-energy diagrams. In the same way you can also have a single photon line, describing a non-interacting photon, but also a diagram with still two external photon lines but with some loops in between. One is a loop consisting of an electron-positron line. These photon self-energy diagrams are also called vacuum polarization diagrams, because it seems as if indeed there were electron-positron pairs emitted and recombined back to a photon, but that's a wrong suggestion, because for reasons of energy and momentum conservation a single photon can never pop out an electron and a positron. Nevertheless the diagram with this loop is there and it's not zero. In fact it's even not making direct sense, because it leads to a diverging integral, but one has made sense of it with the socalled "renormalization", and such diagrams turn up also in other diagrams describing real particles, which are always depicted by the external legs.

One other important sort of observables are the spectral lines of atoms like the hydrogen atom, which consists of a proton and an electron bound together with the proton to form the hydrogen atom. Now you can calculate, again order by order in the coupling $e$, the energy levels of the hydrogen atom. At lowest order you solve a wave equation called the Dirac equation. The result is already pretty accurate, but there are all the higher-order diagrams with loops giving corrections to these energy levels with more and more powers of $e$ or $\alpha$, and indeed one can observe the tiny shifts of the energy levels corresponding to these correction terms. A famous correction has been measured in 1948 by Lamb, which is why it's known as the Lamb shift, and it triggered the theorists to think harder about the above mentioned divergent loop diagrams, which lead to renormalization (and a Nobel prize for Feynman, Schwinger, and Tomonaga developing this method). The amazing thing is that "subtracting all the infinities" in such a way that you can express everything in terms of the finite observables coupling constants, masses (and wave function norms) of the interacting theory (calculated approximately with the perturbation theory) and push the infinities of the loop diagrams to unobservable "bare" couplings and masses, corresponding to the unobservable fictitious non-interacting particles and photons, and then a kind of miracle indeed occurs: After all these complicated procedures just using a few experimentally found parameters like the charge and mass of the electron you find agreement between experiment and theory concerning the energy levels of the hydrogen atom at an amazing precision of several significant digits. It's among the best agreements between experiment and theory ever achieved in the history of physics.

 

[Vanadium 50]

Lamb shift is 6-9 years ahead of where you are now. That's a lot to expect a book to make up.

You are probably going to be stuck with popularizations, and even good ones (like Feynman's QED: The Strange Theory of Light and Matter) don't always delve as deep as the Lamb shift.

 

[raracon]

Well, forget these handwaving explanations with "virtual particles" and "vacuum fluctuations". It's of course hard to study the real thing, which is quantum field theory, for which you need quite some pretty abstract math, but one can also try to explain the issues without these pretty bad popular-science narratives.

First of all relativistic quantum field theory tells us that the vacuum is indeed the vacuum, i.e., it's really nothing. It doesn't move at all, it looks everywhere and at any time and in any direction the same. Also nothing fluctuates at all. It's just a state, where nothing at all is present (or more precisely all there is, is space and time or rather "spacetime" of special relativity).

Now, as soon as you put something in this empty spacetime its no longer the vacuum, because you put something there, and what's very important to remember is that whenever you want to observe something in fact you must put something in there, i.e., as soon as you want to observe the vacuum, you destroy it in the sense that you must put something you probe it with there (including also a measurement device, which is even a macroscopic object consisting of zillions of atoms and molecules).

Now quantum field theory is so complicated that we are not able to solve it exactly but we have some powerful math to solve it approximately in a formalism called "perturbation theory". All we can describe really exactly in this formalism are non-interacting particles, and that's why we are starting with them. Let's concentrate on electromagnetism and thus quantum electrodynamics, which describes charged particles and the electromagnetic field. Of course charged particles interact via the electromagnetic field and that's why we can observe the particles and the electromagnetic field. E.g., we perceive the electromagnetic field as light, because an electromagnetic wave hits the retina in our eyes and this leads to a signal due to the photoelectric effect.

But now, since we cannot solve the full complicated system of interacting charged particles and the electromagnetic field exactly we start with a fictitious system consisting of non-interacting charged particles and the free electromagnetic field and try to take into account the interactions in perturbative way. The idea behind this is that the strength of interactions between elementary particles like an electron is pretty weak. The coupling constant, quantizing this strength is the finestructure constant $e^2/(4 \pi \epsilon_0 \hbar c) \simeq 1/137$, which is a pretty small value, and the hope is that we can describe the interacting particles and fields by calculating observable quantities as a power series in $e$ (or $\alpha$ for that matter).

In the 1950 Feynman found an ingenious way to depict these complicated pertrubations in terms of his famous Feynman diagrams, which look as if they would depict scattering processes, and to some extent they indeed do this, and that's why you can draw them also in pop-sci textbooks. The only problem is that they have to be understood in a quite delicate way, as particles and fields get a pretty specific meaning in the realm of quantum theory. What these diagrams really stand for are mathematical formulae which help you calculate all kinds of observable quantities like scattering cross sections, which tell you to which extent two particles (e.g., to electrons) are scattered in all possible ways allowed by the natural laws (conservation of charge, momentum, energy, angular momentum, etc.). That's what the formalism of quantum field theory provides to you and thus also the Feynman diagrams which are just a very clever notation for the corresponding formulas. So one possibility is that the electrons just get scattered on each other, so that after the scattering is over you again find two electrons. It can also happen that in addition to the electrons you also emit some radiation, and the quanta of the radiation are the photons. So you can emit one or more photons in addition to the electrons. Another possibility is that you create some photons and also some electron-positron pairs in addition and so on. What the Feynman diagrams tell you is the probability for each of these possilbe precesses to happen in a given way with all the particles in the final state with given momementa and energies.

Now there are also diagrams with loops. E.g., consider just one electron. Just a single electron line depicts a non-interacting electron. But now you can also have a contribution still having only electron lines as external lines but with some other lines building loops. These are called self-energy diagrams. In the same way you can also have a single photon line, describing a non-interacting photon, but also a diagram with still two external photon lines but with some loops in between. One is a loop consisting of an electron-positron line. These photon self-energy diagrams are also called vacuum polarization diagrams, because it seems as if indeed there were electron-positron pairs emitted and recombined back to a photon, but that's a wrong suggestion, because for reasons of energy and momentum conservation a single photon can never pop out an electron and a positron. Nevertheless the diagram with this loop is there and it's not zero. In fact it's even not making direct sense, because it leads to a diverging integral, but one has made sense of it with the socalled "renormalization", and such diagrams turn up also in other diagrams describing real particles, which are always depicted by the external legs.

One other important sort of observables are the spectral lines of atoms like the hydrogen atom, which consists of a proton and an electron bound together with the proton to form the hydrogen atom. Now you can calculate, again order by order in the coupling $e$, the energy levels of the hydrogen atom. At lowest order you solve a wave equation called the Dirac equation. The result is already pretty accurate, but there are all the higher-order diagrams with loops giving corrections to these energy levels with more and more powers of $e$ or $\alpha$, and indeed one can observe the tiny shifts of the energy levels corresponding to these correction terms. A famous correction has been measured in 1948 by Lamb, which is why it's known as the Lamb shift, and it triggered the theorists to think harder about the above mentioned divergent loop diagrams, which lead to renormalization (and a Nobel prize for Feynman, Schwinger, and Tomonaga developing this method). The amazing thing is that "subtracting all the infinities" in such a way that you can express everything in terms of the finite observables coupling constants, masses (and wave function norms) of the interacting theory (calculated approximately with the perturbation theory) and push the infinities of the loop diagrams to unobservable "bare" couplings and masses, corresponding to the unobservable fictitious non-interacting particles and photons, and then a kind of miracle indeed occurs: After all these complicated procedures just using a few experimentally found parameters like the charge and mass of the electron you find agreement between experiment and theory concerning the energy levels of the hydrogen atom at an amazing precision of several significant digits. It's among the best agreements between experiment and theory ever achieved in the history of physics.

Woow, thanks for your answer. I really appreciate it and it really helps me too.
I do know that what I am doing is years ahead, but that's school rn I guess. To get a better understanding of my paper I'm going to post my content table.

Vacuumfluctuations
1.1 vacuumpolarisation
1.2 lamb shift
1.3 ZPE (zero point energy)

Casimir Effect
2.1 What is tze Casimir Effect
2.2 How it was discovered
2.3 Proof for the CE
2.4 Casimir Effect and chiral objects

 

[gentzen]

Since you are from Germany, Klaus Lichtenegger "Schlüsselkonzepte zur Physik" would be an option that is intermediate between popsci and 4th yr university or postgrad level. But ... OMG ... Lamb shift, Casimir effect and zero point energy are in the last (11th) subsection of chapter "11 Quantenfeldtheory" of that book, and only two pages in total. Regarding pure content and information, the wikipedia article certainly contains more. But at least the information in Lichtenegger is not wrong (or at least not popsci level wrong).

 

[raracon]

Since you are from Germany, Klaus Lichtenegger "Schlüsselkonzepte zur Physik" would be an option that is intermediate between popsci and 4th yr university or postgrad level. But ... OMG ... Lamb shift, Casimir effect and zero point energy are in the last (11th) subsection of chapter "11 Quantenfeldtheory" of that book, and only two pages in total. Regarding pure content and information, the wikipedia article certainly contains more. But at least the information in Lichtenegger is not wrong (or at least not popsci level wrong).

Cheers for the reply, mate!
Well I am really desperate for getting some good info about the lamb shift in connection with vacuumfluctuations etc. I would like to know how to explain that there are no random virtual particles appearing from nowhere. Do you guys have any good formulations for this?

 

[gentzen]

The explanation from Lichenegger is basically that the dressed electron (i.e. the electron together with effects related to itself interaction) is more smeared out compared to the electron as an ideal point particle. This shifts the energy level of the electron if it comes very close to the center of the potential. This essentially happens only for electrons in the s-shell.

 

[raracon]

I see I see, do you know where I can read the book for myself? I don't really have money to spend on books rn

 

[gentzen]

Well, I first encountered that book in a public library. I own that book now, but I just checked that you can download it from the place that everybody knows but no one will mention. (No, I will not be the one to mention it now.) Let me instead copy the original paragraph regarding the Lamb shift here. (I won't copy the paragraph on the Casimir effect here, because it is longer, contains 3 pictures, and may be slightly more objectionable if you insist on being fully rigorous)

Der Lamb-Shift In der Atomspektroskopie beobachtet man, dass manchmal zwei Niveaus, die selbst bei sorgfältiger Berechnung I am Kontext der relativistischen Quantenmechanik energetisch entartet sein sollten, doch eine leichte Aufspaltung zeigen. Das ist dann der Fall, wenn bei einem der beiden Orbitale die Aufenthaltswahrscheinlichkeit in Kernnähe deutlich größer ist als beim anderen.
Durch die ständige Wechselwirkung mit Vakuumfluktuationen kommt es zu einer ”Ausweitung“ jedes realen Teilchens gegenüber einem idealen Punktteilchen. Ein so ”aufgeweitetes“ Teilchen ist, verglichen mit einem Punktteilchen, etwas schwächer gebunden.
Relevant ist dieser Effekt aber nur, wenn der Abstand vom Zentrum des Potenzials nicht viel größer ist ist als die Abmessungen des so verschmierten Teilchens. I am Atom haben (aufgrund der für l ≥ 1 bestehenden Zentrifugalbarriere) nur s-Elektronen eine signifikante Aufenthaltswahrscheinlichkeit in Kernnähe, und entsprechend werden nur sie merklich energetisch angehoben.

 

[haushofer]

There's still debate about a proper interpretation of the Casimir effect, afaik.

 

[Demystifier]

vacuumfluctuations

Since you are from Germany,

It makes sense now.

 

[vanhees71]

There's still debate about a proper interpretation of the Casimir effect, afaik.

Is there still debate? The only thing which is sure is that the "vacuum-fluctuation argument" is at least shaky. What's really fluctuating are of course the charges making up the material (in the usual example the plates with net-charge zero):

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.72.021301
https://arxiv.org/abs/hep-th/0503158v1

 

[Vanadium 50]

There's still debate about a proper interpretation of the Casimir effect, afaik.

I don't believe there is. The Jaffe paper seems to pretty much have closed the door. The argument is that if you can derive the effect without any reference to the vacuum, the effect can't be caused by the vacuum.

 

[jtbell]

Welp, I am still in high school,

OMG. Those subjects are normally taught at 4th yr university or postgrad level.

Note that in Germany, a Hochschule is at the pedagogical level of a "college" or "university" in the US. In the US, "high school" comes before "college" or "university", i.e. grades 9-12, or ages 15-18 (more or less).

 

[Demystifier]

The Jaffe paper seems to pretty much have closed the door.

Unfortunately, it didn't. Most authors who work on Casimir effect still use the vacuum energy paradigm. I would say that this paradigm makes sense for macroscopic phenomenology, but misses the fundamental microscopic mechanism. https://arxiv.org/abs/1702.03291