Qualitative description of particles in QFT

[Geofleur]

I would like to be able to qualitatively describe what particles are according to quantum field theory without saying anything wrong. Is it correct to say the following things about, say, an electron?

(1) Electrons are excitations of an underlying quantum field, the electron field. There is a separate field for every fundamental particle, fermion and boson (so an up quark field, a down quark field, eight gluon fields, etc.)

(2) An electron behaving like a particle is a localized wave packet propagating in this field.

(3) An electron behaving like a wave is a spread out disturbance in the underlying field.

(4) When we try to detect an electron, say, using a photon, there is a probability that the electromagnetic field will exchange energy with the electron field; when we detect a particle, it is because this exchange has caused the electron field to "bunch up" at the location the particle is detected.

If all this is way off, will you guys please point me to some articles that would help me to describe correctly what the theory says? Eventually I plan to just learn QFT, but I haven't got there yet and would like to be able to say correct things about it in the meantime.

 

[Demystifier]

(1), (2) and (3) are correct. However, (4) is somewhat problematic. Typically, in the detection process described as a unitary evolution, we don't end up with one bunch; we end up with many bunches. So you need some interpretation of quantum theory to explain why do we see only one bunch. A wave functions collapse, or something more profound. In QFT textbooks, however, you will not find much discussion about quantum interpretations. So you need something else for that purpose. For a start, you can try my http://de.arxiv.org/abs/quant-ph/0609163

 

[Geofleur]

These papers look really helpful! I can't wait to sit down with a warm beverage and read them more carefully - thanks!

 

[Demystifier]

These papers

Note that I recommended to you only the first.
The second is my signature that appears automatically at the end of all my posts. That means that I recommend it to everybody.

 

[martinbn]

I find all of them hard to understand. They are so vague as to be almost meaningless. For example 1) says that electrons are excitations of a field. But what is an excitation of a field is left to the intuition, thus will be misleading.

 

[Geofleur]

What about this:

For a conceptual model of a field, can we say that a field consists of properties of space at each point such that the whole collection of points can support waves, like the electric and magnetic fields in electromagnetism? Or like an invisible fluid that fills the universe, except of course this "fluid" isn't made of atoms. An excitation is some kind of disturbance that transfers energy to the field? Or perhaps like the mattress springs that Zee talks about in his QFT in a Nutshell? Particles would then be analogous to phonons?

It seems reasonable to think that there would be *some* kind of mental pictures that one can have in mind when thinking about these things...

 

[A. Neumaier]

(1) Electrons are elementary excitations of the electron-positron field. This is a 4 component spinor field with two kinds of elementary excitations, electrons and positrons. Elementary excitation means that its states form an irreducible representation of the Poincare group (in this case of spin 1/2).

(2), (3) are ok, but only in combination with (1). Spread out/localized is in terms of the associated 1-particle wave function.

(4): We detect an electron because the field interacts with the matter of the detector, with a probability proportional to the intensity of the field.

 

[Geofleur]

Is there any way to describe what an excitation is to someone who doesn't know about Lie groups, irreducible representations, principle fiber bundles, and all that? I am just getting to that stuff myself!

I found the following descriptions over at stackexchange and Quora (which I will read and try to summarize a little later):

https://physics.stackexchange.com/questions/143600/what-does-an-excitation-in-a-field-mean

https://www.quora.com/In-quantum-fi...ement-particles-are-excitations-of-the-fields

Later: The gist of these answers is that an excitation is when the field is raised from its ground state. In non-relativistic QM, to get a harmonic oscillator (say) to be above its ground state, you have to put energy in; that was why I was thinking that you would have to add energy to excite a quantum field as well. I'd love to know if this is correct and, if so, how that relates to group theory stuff (though for the latter, I realize I'll probably just need to read that QFT book that's been waiting on me) - it sounds incredibly interesting!

 

[Demystifier]

Later: The gist of these answers is that an excitation is when the field is raised from its ground state. In non-relativistic QM, to get a harmonic oscillator (say) to be above its ground state, you have to put energy in; that was why I was thinking that you would have to add energy to excite a quantum field as well. I'd love to know if this is correct and, if so, how that relates to group theory stuff (though for the latter, I realize I'll probably just need to read that QFT book that's been waiting on me) - it sounds incredibly interesting!

That is correct. Group theory may help, but is not essential.

 

[A. Neumaier]

Is there any way to describe what an excitation is to someone who doesn't know about Lie groups, irreducible representations, principle fiber bundles, and all that?

Consider first a classical harmonic oscillator. You may think of it as a violin string. The ground state is the unmoving string, the elementary excitation is the string oscillating in its basic mode. Almost what you get if you rub the string, but not quite, since there are admixtures of overtones, which are multiple elementary excitations. (The overtones arise through nonlinearities - nonlinear functions of a sine give periodic functions whose Fourier components are multiples of the ground frequency.)

Now consider water. The ground state of a lake is when the surface is completely still. You may excite it in many ways; the elementary excitations, the possible basic modes are the sine waves of arbitrary frequency and direction, and other excitations are superpositions of these. All this was classical; the concept of ovetones akes no sense for classical fields.

In the quantum field analogue, similar things happen but at a largely more complex scale. The ground state is now the vacuum state, and for every 1-particle state function there is a corresponding elementary excitation - these form the single electrons or positrons. The shape of this wave function determines whether the electron or positrons behaves like a particle or like a wave. (The possibilities are given by the Dirac wave equation, which comes into play because of the representation theory of the Poincare group. Note that their energies may already be arbitrarily large!) Higher excitations corresponding to overtones also exist in quantum field theories, and define multi-particle states. The general state of a quantum field is a superposition of all these single- and multi-particle states in all their different modes - a complicated mess.

 

[Geofleur]

That's makes sense, thanks!

I've started reading the book by Anthony Duncan, The Conceptual Framework of Quantum Field Theory, and it's super good so far.

In the meantime, now I will be able to say some correct things about QFT to my students :-D

 

[kent davidge]

I've started reading the book by Anthony Duncan, The Conceptual Framework of Quantum Field Theory, and it's super good so far

read Weinberg's first volume on QFT instead. it's the most deep book on this subject ever written.
at the same time Weinberg introduces the concepts needed for QFT. for example he introduces the axioms of QFT / QM and also the principles of group theory needed later on.

it's only after reading all of the introduction that you will find yourself in difficulty understanding what comes ahead. at least that's what happen to me.

but you won't need to go any further, because at this point you will have all you need to explain QFT to your students. anything more than that they won't understand anyways.

 

[MathematicalPhysicist]

That's makes sense, thanks!

I've started reading the book by Anthony Duncan, The Conceptual Framework of Quantum Field Theory, and it's super good so far.

In the meantime, now I will be able to say some correct things about QFT to my students :-D

What do you teach?

 

[Geofleur]

I teach:

intro physics with calculus
classical mechanics and electromagnetism (smooshed into one course)
special relativity and quantum mechanics (smooshed into a different course)

These comprise a physics minor, and I have freedom to include whatever I want and however I want. I got tired of saying only things that are 100 years old :)

I also work with undergraduates on research projects and publish papers. You know, the small liberal arts college thing!

 

[Demystifier]

You know, the small liberal arts college thing!

They might be quite interested to hear more about different quantum interpretations.

 

[A. Neumaier]

read Weinberg's first volume on QFT instead. it's the most deep book on this subject ever written.

It has a lucid exposition but is not easy to read on a first go. Better read it in parallel with a standard book on QFT.