On self-energy

[Magical Realist]

Can anyone explain in layman's terms the concept of self-energy? Is it something only possessed by electrons? What about photons? Do they possess this property too? And how is self-energy related to infinitude?

 

[DaveC426913]

I have never heard of either of these terms.

I looked up self-energy on Wiki and it does seem to be a QFT thing, but I find no scientific reference for "infinitude".

 

[C C]

Can anyone explain in layman's terms the concept of self-energy?

It seems that only physicists who speak in Hindi are willing to do that. Whereas the English...

Is it something only possessed by electrons?

https://arxiv.org/pdf/physics/0608108.pdf

"The self-energy is the energy that an electron in free space, isolated from other particles, fields, or light quanta, possesses. In the classical theory it posed no problem, but after the development of quantum theory, it became a critical problem for theoretical physics. "

What about photons? Do they possess this property too?

Photon self-energy in a magnetized chiral plasma from kinetic theory
https://journals.aps.org/prd/pdf/10.1103/PhysRevD.102.014011

Quark self-energy
https://www.osti.gov/biblio/4018120

Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma
https://arxiv.org/abs/2207.06039

And how is self-energy related to infinitude?

The resulting infinities were a problem to eliminate, requiring "renormalization".

https://arxiv.org/pdf/physics/0608108.pdf
https://www.jstor.org/stable/24313453
https://en.wikipedia.org/wiki/Self-energy
https://en.wikipedia.org/wiki/Feynman_diagram
https://en.wikipedia.org/wiki/Landau_pole
https://en.wikipedia.org/wiki/Renormalization

EXCERPTS: The self-energy is the energy that an electron in free space, isolated from other particles, fields, or light quanta, possesses. In the classical theory it posed no problem, but after the development of quantum theory, it became a critical problem for theoretical physics.

[...] It has been recognized since about 1916 that such a quantity as the self-energy must exist. The problem arose from the fact that attempts to calculate it by conventional methods yielded infinite results. Until recently, however, the self-energy never manifested itself in any observable manner and hence could be ignored in calculations of real processes.

[...] the self-energy is pictorially (and economically) represented by means of Feynman diagrams.

[...] The naïve application of such calculations often produces [Feynman] diagrams whose amplitudes are infinite, because the short-distance particle interactions require a careful limiting procedure, to include particle self-interactions. The technique of renormalization ... compensates for this effect and eliminates the troublesome infinities. After renormalization, calculations using Feynman diagrams match experimental results with very high accuracy.

[...] The question is resolved using quantum field theory by 'summing' all the contributions due to this self-interaction and absorbing the infinite part into a redefinition of the electron wave-function and mass. This redefinition is called renormalization.

[...] In physics, the Landau pole (or the Moscow zero, or the Landau ghost) is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite.

[...] Another important critic was Feynman. Despite his crucial role in the development of quantum electrodynamics, he wrote the following in 1985:

"The shell game that we play is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate."​

Feynman was concerned that all field theories known in the 1960s had the property that the interactions become infinitely strong at short enough distance scales. This property called a Landau pole, made it plausible that quantum field theories were all inconsistent. In 1974, Gross, Politzer and Wilczek showed that another quantum field theory, quantum chromodynamics, does not have a Landau pole. Feynman, along with most others, accepted that QCD was a fully consistent theory.

- - - - - - - -

Infinities and Renormalization
https://phys.libretexts.org/Bookshe...e_Physics/5.05:_Infinities_and_Renormalization

"One of the key features missing in the discussion above is the fact that all the pictures I have drawn are infinite – somewhat of a severe blow. The key point is to understand that this is not a problem, but has to do with a misinterpretation of the series. [...] What it means is that we should try to express all our answers in physically sensible (measurable) quantities. Renormalisation is the mathematical procedure that does this. A theory (such as QED) is called renormalisable if we can make all expressions finite by re-expressing them in a finite number of physical parameters."

Renormalization
https://phys.libretexts.org/Bookshe...d_Cosmology)/Cosmology/Carlip/Renormalization
_

 

[DaveC426913]

I certainly am familiar with renormalization when it comes to resolving infinities when reconciling QM and GR.

 

[James R]

Can anyone explain in layman's terms the concept of self-energy?

Probably somebody can. I don't think I can, because I don't think I understand it well enough.

The wikipedia page doesn't seem to explain it. Maybe to somebody with an appropriate background in quantum field theory, that article makes some sense, but it doesn't give me the impression it was written with laypeople in mind (or even with people who have undergraduate degrees in physics).

Is it something only possessed by electrons?

No. As I understand it (which is poorly, as I mentioned) it's a general feature of the description of particles in quantum field theories. It's due to a sort of self-interaction of a particle or quantum field, if I understand it correctly.

What about photons? Do they possess this property too?

I'm not sure. I have mostly come across the concept in relation to particles with mass. Photons have zero rest mass, so perhaps the concept isn't relevant to them.

And how is self-energy related to infinitude?

In quantum electrodynamics, to take one example, naive calculations of the masses of particles (which are described as excitations of quantum fields in that theory) give infinity as the answer when self-interactions are taken into account. But the "trick" of renormalisation sort of sweeps the issue under the rug, so to speak, using a mathematical method (which I can't explain). The result is a theory that is probably the most accurate in all of science - i.e. it agrees with actual experimental results to the highest level of accuracy of any scientific theory.

 

[exchemist]

It seems that only physicists who speak in Hindi are willing to do that. Whereas the English...



https://arxiv.org/pdf/physics/0608108.pdf

"The self-energy is the energy that an electron in free space, isolated from other particles, fields, or light quanta, possesses. In the classical theory it posed no problem, but after the development of quantum theory, it became a critical problem for theoretical physics. "



Photon self-energy in a magnetized chiral plasma from kinetic theory
https://journals.aps.org/prd/pdf/10.1103/PhysRevD.102.014011

Quark self-energy
https://www.osti.gov/biblio/4018120

Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma
https://arxiv.org/abs/2207.06039



The resulting infinities were a problem to eliminate, requiring "renormalization".

https://arxiv.org/pdf/physics/0608108.pdf
https://www.jstor.org/stable/24313453
https://en.wikipedia.org/wiki/Self-energy
https://en.wikipedia.org/wiki/Feynman_diagram
https://en.wikipedia.org/wiki/Landau_pole
https://en.wikipedia.org/wiki/Renormalization

EXCERPTS: The self-energy is the energy that an electron in free space, isolated from other particles, fields, or light quanta, possesses. In the classical theory it posed no problem, but after the development of quantum theory, it became a critical problem for theoretical physics.

[...] It has been recognized since about 1916 that such a quantity as the self-energy must exist. The problem arose from the fact that attempts to calculate it by conventional methods yielded infinite results. Until recently, however, the self-energy never manifested itself in any observable manner and hence could be ignored in calculations of real processes.

[...] the self-energy is pictorially (and economically) represented by means of Feynman diagrams.

[...] The naïve application of such calculations often produces [Feynman] diagrams whose amplitudes are infinite, because the short-distance particle interactions require a careful limiting procedure, to include particle self-interactions. The technique of renormalization ... compensates for this effect and eliminates the troublesome infinities. After renormalization, calculations using Feynman diagrams match experimental results with very high accuracy.

[...] The question is resolved using quantum field theory by 'summing' all the contributions due to this self-interaction and absorbing the infinite part into a redefinition of the electron wave-function and mass. This redefinition is called renormalization.

[...] In physics, the Landau pole (or the Moscow zero, or the Landau ghost) is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite.

[...] Another important critic was Feynman. Despite his crucial role in the development of quantum electrodynamics, he wrote the following in 1985:

"The shell game that we play is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate."​

Feynman was concerned that all field theories known in the 1960s had the property that the interactions become infinitely strong at short enough distance scales. This property called a Landau pole, made it plausible that quantum field theories were all inconsistent. In 1974, Gross, Politzer and Wilczek showed that another quantum field theory, quantum chromodynamics, does not have a Landau pole. Feynman, along with most others, accepted that QCD was a fully consistent theory.

- - - - - - - -

Infinities and Renormalization
https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Book:_Nuclear_and_Particle_Physics_(Walet)/05:_Basic_Concepts_of_Theoretical_Particle_Physics/5.05:_Infinities_and_Renormalization

"One of the key features missing in the discussion above is the fact that all the pictures I have drawn are infinite – somewhat of a severe blow. The key point is to understand that this is not a problem, but has to do with a misinterpretation of the series. [...] What it means is that we should try to express all our answers in physically sensible (measurable) quantities. Renormalisation is the mathematical procedure that does this. A theory (such as QED) is called renormalisable if we can make all expressions finite by re-expressing them in a finite number of physical parameters."

Renormalization
https://phys.libretexts.org/Bookshe...d_Cosmology)/Cosmology/Carlip/Renormalization
_

Interesting. I never did QED so all I can do is read your links.

It looks as if it arises from the electrostatic field generated by the charge on the electron and that this results in an infinite amount of energy if the electron is a point particle, presumably because the electric field strength then goes to infinity as the distance from it goes to zero. Unfortunately, the electron needs to be a point particle in the model.

The bit I don't get is why the electric field contains energy, in the absence of anything to interact with. Classically, the electrostatic potential energy is defined in terms of the work done against an electrostatic force, when one charge is moved in the presence of a field due to another. For one charge on its own there is no such force, classically. I wonder if it is to do with the vacuum: are there fleeting polarisations of the vacuum in QED? If so there would be an energy due to the interaction of these with the electron charge.

Any idea?

 

[Magical Realist]

"In classical physics the self-energy of a system is the contribution to the energy of the system resulting from the interaction between different parts of the system. In quantum field theory the self-energy of a particle is the contribution to the energy of the particle due to virtual emission and absorption of particles. In the many-body problem in quantum mechanics the self-energy Es of a particle is the difference EQ − EB, where EQ is the energy of the quasiparticle associated with the particle and EB is the energy of the ‘bare’ particle. The particle interacts with its surrounding medium, which in turn acts back on the original particle."--- https://www.oxfordreference.com/dis...hysics the self,different parts of the system.

 

[C C]

Interesting. I never did QED so all I can do is read your links.

It looks as if it arises from the electrostatic field generated by the charge on the electron and that this results in an infinite amount of energy if the electron is a point particle, presumably because the electric field strength then goes to infinity as the distance from it goes to zero. Unfortunately, the electron needs to be a point particle in the model.

The bit I don't get is why the electric field contains energy, in the absence of anything to interact with. Classically, the electrostatic potential energy is defined in terms of the work done against an electrostatic force, when one charge is moved in the presence of a field due to another. For one charge on its own there is no such force, classically. I wonder if it is to do with the vacuum: are there fleeting polarisations of the vacuum in QED? If so there would be an energy due to the interaction of these with the electron charge.

Any idea?

Yah, pair production is rife in it.

There are scores of papers proposing various things, but I couldn't sort Rami Malek from Sami Malek as to which carry any merit.

Casimir self-energy of a free electron
https://arxiv.org/ftp/hep-th/papers/0606/0606227.pdf

Page six: We conclude that a Casimir approach to evaluating the self-energy of the electron strongly indicates that the rest mass energy of the electron comes from the electromagnetic energy arising from the interactions of the electron charge with the virtual photons of the vacuum quantum electromagnetic field.

- - - - - - - - -

How can an electron interact with itself?
https://arxiv.org/pdf/physics/0010080.pdf

Scattered snippets: The self-energy of an electron is an old problem of classical electrodynamics. It assumes an interaction of an electron with the field that the electron produces. [...] An electron-positron pair production and annihilation could thus be visualized as a closed loop by a positive and a negative energy electrons, characterizing the vacuum polarization. [...] An electron may interact with itself through the vacuum polarization induced in the vacuum electrons due to the electron.
_

 

[exchemist]

Yah, pair production is rife in it.

There are scores of papers proposing various things, but I couldn't sort Rami Malek from Sami Malek as to which carry any merit.

Casimir self-energy of a free electron
https://arxiv.org/ftp/hep-th/papers/0606/0606227.pdf

Page six: We conclude that a Casimir approach to evaluating the self-energy of the electron strongly indicates that the rest mass energy of the electron comes from the electromagnetic energy arising from the interactions of the electron charge with the virtual photons of the vacuum quantum electromagnetic field.

- - - - - - - - -

How can an electron interact with itself?
https://arxiv.org/pdf/physics/0010080.pdf

Scattered snippets: The self-energy of an electron is an old problem of classical electrodynamics. It assumes an interaction of an electron with the field that the electron produces. [...] An electron-positron pair production and annihilation could thus be visualized as a closed loop by a positive and a negative energy electrons, characterizing the vacuum polarization. [...] An electron may interact with itself through the vacuum polarization induced in the vacuum electrons due to the electron.
_

OK so that is indeed it, then: polarisation of the vacuum.

But not actual pair production, I think. These would be virtual particles, presumably, rather than real ones.