QED; electrons and photons, different fields, modes of a common field?

[Spinnor]

In the Standard Model of particle physics are we to think of the electron(positron) field and the photon field as separate fields?

Is it possible to think of the electron(positron) field and the photon field as just different "modes of vibration" of some more basic field?

Can this line of thought be take with the entire Standard Model, there is a fundamental field that can "move" or "vibrate" in different ways to give us all the fundamental fields?

Is this simplification part of what string theory does?

Thanks for any help!

 

[fzero]

In the Standard Model of particle physics are we to think of the electron(positron) field and the photon field as separate fields?

Not within the Standard Model. There are several glaring obstacles to doing so. First the electron is a spin 1/2 fermion, whereas the photon is a spin 1 boson. Second, the photon has zero electric charge, while the electron has unit charge. Along the same lines, the properties of electron and photon are also different with respect to the weak interactions. We also should not overlook the fact that the photon is the gauge boson of the EM interaction. For all these reasons, the photon and electron are very different species within the Standard Model.

Is it possible to think of the electron(positron) field and the photon field as just different "modes of vibration" of some more basic field?

Can this line of thought be take with the entire Standard Model, there is a fundamental field that can "move" or "vibrate" in different ways to give us all the fundamental fields?

Is this simplification part of what string theory does?

Thanks for any help!

There are a few theoretical ways to, at least partially, unify the fields of the Standard Model. One area, called Grand Unified Theories (GUTs), presumes that, at very high energies, the Standard Model gauge group is enhanced to a larger, in a certain sense simpler, group. The leptons and quarks are then supposed to be different components of more basic fermionic fields (sometimes called leptoquarks), while the photon, W and Z bosons are components of a single GUT gauge field. This GUT symmetry is assumed to be broken via a Higgs-type mechanism.

The general concept of a GUT still treats fermions and bosons as very different objects. But there is another theoretical framework called supersymmetry (SUSY) that incorporates fundamental fields that have both bosonic and fermionic components. However, because of the different fundamental charges of fields like the electron and photon, we cannot put the electron and photon into the same GUT field, even with SUSY.

Superstring theory involves an even more complicated path to a unification. There the fundamental fields can be thought of as objects defined on the 2D string worldsheet. By putting those objects together in certain ways, we can create both spacetime bosons and fermions. In certain models, it is also possible to generate fields with the types of charges found in GUTs and the Standard Model. In superstring models, the electron and photon would not really be part of the same fundamental field, but it is more correct to say that they would be constructed from the same building blocks. Superstring models are not without their difficulties. They tend to predict many, many new particles in addition to the Standard Model-like ones. Also, in many models it is also not possible to compute observable quantities like the electron mass.

 

[Polyrhythmic]

Not within the Standard Model.

You meant to say yes. Within the Standard Model, as you say, the photon and electron fields have different properties, therefore have to be treated as separate.

 

[Spinnor]

In theory one can have a string, under tension, fixed at two end points A and B that lie on the z axis, and with an additional restoring force that acts on the string only in say the vertical direction. In the vertical direction the string satisfies E^2 = P^2 + M^2 and in the horizontal direction the string satisfies E^2 = P^2. With the system above we have a single "field" that has both mass-less and massive modes? (I think there is even a coupling between the modes, large waves in one mode change the tension for both modes. This gives rise what if any term in the Lagrangian?)

I agree that the fields of the fundamental fermions are very different from the fields of the bosons that give rise to force but I hoped that some very complicated version of my example above could explain all fields.

Thanks for your help!

 

[fzero]

In theory one can have a string, under tension, fixed at two end points A and B that lie on the z axis, and with an additional restoring force that acts on the string only in say the vertical direction. In the vertical direction the string satisfies E^2 = P^2 + M^2 and in the horizontal direction the string satisfies E^2 = P^2. With the system above we have a single "field" that has both mass-less and massive modes? (I think there is even a coupling between the modes, large waves in one mode change the tension for both modes. This gives rise what if any term in the Lagrangian?)

I agree that the fields of the fundamental fermions are very different from the fields of the bosons that give rise to force but I hoped that some very complicated version of my example above could explain all fields.

Thanks for your help!

Yes, it is true that the spectrum of a string includes a tower of massive states corresponding to higher frequency oscillations. However, there is a problem of scales between the mass of elementary particles and the mass of string oscillator modes. The fundamental mass scale of the string is essentially set by the scale of gravity. In most scenarios, the string scale is then within an order of magnitude or two of the Planck mass, $M_P\sim 10^{19}~\text{GeV}$. The mass of particles corresponding to the higher vibrational modes is much too large to correspond to any observed particles, so model building focuses on building the known elementary particles from the massless modes of the string. The observed masses are then expected to be generated from quantum effects. This last part is definitely one of the areas that has not been solved to general satisfaction.

In this picture, it is the case that all fundamental fields are in a sense part of the same field at the string scale. At lower energies the symmetry of the "unified field" is broken, leading to the different masses and quantum numbers of the observed particles. Exactly how to get the low-energy spectrum out of string theory is the unsolved problem I've been alluding to.