When quanta are aligned along one or more of the Higgs Field dimensions, those quanta exhibit no inertia...they are massless, like photons.

Thus, both D and E vary with v^2. But D needs a gas (like air) for it to exist, what does E have...the hypothesized Higgs Field. This WAG, because it has not been proved, is a multidimensional field that pervades all of our known universe. It's something like air to bring in the analogy. But unlike air, it exists both in and outside our 4 dimensional world.

When quanta are aligned along one or more of the Higgs Field dimensions, those quanta exhibit no inertia...they are massless, like photons. But when they are not aligned (e.g., counter to) the field dimensions, the quanta have inertia...they show mass in our 4D universe that we can see. And when they are moving faster and faster against the grain (so to speak), they encounter more and more resistance to further increases in velocity...more inertia and, therefore, we say mass has increased even though that is not strictly correct.

The Higgs Field is quite controversial, but it does offer one way to explain what I believe is erroneously called the increase in mass. It is really the increase in the inertia of a mass as its speed approaches that of light.


How many degrees of freedom does the photon have in 2+1 dimensions ?

In ordinary theory of QED, the photon has two degrees of freedom, so when we want to quantize the electromagnetic field we impose two conditions to eliminate two degrees of freedom and get a photon with two degrees of freedom.

Do we impose two conditions to quantize the electromagnetic field in 2+1 dimensions?

Topics

• Photons ×
  101 Questions

  45 Followers

  Follow
• Quantum Field Theory ×
  157 Questions

  2,275 Followers

  Follow

Oct 11, 2012 · Modified Oct 11, 2012 by the commenter.

Share

• Facebook
• Twitter
• LinkedIn
• Google+

0 / 0

All Answers (6)

• 
  Jakson M. Fonseca · Universidade Federal de Viçosa (UFV)

  In 2+1 dimensions like in 3+1, we have 2 conditions that fixes the number of degrees of freedon: gauge invariance and motion equation, then only one of the three components of the potencial is physical and the photon has only one degree freedon in 2+1 dimensions.

  Oct 11, 2012
• 
  Brian P Dolan · National University of Ireland, Maynooth

  The answer depends on what 2+1 dimensional theory you wish to consider. Jakson's answer above is perfectly correct for the 2+1 dimensional version of Maxwell's theory, with action E^2 - B^2. But in 2+1 dimensions the dynamics of the photon can be changed in a way that is not possible in 3+1 dimensions, by adding a Chern-Simons term to the action. When this is done a photon in 2+1 dimensions can acquire a mass
  in a consistent way and it would then have two degrees of freedom, one longitudinal and one transverse. This is not possible in 3+1 dimensions. Without the Chern-Simons term a 2+1 dimensional photon is massless, it only has one transverse degree of freedom as Jakson said.

  Oct 11, 2012
• 
  Jakson M. Fonseca · Universidade Federal de Viçosa (UFV)

  I think this is a very confusion discussion. In a topological Maxwell-Chern-Simons
  theory we have two conditions that fixes the number of degree freedon: gauge invariance and motion equation, like in massless case, but in a pure Maxwell case the spin of the photon is zero, being the photon in 2+1 dimensions a scalar particle. When we considerer the Maxwell-Chern-Simons action the photon has two possiblities that dependes on the mass sinal, and the photon's spin can be +1 (positive mass) or -1 (negative mass), but only one is possible, being the Maxwell-Chern-Simons one particle with only one degree of freedon. I think that the article "Topologically Massive Gauge Theories" (Annals of Physics 281, 409 449 (2000)) is a good reference about this question.