# Massless complex field+assumption(s)=massive field. Doable?

1. Jan 20, 2015

### Spinnor

Suppose we have a massless complex field in 3+1 spacetime where E^2 = P^2. Suppose that the only excitations that are possible are those that in some rest frame consist of an excitation of a pair of states p1 and p2 such that

p1 = -p2 and ιp1ι = ιp2ι = mc^2 = (+or-)E, and
the pair of states p1 and p2 couple (sum) together somehow.

In such a "rest frame", (with the right choice of constants), we would have functions like (?) ,
ψ+ = cos(x+α)exp(-iEt)exp(iθ+) and
Ψ- = cos(x+β)exp(iEt)exp(iθ-)

where exp(iθ+) and exp(iθ-) are phase factors and α and β are real numbers.

Momentum sums to zero and "rest" energy is mc^2?

If we could consider such a state that was made up of such a pair would the pair considered as one state transform in another Lorentz frame as a massive complex field?

Thanks for any help!

Last edited: Jan 20, 2015
2. Jan 21, 2015

### DEvens

The parts of your theory that you describe are not enough to produce a massive particle.

Generally mass arises from self interaction. For electrons, for example, you look at radiative corrections. Or to think of it another way, the electron's mass comes from the electric field it carries with it.

There is quite a bit more if you are keen to learn this stuff. Look up the Higgs mechanism, just for example.