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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!

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!

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