Solve Bound State Problems in QFT | Identify Space of States

[Prathyush]

How does one solve bound state problems in QFT(like an electron positron atom)? How does one identify the space of states. The Fock space seems to lose it definition when a bound state problem is discussed. There is also no meaning to wave functions or potentials that are used in standard quantum mechanics.

 

[meopemuk]

How does one solve bound state problems in QFT(like an electron positron atom)? How does one identify the space of states. The Fock space seems to lose it definition when a bound state problem is discussed. There is also no meaning to wave functions or potentials that are used in standard quantum mechanics.

Take a look at Berestetskii, Lifgarbagez, Pitaevskii, "Quantum electrodynamics" sections 83 (Breit equation) and 84 (Positronium). They suggest to "fit" an interaction potential between the electron and the positron so that QFT-calculated scattering amplitudes are reproduced with this potential. In the 2nd perturbation order their fitted potential is Coulomb + spin-orbit + other relativistic corrections, so that bound states are reproduced pretty well with this potential.

This idea can be extended to higher perturbation orders. See, for example, chapter 10 in http://www.arxiv.org/abs/physics/0504062.

Eugene.