- #1
pscplaton
- 6
- 1
Hi All,
The S-matrix is defined as the inner product of the in- and out-states, as in Eq. (3.2.1) in Weinberg's QFT vol 1:
[itex]S_{βα}=(Ψ−β,Ψ+α)[/itex]
[itex]\Psi_{±α}[/itex] are the eigenstates of the full Hamiltonian with a non-zero interaction term.
Can [itex]\alpha[/itex] describes a neutron ? Since it is not stable, it is not an eigenstate of the full Hamiltonian, so it should not... But then how can you compute the decay rate of the neutron within the S matrix formalism ?
I am also wondering how to take neutrinon into account. Supposing [itex]\alpha[/itex] can describe a neutron,
the neutron may decays as: n → p + [itex]e^−[/itex] + [itex]\overline{\nu}_e[/itex]. But [itex]\overline{\nu}_e[/itex] is not an eigenstate of the full Hamiltonian ; I would rather use the mass eigenstates [itex]\nu_1, \nu_2, \nu_3[/itex]. But then it means that the S matrix formalism is unable to predict that it is really a [itex]\nu_e[/itex] that is created at the time of the interaction, which could lead to false predictions... What do you think ?
The S-matrix is defined as the inner product of the in- and out-states, as in Eq. (3.2.1) in Weinberg's QFT vol 1:
[itex]S_{βα}=(Ψ−β,Ψ+α)[/itex]
[itex]\Psi_{±α}[/itex] are the eigenstates of the full Hamiltonian with a non-zero interaction term.
Can [itex]\alpha[/itex] describes a neutron ? Since it is not stable, it is not an eigenstate of the full Hamiltonian, so it should not... But then how can you compute the decay rate of the neutron within the S matrix formalism ?
I am also wondering how to take neutrinon into account. Supposing [itex]\alpha[/itex] can describe a neutron,
the neutron may decays as: n → p + [itex]e^−[/itex] + [itex]\overline{\nu}_e[/itex]. But [itex]\overline{\nu}_e[/itex] is not an eigenstate of the full Hamiltonian ; I would rather use the mass eigenstates [itex]\nu_1, \nu_2, \nu_3[/itex]. But then it means that the S matrix formalism is unable to predict that it is really a [itex]\nu_e[/itex] that is created at the time of the interaction, which could lead to false predictions... What do you think ?