I am new to nuclear and particle physics, but am familiar with the concept of a Hamiltonian and nonrelativistic quantum physics.

In this paper by Yang and Lee on parity conservation in weak interactions (published 1956), the appendix reads:

"If parity is not conserved in β decay, the most general form of Hamiltonian can be written as:

$$ H_{int} = (ψ_p^{\dagger}γ_4ψ_n)(C_Sψ_e^{\dagger}γ_4ψ_ν+C_S^{'}ψ_e^{\dagger}γ_4γ_5ψ_ν) +(ψ_p^{\dagger}γ_4γ_μψ_n)(C_Vψ_e^{\dagger}γ_4γ_μψ_ν+C_V^{'}ψ_e^{\dagger}γ_4γ_μγ_5ψ_ν)+\frac{1}{2}(ψ_p^{\dagger}γ_4σ_{λμ}ψ_n)(C_Tψ_e^{\dagger}γ_4σ_{λμ}ψ_ν+C_T^{'}ψ_e^{\dagger}γ_4σ_{λμ}γ_5ψ_ν)+(ψ_p^{\dagger}γ_4γ_μγ_5ψ_n)\times(-C_Aψ_e^{\dagger}γ_4γ_μγ_5ψ_ν-C_A^{'}ψ_e^{\dagger}γ_4γ_5ψ_ν)+(ψ_p^{\dagger}γ_4γ_5ψ_n)(C_Pψ_e^{\dagger}γ_4γ_5ψ_ν+C_P^{'}ψ_e^{\dagger}γ_4γ_5ψ_ν) $$ where $σ_{λμ}=-\frac{1}{2}i(γ_λγ_μ-γ_μγ_λ)$ and $γ_5=γ_1γ_2γ_3γ_4$ [...]"

The different terms $C$ and $C^{'}$ are constants, but the rest is completely unknown to me. I am guessing that the $ψ$ terms refer to wavefunctions of the emitted electron, neutrino, and perhaps nucleus of the atom undergoing $β$ decay, and perhaps the $γ$ terms are Lorentz factors, but aside from that I have no idea.

The paper mentions that the notation is explained in M. E. Rose, in Beta and Gamma Ray Spectroscopy-(Interscience Publishers, Inc. & New York, 1955), pp. 271-291, but upon searching I only found this document in Chinese, containing the same Hamiltonian formula. I figured an online translator will not adequately convey the intended meaning.

Anyone with any ideas whatsoever about this please do get in touch.

  • 1
    $\begingroup$ Search term: gamma matrices $\endgroup$
    – rob
    Feb 10 at 2:07


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