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Hello,

This problem is related to the beta decay of a neutron in a proton an electron and a anti-neutrino. I need to prove that, in the limit where the mass of the neutron and the proton goes to infinity, [itex]m_P, m_N \to \infty[/itex], we have

[tex]

\bar{u}\gamma^\mu(1-\alpha \gamma_5)(\gamma^\alpha k_\alpha + m_P)\gamma^\nu(1-\alpha \gamma_5)u = 4m_P^2(c^\mu g^{\mu \nu} - \alpha(\delta^\mu_0 \delta^\nu_3+\delta^\mu_3 \delta^\nu_0)-i\alpha \epsilon^{0 \mu \nu 3})

[/tex]

where [itex]k[/itex] is the momentum 4-vector of the proton and

[tex]

u=\sqrt{m_N}(1,0,1,0)

[/tex]

is the spinor of the neutron, which is at rest, aligned with positive z-axis and [itex]c^0=1[/itex], [itex]c^i=-\alpha^2[/itex] for [itex]i=1,2,3[/itex] and [itex]\alpha = 1.22[/itex].

I really can't figure out how to do this...

Any help greatly appreciated

This problem is related to the beta decay of a neutron in a proton an electron and a anti-neutrino. I need to prove that, in the limit where the mass of the neutron and the proton goes to infinity, [itex]m_P, m_N \to \infty[/itex], we have

[tex]

\bar{u}\gamma^\mu(1-\alpha \gamma_5)(\gamma^\alpha k_\alpha + m_P)\gamma^\nu(1-\alpha \gamma_5)u = 4m_P^2(c^\mu g^{\mu \nu} - \alpha(\delta^\mu_0 \delta^\nu_3+\delta^\mu_3 \delta^\nu_0)-i\alpha \epsilon^{0 \mu \nu 3})

[/tex]

where [itex]k[/itex] is the momentum 4-vector of the proton and

[tex]

u=\sqrt{m_N}(1,0,1,0)

[/tex]

is the spinor of the neutron, which is at rest, aligned with positive z-axis and [itex]c^0=1[/itex], [itex]c^i=-\alpha^2[/itex] for [itex]i=1,2,3[/itex] and [itex]\alpha = 1.22[/itex].

I really can't figure out how to do this...

Any help greatly appreciated

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