Einstein-Podolsky-Rosen correlations of Dirac particles: Quantum field theory approach

We calculate correlation function in the Einstein-Podolsky-Rosen type of experiment with massive relativistic Dirac particles in the framework of the quantum field theory formalism. We perform our calculations for states which are physically interesting and transform covariantly under the full Lorentz group action—i.e., for pseudoscalar and vector states.

Figure 1

Function $\Delta C$ [Eq. (59)] in the parametrization $\mathbf{n}=(0,0,1)$, $\mathbf{a}=(\sin {\theta }_a,0,\cos {\theta }_a)$, $\mathbf{b}=(\cos {\phi }_b\sin {\theta }_b,\sin {\phi }_b\sin {\theta }_b,\cos {\theta }_b)$. We have plotted the graph of the function $\Delta C$ for two arbitrarily chosen values of ${\phi }_b$ and for $\beta =0.999$, which is the value for an electron-positron pair created in the ${\pi }^0$ decay.

Figure 2

Function $\Delta C$ [Eq. (66)] in the parametrization$\mathbf{\phi }=(0,0,1)$, $\mathbf{n}=(\sin \theta ,0,\cos \theta )$, $\mathbf{a}=(\cos {\phi }_a,\sin {\phi }_a,0)$, $\mathbf{b}=(\cos {\phi }_b,\sin {\phi }_b,0)$. In this parametrization $\Delta C=-2\cos {\phi }_a\cos {\phi }_b{\cos }^2\theta$. We have plotted the graph for the value $\theta$ such that ${\cos }^2\theta =1$. We see that $\Delta C$ is of the same order of magnitude as the correlation function.