We give a general $SU(2)_Ltimes SU(2)_R$ $times U(1)_{EM}$ sigma model with external sources, dynamical breaking and spontaneous vacuum symmetry breaking, and present the general formulation of the model. It is found that $sigma $ and $pi ^0$ without electric charges have electromagnetic interaction effects coming from their internal structure. A general Lorentz transformation relative to external sources $J_{gauge}$ $=(J_{A_mu},J_{A_mu ^kappa})$ is derived, using the general Lorentz transformation and the four-dimensional current of nuclear matter of the ground state with $J_{gauge}$ = 0, we give the four-dimensional general relations between the different currents of nuclear matter systems with $J_{gauge} eq 0$ and those with $J_{gauge}=0$. The relation of the densitys coupling with external magnetic field is derived, which conforms well to dense nuclear matter in a strong magnetic field. We show different condensed effects in strong interaction about fermions and antifermions, and give the concrete scalar and pseudoscalar condensed expressions of $sigma_0$ and $pi_0$ bosons. About different dynamical breaking and spontaneous vacuum symmetry breaking, the concrete expressions of different mass spectra are obtained in field theory. This paper acquires the running spontaneous vacuum breaking value $sigma_0^{prime},$ and obtains the spontaneous vacuum breaking in terms of the running $sigma_0^{prime}$, which make nucleon, $sigma $ and $pi $ particles gain effective masses. We achieve both the effect of external sources and nonvanishing value of the condensed scalar and pseudoscalar paticles. It is deduced that the masses of nucleons, $sigma $ and $pi $ generally depend on different external sources.
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