MG12 - Talk detail
 

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The roles of gravitational, strong and electroweak interactions in Neutron Star

Applying both general relativity and non-linear $\sigma$-model of nuclear physics to massive Neutron Star cores over the nuclear density,we study the density distributions of baryons and leptons and electrostatic properties based on the global neutrality condition. Einstein-Maxwell equations and dynamical equation for massive $sigma$ field together with equilibrium conditions for Fermi-energies of particles, including the $\beta$-equilibrium establish a closed set of differential equations. Numerically solving these equations we show: (1) the size of massive cores is determined by gravity; (2) sharp density distribution on core’s surface is determined by the $\sigma$ field; (3) an overcritical electric field appears on surface due to the fact that electrons are blind to strong force. In addition, we calculate pressure , energy density and Equation of State and study the stiffness of cores and the relation between total mass and size of cores.

Regularization and quantization of Einstein-Cartan theory

We study regularization and quantization of Einstein-Cartan theory for describing the dynamics of 4-dimensional Euclidean manifold discretized as a 4-simplices complex. Tetrad field e_\mu(x) and spin-connection field \omega_\mu(x) are assigned to each 1-simplex. Applying the torsion-free Cartan structure equation to each 2-simplex, we discuss parallel transports and construct a diffeomorphism and {\it local} gauge-invariant regularization of Einstein-Cartan action. The {\it global} holonomy of field \omega_\mu(x) along a large loop in the 4-simplices complex is also presented. Quantization is defined by a bounded Euclidean partition function with the measure of SO(4)-group valued \omega_\mu(x) fields and Grassmann anticommuting e_\mu(x) fields over the 4-simplices complex. In the 2-dimensional case (2-simplices complex), we calculate: (i) system's entropy and free-energy, being proportional to its surface; (ii) the average of regularized Einstein-Cartan action, implying that the Planck length sets the scale for the minimal distance between two space-time points.

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