Abstract
Studies about a formal analogy between the gravitational and the electromagnetic fields lead to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. In fact, the GEM equations correspond to the weak-field approximation of the gravitation field. Here, a non-abelian extension of the GEM theory is considered. Using the Thermo Field Dynamics (TFD) formalism to introduce temperature effects, some interesting physical phenomena are investigated. The non-abelian GEM Stefan-Boltzmann law and the Casimir effect at zero and finite temperatures for this non-abelian field are calculated.
Highlights
The Standard Model (SM) is a non-abelian gauge theory with symmetry group Uð1Þ × SUð2Þ × SUð3Þ
The electroweak interaction is described by an SUð2Þ × Uð1Þ group and while the SUð3Þ group satisfies the quantum chromodynamics [2,3,4]
Our results show that the non-abelian quantities are similar to the abelian quantities
Summary
The Standard Model (SM) is a non-abelian gauge theory with symmetry group Uð1Þ × SUð2Þ × SUð3Þ. An extension of nonabelian gravity is discussed Some applications of such a theory are developed. Several studies about the GEM theory have been developed [8,9,10,11,12,13,14] These ideas arise from the analogybetween equations for the Newton and Coulomb laws and the interest has increased with the discovery of the Lense-Thirring effect, where a rotating mass generates a gravitomagnetic field [15,16,17]. An extension to non-abelian GEM fields is introduced. The Stefan-Boltzmann law and the Casimir effect for the non-abelian GEM field at finite temperature are calculated.
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