Narrow Results

We write solutions of relativistic quantum equations explicitly in the helicity basis for S = 1/2 and S = 1. We present the analyses of relations between Dirac-like and Majorana-like field operators. Several interesting features of bradyonic and tachyonic solutions are presented.

We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane ideal conductor. We employ both the Quantum Field Theory (QFT) approach, and the Lifshitz formula generalizations. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak but experimentally measurable. It exhibits a strong dependence on the mass of the quasi-particles in graphene.

We study the field theoretical model of a scalar field in presence of spacial inhomogeneities in form of one and two finite width mirrors (material slabs). The interaction of the scalar field with the defect is described with position-dependent mass term. Within this model we derive the interaction of two finite width mirrors, establish the correspondence of the model to the Lifshitz formula and construct limiting procedure to obtain finite self-energy of a single mirror without any normalization condition.

The Supernovae data, the small value of the Higgs particle mass, and the matter content of the Universe are explained via joint nonlinear realization of the affine and conformal symmetry groups (in spirit of the effective Chiral Lagrangians). This nonlinear realization is used to classify observable physical processes in the Universe, including its origin from the quantum vacuum. All dimension parameters of the theory (including masses and field condensates) arise via quantum anomalies in the beginning of the Universe as consequences of the vacuum postulate. The obtained results are in agreement with last observational and experimental data. These results testify to a super-analog of the joint nonlinear realization as the super-unification of the GR and SM that can be based on the quaternionic supertwistor construction.