The origin of the fermion generations is discussed. A strong interactions spin IS is introduced which unifies the quarks and leptons as two multiplets of this spin. The electroweak vector bosons and gluons emerge as the fused states of these fermion multiplets. We discussed the possibility of existence of the electroweak spin quantum number IW = 1 2 for all fermions besides their space time spi...

We present a new staggered discretization of the Dirac operator. In comparison with standard staggered fermions, real and imaginary parts are located in different nodes. Doubling gives only a doublet of Dirac fermions which we propose to interpret as a physical (lepton or quark) doublet. Contrary to usual staggered fermions, we have no exact chiral symmetry but obtain a generalization of the Gi...

The high Landau level filling fractions 5/2, 7/3 and 8/3 are interpreted by using the angular momentum model. It is found that for the odd number of flux quanta, the quasiparticles called the " composite fermions " are fermions but for even number-, the quasiparticles are a mixture of bosons and fermions.Therefore, the theory of " composite fermions " is internally inconsistent.

The thesis will present results in Quantum Chromo Dynamics (QCD) with dynamical lattice fermions. The topological susceptibilty in QCD is determined, the calculations are carried out with dynamical overlap fermions. The most important properties of the quark-gluon plasma phase of QCD are studied, for which dynamical staggered fermions are used.

We present a new staggered discretization of the Dirac operator. In comparison with standard staggered fermions, real and imaginary parts are located in different nodes. Doubling gives only a doublet of Dirac fermions which we propose to interpret as a physical (lepton or quark) doublet. Contrary to usual staggered fermions, we have no exact chiral symmetry but obtain a generalization of the Gi...

Observing condensation in a gas of fermions has been another interesting topic after the realization of the Bose-Einstein Condensation in atomic gases. The condensation of fermions may happen either in the BEC or the BCS manner, depending on how the fermions are paired to each other. This paper gives a brief review on the recent breakthroughs in this

We discuss the construction of a chiral random matrix model for staggered fermions. This model includes O(a) corrections to the continuum limit of staggered fermions and is related to the zero momentum limit of the Lee-Sharpe Lagrangian for staggered fermions. The naive construction based on a specific expansion in lattice spacing (a) of the Dirac matrix produces the term which gives the domina...

Fermions coupled to Yang-Mills matrix models are studied from the point of view of emergent gravity. We show that the simple matrix model action provides an appropriate coupling for fermions to gravity, albeit with a nonstandard spin connection. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action and a dilaton-like term, at least for on...

Standard decoupling of heavy fermions may fail when there are non-perturbative variations in a scalar field which gives masses to the fermions. One situation of phenomenological relevance is the case of sphalerons in the presence of fermions at finite temperatures. The free energy of a simple model is determined using a non-perturbative technique to study the effect of fermions on the scalar fi...