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We consider the scalar field solitons and their interaction with the fermions in the early Universe. The analytical form of the reflection coefficient is obtained. The fermion mass is a function of the distance between the fermion and the…
Radiatively induced symmetry breaking is considered for a toy model with one scalar and one fermion field unified in a superfield. It is shown that the classical quartic self-interaction of the superfield possesses a quantum infrared…
An integrable two-dimensional system related to certain fermion-soliton systems is studied. The self-consistent solutions of a static version of the system are obtained by using the tau function approach. The self-consistent solutions…
We study cluster-cluster collisions in one-dimensional Fermi systems with particular emphasis on the non-trivial quantum effects of the collision dynamics. We adopt the Fermi-Hubbard model and the time-dependent density matrix…
We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard…
We examine recent claims that nonperturbative effects can prevent the decoupling of a heavy fermion whose mass arises from a Yukawa coupling to a scalar field. We show that in weakly coupled, four dimensional models such as the standard…
We have constructed a very different type of particle than any presently known. It is a boson and resides in the $(1/2,0)\oplus(0,1/2)$ representation space. The associated local field has mass dimension three half. These new bosons can…
It is shown that a constant magnetic field in 3+1 and 2+1 dimensions is a strong catalyst of dynamical chiral symmetry breaking, leading to the generation of a fermion dynamical mass even at the weakest attractive interaction between…
Casimir forces from fermions in an extra dimension can stabilise Randall-Sundrum models. Contrary to previous expectations, the stabilisation can produce large electroweak hierarchies without fine tuning. The Casimir stabilisation occurs in…
The fermion representations and boundary conditions in five dimensional anti de Sitter space are described in detail. In each case the one loop effective action is calculated for massless fermions. The possibility of topological or Wilson…
The quantum-mechanical problem of constructing a self-adjoint Hamiltonian for the Dirac equation in an Aharonov--Bohm field in 2+1 dimensions is solved with taking into account the fermion spin. The one-parameter family of self-adjoint…
We present the calculation of the spectral function of an unstable scalar boson coupled to fermions as resulting from the resummation of the one loop diagrams in the scalar particle self energy. We work with a large but finite high-energy…
It is shown that it is possible to bosonize fermions in any number of dimensions using the hydrodynamic variables, namely the velocity potential and density. The slow part of the Fermi field is defined irrespective of dimensionality and the…
We analyse a nonlinear QW model which can be experimentally implemented using the components of the electric field on an optical nonlinear Kerr medium, which translates into a rotation in the coin operator, with an angle which depends (in a…
The spectrum consistency of the three fermion family $U(1)\times U(1)$ quantum electrodynamics in three space-time dimensions [Phys. Rev. Lett. 124 (2020) 131601] is analyzed. It has been verified that the originally proposed action…
We describe a possibility of creation of an odd number of fractionally charged fermions in 1+1 dimensional Abelian Higgs model. We point out that for 1+1 dimensions this process does not violate any symmetries of the theory, nor makes it…
We consider 1+1-dimensional QCD coupled to Majorana fermions in the adjoint representation of the gauge group $SU(N)$. Pair creation of partons (fermion quanta) is not suppressed in the large-$N$ limit, where the glueball-like bound states…
We construct solitary wave solutions in a $1+1$ dimensional massless scalar ($\phi$) field theory with a specially chosen potential $V(\phi)$. The equation governing perturbations about this solitary wave has an effective potential which is…
In the past year domain wall fermion simulations have moved from exploratory stages to the point where systematic effects can be studied with different gauge couplings, volumes, and lengths in the fifth dimension. Results are presented here…
Generically, string models with $N=1$ supersymmetry are not expected to have moduli beyond perturbation theory; stringy non-perturbative effects as well as low energy field-theoretic phenomena such as gluino condensation will lift any flat…