Related papers: On the supersymmetric nonlinear evolution equation…
A carefully motivated symmetric variant of the Poisson bracket in ordinary (not Grassmann) phase space variables is shown to satisfy identities which are in algebraic correspondence with the anticommutation postulates for quantized Fermion…
This work challenges the conventional notion that in spacetime dimension higher than one, a supersymmetric Lagrangian invariably consists of purely bosonic terms, purely fermionic terms, as well as boson-fermion mixing terms. By recasting a…
In this paper, colorless bilocal fields are employed to study the large $N$ limit of both fermionic and bosonic vector models. The Jacobian associated with the change of variables from the original fields to the bilocals is computed…
We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and {\it twisted} versions of conventional supersymmetric sigma models with N=2…
A gauge theory for a superalgebra that includes an internal gauge (G) and local Lorentz algebras, and that could describe the low energy particle phenomenology is constructed. These two symmetries are connected by fermionic supercharges.…
Supersymmetry between bosons and fermions is modeled within PT- symmetric quantum mechanics. A non-Hermitian alternative to the Witten's supersymmetric quantum mechanics is obtained.
We extend standard path-integral techniques of bosonization and duality to the setting of noncommutative geometry. We start by constructing the bosonization prescription for a free Dirac fermion living in the noncommutative plane…
Assuming that there exist at least two fermionic parameters, the classical N= 1 supersymmetric Korteweg-de Vries (SKdV) system can be transformed to some coupled bosonic systems. The boson fields in the bosonized SKdV (BSKdV) systems are…
Unlike their fermionic counterparts, the dynamics of Hermitian quadratic bosonic Hamiltonians are governed by a generally non-Hermitian Bogoliubov-de Gennes effective Hamiltonian. This underlying non-Hermiticity gives rise to a dynamically…
The origin of the bosonic and fermionic solutions, constructed in [1,2,3], to the symmetry equations corresponding to the two-dimensional bosonic and N=(2|2) supersymmetric Toda lattices is established, and algebras of the corresponding…
We present a supersymmetric version of Dirac-Born-Infeld (DBI) theory in noncommutative space-time, both for Abelian and non-Abelian gauge groups. We show, using the superfield formalism, that the definition of a certain ordering with…
Following the approach of Callan and Thorlacius applied to the superstring, we derive a supersymmetric extension of the non-local dissipative action of Caldeira and Leggett. The dissipative term turns out to be invariant under a group of…
We present a path-integral bosonization approach for systems out of equilibrium based on a duality transformation of the original Dirac fermion theory combined with the Schwinger-Keldysh time closed contour technique, to handle the…
We study invariants of bosonic and fermionic (Grassmann-valued) matrices under the adjoint action of $U(N)$, weighted by the fermion number. Such models naturally appear as the supersymmetric indices of supersymmetric gauge theories and are…
Non-Hermitian physics has emerged as a rapidly advancing field of research, revealing a range of novel phenomena and potential applications. Traditional non-Hermitian Hamiltonians are typically simulated by constructing asymmetric couplings…
Motivated by the fundamental role that bosonic and fermionic symmetries play in physics, we study (non-invertible) one-form symmetries in $2 + 1$d consisting of topological lines with bosonic and fermionic self-statistics. We refer to these…
We discuss the bosonization of non-relativistic fermions in one space dimension in terms of bilocal operators which are naturally related to the generators of $W$-infinity algebra. The resulting system is analogous to the problem of a spin…
We study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations described in our earlier papers. It is shown that subsolutions of the Duffin-Kemmer-Petiau equations and those of the Dirac equation obey the same Dirac equation with…
We consider a electron in a external field in D=5, through the Dirac equation in the Galilean symmetry approach, and in the Lorentz symmetry approach; from these we perform the nonrelativistic limit, then we procede the supersymmetry of the…
In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites…