Related papers: Nonlinear Fermions and Coherent States
Fermions with the internal degrees of freedom described in Clifford space carry in any dimension a half integer spin. There are two kinds of spins in Clifford space. The spin-charge-family theory,assuming even d=13+1, uses one kind of spins…
The 2:1 two-dimensional anisotropic quantum harmonic oscillator is considered and new sets of states are defined by means of normal-ordering non-linear operators through the use of non-commutative binomial theorems as well as solving…
We construct a parafermionic conformal theory with the symmetry Z_N, for N odd, based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. Primary operators are classified according to their…
We present in Part II the description of the internal degrees of freedom of fermions by the superposition of odd products of the Clifford algebra elements, either $\gamma^a$'s or $\tilde{\gamma}^a$'s, which determine with their oddness the…
Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the $N$-fermion canonical partition function on the positive real $\beta$ axis (or very close to it), even for a small number of particles.…
We examine the weakly interacting atoms in an ultracold Fermi gas leading to a state of macroscopic coherence, from a theoretical perspective. It has been shown that this state can be described as a fermionic coherent state. These coherent…
The defining relations (triple relations) of n pairs of parafermion operators f_j^\pm (j=1,...,n) are known to coincide with a set of defining relations for the Lie algebra so(2n+1) in terms of 2n generators. With the common Hermiticity…
This paper reviews the well-known fact that nilpotent Hermitian operators on physical state spaces are zero, thereby indicating that the supersymmetries and "Grassmann numbers" are also zero on these spaces. Next, a positive definite inner…
I solve a quantum chain whose Hamiltonian is comprised solely of local four-fermi operators by constructing free-fermion raising and lowering operators. The free-fermion operators are both non-local and highly non-linear in the local…
In the spirit of some earlier work on the construction of vector coherent states over matrix domains, we compute here such states associated to some physical Hamiltonians. In particular, we construct vector coherent states of the…
After transition from the Dirac equation to the Schr\"{o}dinger-type relativistic equation with effective potentials of the Schwarzschild and Reissner-Nordstr\"{o}m (RN) fields, the existence of the stationary state of fermions with real…
Quantum fields are considered as generators of infinite-dimensional Clifford algebra $Cl(\infty)$, which can be either orthogonal (in case of fermions) or symplectic (in case of bosons). A generic quantum state can be expressed as a…
A connection between a unitary quantization scheme and para-Fermi statistics of order 2 is considered. An appropriate extension of Green's ansatz is suggested. This extension allows one to transform bilinear and trilinear commutation…
Redefining the vacuum state of a free two-fold $N=1$ covariant supersymmetric string action as the one with all the excited states of world-sheet fermions occupied, makes the theory anomaly free in (3+1)+4 dimensions. While in the $NS$…
In contrast to the determinant, no algorithm is known for the exact determination of the permanent of a square matrix that runs in time polynomial in its dimension. Consequently, non interacting fermions are classically efficiently…
Significant effort has been devoted to the study of "non-Fermi liquid" (NFL) metals: gapless conducting systems that lack a quasiparticle description. One class of NFL metals involves a finite density of fermions interacting with soft order…
In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs) described by Grassmann numbers for $n>2$ degree of nilpotency. Choosing an appropriate weight function, we show that it is possible to…
We build the coherent states for a family of solvable singular Schr\"odinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their…
One of the traditional ways of introducing bosons and fermions is through creation-annihilation algebras. Historically, these have been associated with emission and absorption processes at the quantum level and are characteristic of the…
The non-standard Schwinger fermionic representation of the unitary group is studied by using $n$-fermion operators. One finds that the Schwinger fermionic representation of the U(n) group is not unique when $n\ge 3$. In general, based on…