Related papers: Fermionic Operators from Bosonic Fields in 3+1 Dim…

Coherent states are usually defined as eigenstates of an unbounded operator, the so-called annihilation operator. We propose here possible constructions of {\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a…

We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means…

We discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological parameters which label such phases and the connection with…

We study the $N=2$ string with a real structure on the $(2,2)$ spacetime, using BRST methods. Several new features emerge. In the diagonal basis, the operator $\exp(\lambda \int^z J^{\rm tot})$, which is associated with the moduli for the…

We present a general derivation of semi-fermionic representation for generators of SU(N) group as a bilinear combination of Fermi operators. The constraints are fulfilled by means of imaginary Lagrange multipliers. The important case of…

Bosonic quantum field theories with holomorphic action functionals are realized by two types of constructions involving supersymmetric quantum field theories, compactified on an interval in one type and compactified on a disk and deformed…

We present a numerical study of the fermion-induced effective action in the presence of a static inhomogeneous magnetic field for both 3+1 and 2+1 dimensional QED using a novel approach. This approach is appropriate for cylindrically…

We describe the integrable structure of the space of local operators for the supersymmetric sine-Gordon model. Namely, we conjecture that this space is created by acting on the primary fields by fermions and a Kac-Moody current. We proceed…

We propose a realisation of partially-massless higher spin algebras in four dimensions in terms of bosonic and fermionic oscillators, using Howe duality between $sp(4,\mathbb R) \cong so(2,3)$ and $osp(1|2(\ell-1), \mathbb R)$. More…

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…

Using the recently discovered connection between bosonization and duality transformations (hep-th/9401105 and hep-th/9403173), we give an explicit path-integral representation for the bosonization of a massive fermion coupled to a U(1)…

In quantum mechanics, bosonic operators are mathematical objects that are used to represent the creation ($a^\dagger$) and annihilation ($a$) of bosonic particles. The natural power of a linear combination of bosonic operators represents an…

We derive an exact operator bosonization of a finite number of fermions in one space dimension. The fermions can be interacting or noninteracting and can have an arbitrary hamiltonian, as long as there is a countable basis of states in the…

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is…

We consider theories with fermionic degrees of freedom that have a fixed point of Wilson-Fisher type in non-integer dimension $d = 4-2\epsilon$. Due to the presence of evanescent operators, i.e., operators that vanish in integer dimensions,…

I review the covariant quantization of the critical $N{=}2$ fermionic string with and without a global ${\bf Z}_2$ twist. The BRST analysis yields massless bosonic and fermionic vertex operators in various ghost and picture number sectors,…

We introduce a parafermionic version of the Jaynes Cummings Hamiltonian, by coupling $k$ Fock parafermions (nilpotent of order $F$) to a 1D harmonic oscillator, representing the interaction with a single mode of the electromagnetic field.…

Efficient encoding of electronic operators into qubits is essential for quantum chemistry simulations. The majority of methods map single electron states to qubits, effectively handling electron interactions. Alternatively, pairs of…

Quadratic algebras of the type $\lsb Q_0, Q_\pm \rsb$ $=$ $\pm Q_\pm$, $\lsb Q_+, Q_- \rsb$ $=$ $aQ_0^2 + bQ_0 + c$ are studied using three-mode bosonic realizations. Matrix representations and single variable differential operator…

Generalizing the kink operator of the Heisenberg spin 1/2 model, we construct a set of Klein factors explicitly such that $(1+1)$ dimensional fermion theories with arbitrary number of species are mapped onto the corresponding boson theories…