Related papers: Fermion to Boson Mapping
This manuscript is devoted to introduce a gauge theory of the Lorentz Group based on the ambiguity emerging in dealing with isometric diffeo-morphism-induced Lorentz transformations. The behaviors under local transformations of fermion…
The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing…
We investigate simple examples of supersymmetry algebras with real and Grassmann parameters. Special attention is payed to the finite supertransformations and their probability interpretation. Furthermore we look for combinations of bosons…
We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and…
We extend superspace by introducing an antisymmetric tensorial coordinate. The resulting theory presents a supersymmetry with central charge. After integrating over the tensorial coordinate, an effective action describing massive bosons and…
We give the supersymmetric extension of exceptional field theory for E$_{7(7)}$, which is based on a $(4+56)$-dimensional generalized spacetime subject to a covariant constraint. The fermions are tensors under the local Lorentz group ${\rm…
A one-parameter generalized fermion algebra ${\cal B}_{\kappa}(1)$ is introduced. The Fock representation is studied. The associated coherent states are constructed and the polynomial representation, in the Bargmann sense, is derived. A…
We argue that fermion-boson mapping techniques represent a natural tool for studying many-body supersymmetry in fermionic systems with pairing. In particular, using the generalized Dyson mapping of a many-level fermion superalgebra with the…
Building upon Dyson's fundamental 1962 article known in random-matrix theory as 'the threefold way', we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important examples are…
We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form $\mathbb{Z}_2$ gauge theory with an unusual Gauss law. An important property of this map is that it…
In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories…
The article proposes the description of internal spaces of fermion (quarks and leptons and antiquarks and antileptons) and boson (photons, weak bosons, gluons, gravitons and scalars) second quantized fields in a unique way if they all are…
We construct the supersymmetric completion of E$_{6(6)}$-covariant exceptional field theory. The theory is based on a $(5+27)$-dimensional generalized space-time subject to a covariant section constraint. The fermions are tensors under the…
We study the underlying extended supersymmetric structure in a system composed of fermions scattered off an infinitely extended static domain wall in the $xz$-plane. As we shall demonstrate, the fermionic scattered states are associated to…
On a lattice, we construct an overlap Dirac operator which describes the propagation of a Dirac fermion in external gravity. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate…
A class of algebras is constructed using free fermions and the invariant antisymmetric tensors associated with irreducible holonomy groups. (This version contains minor typographical corrections and some additional references. )
The two-dimensional d-p model (or extended Hubbard model) on a square lattice is investigated for fermion pairing by a slave boson method. The inter-site d-fermion interaction is introduced additionally. The momentum space counterpart of…
The algebra of multi-species anyons characterized by different statistical parameters $\nu_{ij}=e_{i}e_{j}\Phi_{i}\Phi_{j}/(2\pi)$, $i,j=1,...,n$ is redefined by basing on fermions and $k_{i}$-fermions ($k_{i}\in\bf{N}\rm /\{0,1\}$ with…
The dynamics of fermions in curved spacetime is governed by a spin connection, a part of which is contorsion, an auxiliary field independent of the metric, without dynamics but fully expressible in terms of the axial current density of…
Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, various formulations (equations, commutation relations, propagators, Jacobi identities,…