Related papers: Fermions, differential forms and doubled geometry
With a view towards future applications in nuclear physics, the fermion realization of the compact symplectic sp(4) algebra and its q-deformed versions are investigated. Three important reduction chains of the sp(4) algebra are explored in…
A question is addressed pertinent to models of fundamental fermions in a world of high dimensions. Tex extra compactified dimensions are needed to accommodate quarks and leptons of each generation in a single spinor space carrying a…
We perform the complete bosonization of 2+1 dimensional QED with one fermionic flavor in the Hamiltonian formalism. The Fermi operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify…
Conventional descriptions of higher-spin fermionic gauge fields appear in two varieties: the Aragone-Deser-Vasiliev frame-like formulation and the Fang-Fronsdal metric-like formulation. We review, clarify and elaborate on some essential…
Standard model is reconstructed using the generalized differential calculus extended on the discrete space $M_4\times Z_3$. $Z_3$ is necessary for the inclusion of strong interaction. Our starting point is the generalized gauge field…
A functional integral approach is developed to discuss the bosonisation of the massive Thirring and the massive Schwinger models in arbitrary D-dimensions. It is found that these models, to {\it all} orders in the inverse fermi mass,…
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…
We introduce a phase space with spinorial momenta, corresponding to fermionic derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is a generalisation of the covariant De Donder-Weyl Hamiltonian formulation on this…
The ${\mathcal D}$-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group ${\rm GL}(2,{\mathbb C})$ of…
We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that…
We examine a quantum group extension of the standard model. The field operators of the extended theory are obtained by replacing the field operators $\psi$ of the standard model by ${\psi}$D$^j_{mm'}$, where D$^{j}_{mm'}$ are elements of a…
In this paper, we explore a new type of global symmetries$-$the fermionic higher-form symmetries. They are generated by topological operators with fermionic parameter, which act on fermionic extended objects. We present a set of field…
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…
The most general theory of gravity in d-dimensions which leads to second order field equations for the metric has [(d-1)/2] free parameters. It is shown that requiring the theory to have the maximum possible number of degrees of freedom,…
Supersymmetry can be consistently generalized in one and two dimensional spaces, fractional supersymmetry being one of the possible extension. 2D fractional supersymmetry of arbitrary order $F$ is explicitly constructed using an adapted…
The general seven-dimensional maximal supergravity is presented. Its universal Lagrangian is described in terms of an embedding tensor which can be characterized group-theoretically. The theory generically combines vector, two-form and…
Two-component spinors are the basic ingredients for describing fermions in quantum field theory in four space-time dimensions. We develop and review the techniques of the two-component spinor formalism and provide a complete set of Feynman…
This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will…
We revisit the classical aspects of $\mathcal{N}=(2,2)$ supersymmetric sigma models with Hermitian symmetric target spaces, using the so-called Gross-Neveu (first-order GLSM) formalism. We reformulate these models for complex Grassmannians…
A spontaneously broken SU(2)xU(1) gauge theory with just one "primordial" generation of fermions is formulated in the context of generally covariant theory which contains two measures of integration in the action: the standard…