Related papers: (J,0)+(0,j) Representation Space: Majorana-Like Co…
A class of interacting classical random fields is constructed using deformed *-algebras of creation and annihilation operators. The fields constructed are classical random field versions of "Lie fields". A vacuum vector is used to construct…
The aim of this paper is to introduce and to study the space $\mathcal{O}_{M,\omega}(\mathbb{R}^N)$ of the multipliers of the space $\mathcal{S}_{\omega}(\mathbb{R}^N)$ of the $\omega$-ultradifferentiable rapidly decreasing functions of…
We ask the question whether neutrino physics with momentum space Majorana spinors, the eigenvectors of the particle--antiparticle conjugation operator, C=i\gamma_2 K (with K standing for complex conjugation), is different but physics with…
This paper investigates the irreducibility of certain representations for the Lie algebra of divergence zero vector fields on a torus. In "Irreducible Representations of the Lie-Algebra of the Diffeomorphisms of a d-Dimensional Torus," S.…
N=4 supersymmetric extensions of the l-conformal Galilei algebra are constructed by properly extending the Lie superalgebra associated with the most general N=4 superconformal group in one dimension D(2,1;a). If the acceleration generators…
We discuss some aspects of perturbative $(0,2)$ Calabi-Yau moduli space. In particular, we show how models with different $(0,2)$ data can meet along various sub-loci in their moduli space. In the simplest examples, the models differ by the…
We review and extend recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N=4 super Yang-Mills theories. We present a simple worldsheet…
Using the recent parity-based construction of a covariant basis for operators acting on the $(j,0)\oplus(0,j)$ representation of the HLG, we propose a formalism for the description of high spin matter fields, based on the projection over…
We construct the higher-spin massive fermionic fields in 2+1 dimensions. Their field equations and propagators are derived from first principle. For fields with j>1/2, complications arise from the non-linear behaviour of the boost…
Using a sequence of Bogoliubov transformations, we obtain an exact expression for the vacuum state of a Dirac field in 2+1 dimensions in presence of a constant magnetic field. This expression reveals a peculiar two level pairing structure…
Recently, the ModMax theory has been proposed as a unique conformal nonlinear extension of electrodynamics. We have shown in [1] that this modification can be reproduced a marginal $T\bar{T}$-like deformation from pure Maxwell theory.…
In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some…
Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The…
Based on a brief review on developments of number system, a new developed pattern is proposed. The quaternion is extended to a matrix form aI+bC+cB+dA, in which the unit matrix I and three special matrices C,B,A correspond to number 1 and…
The purpose of this article is to extend certain results of Roso (2023) which concerned equivariant contact structures on minimal L-spaces to the more general setting of mod p L-spaces. This is achieved by considering the Serre spectral…
The parameter-space orbifold construction of open and unoriented toroidal and (target-space) orbifold compactifications is briefly reviewed, with emphasis on the underlying geometrical framework. A class of chiral four-dimensional type-I…
These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial…
We argue that having an odd number of Majorana fermion zero modes on a dynamical point-like soliton signifies an inconsistency in a theory with 3+1 and higher dimensions. We check this statement in a couple of examples in field theory and…
Using the Dirac (Clifford) algebra $\gamma^{\mu}$ as initial stage of our discussion, we summarize and extend previous work with respect to the isomorphic 15dimensional Lie algebra su$*$(4) as complex embedding of sl(2,$\mathbb{H}$), the…
3+1 decompositions of differential forms on a Lorentzian manifold (M,g;+ - - -) with respect to arbitrary observer field and the decomposition of the standard operations acting on them are studied, making use of the ideas of the theory of…