Related papers: Supersymmetry with Cadabra
The progress brought to the study of chiral fermions and gauge theories by quantization methods with a bulk time suggests their usefulness in supersymmetric theories. Using superspace methods, we show how an explicitly supersymmetric…
A fundamental challenge in supersymmetric field theory is that supersymmetry transformations on field variables generally form an algebra only on-shell, i.e. upon imposing the field equations. We show that this issue is defused in a…
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…
To construct actions for describing superbranes propagating in AdS x S superbackgrounds we propose a coset space realization of these superbackgrounds which results in a short polynomial fermionic dependence (up to the sixth power in…
Some key features of the symmetries of the Schr\"odinger equation that are common to a much broader class of dynamical systems (some under construction) are illustrated. I discuss the algebra/superalgebra duality involving first and…
Supersymmetry transformations may be represented by unitary operators in a formulation of supersymmetry without numbers that anti-commute. The physical relevance of this formulation hinges on whether or not one may add states of even and…
We discuss several applications and extensions of our previous operator solution of the $N$-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i -…
We define a new algebraic extension of the Poincar\'e symmetry; this algebra is used to implement a field theoretical model. Free Lagrangians are explicitly constructed; several discussions regarding degrees of freedom, compatibility with…
Surface charges and their algebra in interacting Lagrangian gauge field theories are investigated by using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a…
We explore $\mathcal{N}=1$ supersymmetric extensions of algebras going beyond the Poincar\'e and AdS ones in three spacetime dimensions. Besides reproducing two known examples, we present new superalgebras, which all correspond to…
We discuss the relation between supersymmetric gauge theory of branes and supergravity; as it was discovered in D-brane physics, and as it appears in Matrix theory, with emphasis on motion in curved backgrounds. We argue that gauged sigma…
Recently proposed supergravity theories in odd dimensions whose fields are connection one-forms for the minimal supersymmetric extensions of anti-de Sitter gravity are discussed. Two essential ingredients are required for this construction:…
Cluster variables have recently revolutionized numerical work in certain models involving fermionic variables. This novel representation of fermionic partition functions is continuing to find new applications. After describing results from…
The paper considers a Clifford extension of the Grassmann algebra, in which operators are built from Grassmann variables and by the derivatives with respect to them. It is shown that a subalgebra which is isomorphic to the usual matrix…
The Grassmann representation for the system of qubits, is considered. The treatment is based on natural description of the qubits system as fermions and uses coherent states of fermions. The quantum logic gates are represented in two forms…
It is advocated that the superembedding approach is a generic covariant method for the description of superbranes as models of (partial) spontaneous supersymmetry breaking. As an illustration we construct (in the framework of…
We reformulate the Bagger-Lambert-Gustavsson model using an N=8 superspace, thus making the full supersymmetry manifest. The formulation is based on appropriate "pure spinor wave functions" for the Chern-Simons and matter multiplets. The…
Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on…
Considered are superparticle and superstring models invariant under supersymmetry in a target superspace and local extended worldsheet supersymmetry the latter replacing the fermionic $\kappa$--symmetry of the conventional Green--Schwarz…
The Carroll algebra is constructed as the $c\to0$ limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null…