Related papers: Grassmann Duality and the Particle Spectrum
We build a supersymmetric model with $SU(2)_{L}\otimes SU(2)_{R}\otimes U(1)_{(B-L)}$ electroweak gauge symmetry, where $SU(2)_{L}$ is the left-handed currents while $SU(2)_{R}$ is the right-handed currents and $B$ and $L$ are the usual…
Representability conditions on the one- and two-particle density matrix for fermion systems are formulated by means of Grassmann integrals. A positivity condition for a certain kind of Grassmann integral is established which, in turn,…
An approach to gauge theory in the context of locally conformally flat space-time is described. It is discussed how there are a number of natural principal bundles associated with any given locally conformally flat space-time $X$. The…
We show that homologically projectively dual varieties for Grassmannians Gr(2,6) and Gr(2,7) are given by certain noncommutative resolutions of singularities of the corresponding Pfaffian varieties. As an application we describe the derived…
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:…
We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all…
Gauge theories have been a cornerstone of the description of the world at the level of the fundamental particles. The Lagrangian or the action describing the corresponding interactions is invariant under certain gauge transformations. This…
We analyze mathematical and physical properties of a previously introduced [J. Phys. A47, 115302 (2014)] family of $U(4)$ coherent states (CS). They constitute a matrix version of standard spin $U(2)$ CS when we add an extra (pseudospin)…
The duality principle for group representations developed in \cite{DHL-JFA, HL_BLM} exhibits a fact that the well-known duality principle in Gabor analysis is not an isolated incident but a more general phenomenon residing in the context of…
General properties of global covariance matrices representing bipartite Gaussian states can be decomposed into properties of local covariance matrices and their Schur complements. We demonstrate that given a bipartite Gaussian state…
We impose partial-wave unitarity on $2 \to 2$ tree-level scattering processes to derive constraints on the dimensions of large scalar and fermionic multiplets of arbitrary gauge groups. We apply our results to scalar and fermionic…
Lagrange scalar densities which are concomitants of two scalar fields, a pseudo-Riemannian metric tensor, and their derivatives of arbitrary differential order are investigated in a space of four-dimensions. I construct the most general…
A self-dual and anti-self-dual decomposition of the teleparallel gravity is carried out and the self-dual Lagrangian of the teleparallel gravity which is equivalent to the Ashtekar Lagrangian in vacuum is obtained. Its Hamiltonian…
We propose a duality in the relative Langlands program. This duality pairs a Hamiltonian space for a group $G$ with a Hamiltonian space under its dual group $\check{G}$, and recovers at a numerical level the relationship between a period on…
It is shown how gauge invariance is obtained for the coupling of a photon to a two-body state described by the solution of the Bethe-Salpeter equation. This is illustrated both for a complex scalar field theory and for interaction kernels…
We revisit and clarify the gauge dependence of gravitational waves generated at second order from scalar perturbations. In a universe dominated by a perfect fluid with a constant equation-of-state parameter $w$, we compute the energy…
In this paper we continue our investigation of the N = 2 supergravity models, where scalar fields of hypermultiplets parameterize the nonsymmetric quaternionic manifolds. Using the results of our previous paper, where we have given an…
Coupling gauge fields to the chiral currents from an effective Lagrangian for pseudoscalar mesons naturally gives rise to a species doubling phenomenon similar to that seen with fermionic fields in lattice gauge theory.
The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge…
We elaborate on a new representation of Lagrangians of 4D nonlinear electrodynamics including the Born-Infeld theory as a particular case. In this new formulation, in parallel with the standard Maxwell field strength $F_{\alpha\beta},…