Related papers: Heisenberg versus the Covariant String

In Ukrain. J. Phys., 1967, V.12, N 5, p.741-746 it was shown how, for a given (discrete) mass spectrum of elementary or hypothetical particles, it was possible to construct a non-trivial algebra G containing a Poincare algebra P as a…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…

Our main proposition is that field equations for all spins can be obtained from Casimir eigenvalue equations for Poincare group. We have already confirm that statement for massive scalar, spinor and vector fields in Ref.[1]. In the present…

We consider Hilbert's sixth problem on the axiomatization of physics starting with a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. The two sided version of the commutation…

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the…

We construct the covariant, spinor sets of relativistic wave equations for a massless field on the basis of the two copies of the R-deformed Heisenberg algebra. For the finite-dimensional representations of the algebra they give a universal…

In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only if every pair of idempotents with a quasinilpotent commutator has a non-trivial common closed…

For any massless, irreducible representation of the covering of the proper, orthochronous Poincar\'e group we construct covariant, free quantum fields that generate the representation space from the vacuum and are localized in semi-infinite…

It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the $Sp(2)$ group which is isomorphic to the Lorentz group applicable to one time-like dimension and two space-like dimensions, known as the…

This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed Wheeler-DeWitt quantum constraint operator. 1)…

The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp(2)$. It is shown that this oscillator system contains the…

We study the Lie algebras of the covariant representations transforming the matter fields under the de Sitter isometries. We point out that the Casimir operators of these representations can be written in closed forms and we deduce how…

Let $\mathbf{A}$ be a bounded self-adjoint operator on a separable Hilbert space $\mathfrak{H}$ and $\mathfrak{H}_0\subset\mathfrak{H}$ a closed invariant subspace of $\mathbf{A}$. Assuming that $\mathfrak{H}_0$ is of codimension 1, we…

We construct an obstruction theory for relative Hilbert schemes in the sense of Behrend-Fantechi and compute it explicitly for relative Hilbert schemes of divisors on smooth projective varieties. In the special case of curves on a surface…

Reviewing the construction of induced representations of the Poincar\'e group of four-dimensional spacetime we find all massive representations, including the ones acting on interacting many-particle states. Massless momentum wavefunctions…

The local two-dimensional Poincar\'e algebra near the horizon of an eternal AdS black hole, or in proximity to any bifurcate Killing horizon, is generated by the Killing flow and outward null translations on the horizon. In holography, this…

The formulation of quantum mechanics with a complex Hilbert space is equivalent to a formulation with a real Hilbert space and particular density matrix and observables. We study the real representations of the Poincare group, motivated by…

We generalize to arbitrary dimension the construction of a covariant and supersymmetric constraint for the massless superPoincare algebra, which was given for the eleven-dimensional case in a previous work. We also contrast it with a…

Given any finite quiver, we consider a complete flag of vector spaces over each vertex. Consider the unipotent invariant subalgebra of the coordinate ring of the filtered quiver representation subspace. We prove that the dimension of the…

Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the…