Related papers: Heisenberg versus the Covariant String

If the algebra of the Poincar\'e generators is enlarged by the spacetime position operator $X=(X_0,\dots, X_{D-1})$ then the spectra of the momentum $P$ and the mass $P^2$ are unbounded and continuous. In particular, the constraint $(P^2 -…

As established by Sol\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this…

We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended $h$-deformed quantum plane and solve the Schr\"odinger equations explicitly for some physical systems on the quantum plane. In the…

We extend some results of group representation theory and von Neumann algebras to the quaternionic Hilbert space case, proving the double commutant theorem (whose quaternionic proof requires a different procedure) and extend to the…

The unitary irreducible representations of a Lie group defines the Hilbert space on which the representations act. If this Lie group is a physical quantum dynamical symmetry group, this Hilbert space is identified with the physical quantum…

We study a quantum mechanics with the usual postulates but in which the Heisenberg algebra of canonical commutation relations and the Poincare algebra are replaced by the Lie algebra of the homogeneous Lorentz group SO(5,1). It arises from…

Let $\mathcal{A}$ be the $C^*$-algebra associated with $SU_q(2)$, $\pi$ be the representation by left multiplication on the $L_2$ space of the Haar state and let $D$ be the equivariant Dirac operator for this representation constructed by…

Let T be a C_{\cdot 0}-contraction on a Hilbert space H and S be a non-trivial closed subspace of H. We prove that S is a T-invariant subspace of H if and only if there exists a Hilbert space D and a partially isometric operator \Pi :…

We previously introduced the class of DT--operators, which are modeled by certain upper triangular random matrices, and showed that if the spectrum of a DT-operator is not reduced to a single point, then it has a nontrivial, closed,…

Generators of spacetime translations and Lorentz group transformations form the Lie algebra of the Poincar\'e group and give rise to the Casimir invariants for a specification of elementary particle characteristics. Moreover quantum…

We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…

We show that if a nonscalar operator on a separable Hilbert space has a nontrivial invariant subspace, then it has also a nontrivial hyperinvariant subspace. Thus the hyperinvariant subspace problem is equivalent to the invariant subspace…

We study a noncanonical Hilbert space representation of the polymer quantum mechanics. It is shown that Heisenberg algebra get some modifications in the constructed setup from which a generalized uncertainty principle will naturally come…

We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…

Let $\H= < a,b | a[a,b]=[a,b]a \wedge b[a,b]=[a,b]b>$ be the discrete Heisenberg group, equipped with the left-invariant word metric $d_W(\cdot,\cdot)$ associated to the generating set ${a,b,a^{-1},b^{-1}}$. Letting $B_n= {x\in \H:…

Let $X=(X(n))_{n \in \mathbb{Z_+}}$ be a standard subproduct system of $C^*$-correspondences over a $C^*$-algebra $\mathcal M.$ Assume $T=(T_n)_{n \in \mathbb{Z_+}}$ to be a pure completely contractive, covariant representation of $X$ on a…

Inspired by the recent work of Filho et al., a Hermitian momentum operator is introduced in a general curved space with diagonal metric. The modified Hamiltonian associated with this new momentum is calculated and discussed. Furthermore,…

This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…

The structure of representations describing systems of free particles in the theory with the invariance group SO(1,4) is investigated. The property of the particles to be free means as usual that the representation describing a…

There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the…