Related papers: Heisenberg Algebra and String Theory
We investigate the most general phase space of configurations, consisting of all possible ways of assigning elementary attributes, ``energies'', to elementary positions, ``cells''. We discuss how this space possesses structures that can be…
We argue that any non-gravitational holographic dual to asymptotically flat string theory in $d$-dimensions naturally resides at spacelike infinity. Since spacelike infinity can be resovled as a $(d-1)$-dimensional timelike hyperboloid…
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…
Poincar\'e invariance is a well-tested symmetry of nature and sits at the core of our description of relativistic particles and gravity. At the same time, in most systems Poincar\'e invariance is not a symmetry of the ground state and is…
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…
We study the space-time invariances of the relativistic particle action for both the massive and massless cases. While the massive action has only the invariances associated to the Poincare algebra, we find that the invariances of the…
Although the energy spectrum of the Heisenberg spin chain on a circle defined by $H=\frac{1}{4}\sum_{k=1}^M(\sigma_k^x\sigma_{k+1}^x+\sigma_k^y\sigma_{k+1}^y +\Delta\sigma_k^z\sigma_{k+1}^z)$ is well known for any fixed $M$, the boundary…
Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever…
We prove that the commutation relations among the generators of the quadratic Heisenberg algebra of dimension $n\in\mathbb{N}$, look like a kind of \textit{non-commutative extension} of $\hbox{sl}(2, \mathbb{C})$ (more precisely of its…
We consider the relativistic phase space coordinates (x_{\mu},p_{\mu}) as composite, described by functions of the primary pair of twistor coordinates. It appears that if twistor coordinates are canonicaly quantized the composite space-time…
Phase-space and its relativistic extension is a natural space for realizing Sp(2,R) symmetry through canonical transformations. On a Dx2 dimensional covariant phase-space, we formulate noncommutative field theories, where Sp(2,R) plays a…
We identify momentum/helicity probability amplitudes for the photon and find their relativistic transformation properties. We also find their behaviour under space inversion and time reversal. The discussion begins with a review of the…
Massive quantum matter of prescribed spin permits infinitely many possibilities of covariantization in terms of spinorial (undotted/dotted) pointlike fields, whereas massless finite helicity representations lead to large gap in this…
The helicity operator of massless particles has only two polarisations like it takes place for photons and gravitons. For them not all of the 2s+1 spin magnetic quantum states exist, with two exceptions, and the spin operator ceases to be…
Solutions of the sourceless Einstein's equation with weak and strong cosmological constants are discussed by using In\"on\"u-Wigner contractions of the de Sitter groups and spaces. The more usual case corresponds to a weak…
Relations between states and maps, which are known for quantum systems in finite-dimensional Hilbert spaces, are formulated rigorously in geometrical terms with no use of coordinate (matrix) interpretation. In a tensor product realization…
Upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into Stringy Gravity, i.e. the stringy augmentation of General Relativity. Equipped with an $\mathrm{O}(D,D)$ covariant…
In two-dimensional noncommutive space for the case of both position - position and momentum - momentum noncommuting, a constraint between noncommutative parameters is investigated. The related topic of guaranteeing Bose - Einstein…
It is shown that the algebraic structure of finite Heisenberg groups associated with the tensor product of two Hilbert spaces leads to a simple demonstration valid in all Hilbert space dimensions of the impossibility of non-contextual…
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…