Related papers: Formal GNS Construction and States in Deformation …
We present a general construction of KMS states in the framework of perturbative algebraic quantum field theory (pAQFT). Our approach may be understood as an extension of the Schwinger-Keldysh formalism. We obtain in particular the Wightman…
Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…
Exploring the concept of the extended Galilei group G. Representations for field theories in a symplectic manifold have been derived in association with the method of the Wigner function. The representation is written in the light-cone of a…
We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…
W consider the problem of testing if a given matrix in the Hilbert space formulation of quantum mechanics or a function in the phase space formulation of quantum theory represent a quantum state. We propose several practical criteria to…
We present a complete solution to the problem of Formal Higher Spin Gravities --- formally consistent field equations that gauge a given higher spin algebra and describe free higher spin fields upon linearization. The problem is shown to be…
Let ${\cal S}(\mathcal{H})$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $\mathcal{H}$, which is the set of all physical quantities on a quantum system $\mathcal{H}$. We introduce a binary…
Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the…
Elaborating on our joint work with Abramsky in quant-ph/0402130 we further unravel the linear structure of Hilbert spaces into several constituents. Some prove to be very crucial for particular features of quantum theory while others…
A method to construct free field realizations for the form factors of diagonal factorized scattering theories is described. Form factors are constructed from linear functionals over an associative `form factor algebra', which in particular…
Hilbert spaces of states can be constructed in standard quantum field theory only for infinitely extended spacelike hypersurfaces, precluding a more local notion of state. In fact, the Reeh-Schlieder Theorem prohibits the localization of…
The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in: K. Kowalski and J. Rembielinski, J. Phys. A: Math. Gen. 33, 6035 (2000). The connection is discussed between the…
Holonomy algebras arise naturally in the classical description of Yang-Mills fields and gravity, and it has been suggested, at a heuristic level, that they may also play an important role in a non-perturbative treatment of the quantum…
It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the…
These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…
Superanalysis can be deformed with a fermionic star product into a Clifford calculus that is equivalent to geometric algebra. With this multivector formalism it is then possible to formulate Riemannian geometry and an inhomogeneous…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give…
Solution of the momentum space Schr\"odinger equation in the case of deformed fields is being addressed. In particular it is shown that a complete set of single particle states which includes bound, resonant and complex continuum states may…
A non-standard quantum deformation of the two-photon algebra $h_6$ is constructed, and its quantum universal R-matrix is given. Representations of this new quantum algebra are studied on the Fock space and translated into Fock-Bargmann…