Related papers: WKB approximation in deformed space with minimal l…
Deformation quantization is applied to quantize gravitational systems coupled with matter. This quantization procedure is performed explicitly for quantum cosmology of these systems in a flat minisuper(phase)space. The procedure is employed…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the…
In this paper we study the quantisation of scalar field theory in $\kappa$-deformed space-time. Using a quantisation scheme that use only field equations, we derive the quantisation rules for deformed scalar theory, starting from the…
We solve a general equation describing the lowest order corrections arising from quantum gravitational effects to the spectrum of cosmological fluctuations. The spectra of scalar and tensor perturbations are calculated to first order in the…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
In this work, we present a new formulation of the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a Schrodinger operator within the algebraic and microlocal framework of B. Helffer and J. Sjostrand; BS holds precisely when…
Minimal and maximal uncertainties of position measurements are widely considered possible hallmarks of low-energy quantum as well as classical gravity. While General Relativity describes interactions in terms of spatial curvature, its…
The mergings of energy levels associated with the breaking of PT symmetry in the model of Bender and Boettcher, and in its generalisation to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques…
The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is applied to cosmological models in the minisuperspace. The quantization procedure is performed explicitly for quantum cosmology in a flat minisuperspace. The de Sitter…
Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson,…
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…
In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is…
Considering quantum cosmological minisuperspace models with positive potential, we present evidence that (i) despite common belief there are perspectives for defining a unique, naturally preferred decomposition of the space H of wave…
The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic…
In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an…
A $q$-deformed Weyl-Heisenberg algebra is used to define a deformed displacement operator giving rise to a naturally normalized nonlinear coherent states type. Robust maximally entangled deformed coherent states are studied and the effect…
We revisit the well known Bohr-Sommerfeld quantization rule (BS) for a 1-D Pseudo-differential self-adjoint Hamiltonian within the algebraic and microlocal framework of Helffer and Sj\"ostrand; BS holds precisely when the Gram matrix…
We use the method of homological quantum reduction to construct a deformation quantization on singular symplectic quotients in the situation, where the coefficients of the moment map define a complete intersection. Several examples are…
Within the framework of warped convolutions we deform the massless free scalar field. The deformation is performed by using the generators of the special conformal transformations. The investigation shows that the deformed field turns out…