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Generators of the Poincare group, for a free massive scalar field, are usually expressed in the momentum space. In this work we perform a transformation of these generators into the coordinate space. This (spatial)-position space is spanned by eigenvectors of the Newton-Wigner-Pryce operator. The motivation is a deeper understanding of the commutative spatial coordinate space in QFT, in order to investigate the non-commutative version thereof.
Using the formalism of quantizers and dequantizers, we show that the characters of irreducible unitary representations of finite and compact groups provide kernels for star products of complex-valued functions of the group elements. Examples of permu
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can
The non-associativity of translations in a quantum system with magnetic field background has received renewed interest in association with topologically trivial gerbes over $mathbb{R}^n.$ The non-associativity is described by a 3-cocycle of the group
Localization is a characteristic phenomenon of space-inhomogeneous quantum walks in one dimension, where particles remain localized at their initial position. Eigenvectors of time evolution operators are deeply related to the amount of trapping. In t
The quantum theory of indirect measurements in physical systems is studied. The example of an indirect measurement of an observable represented by a self-adjoint operator $mathcal{N}$ with finite spectrum is analysed in detail. The Hamiltonian genera