Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRemarks on QFT in the Coordinate Space
70
0
0.0
(
0
)
Authors
Albert Much
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 permutation groups of two and three elements, as well as the SU(2) group, are considered. The k-deformed star products of functions on finite and compact groups are presented. The explicit form of the quantizers and dequantizers, and the duality symmetry of the considered star products are discussed.
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 be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrodinger equation modified with the Gaussian and the mean curvature.
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 $mathbb{R}^n$ with values in the unit circle $S^1.$ The gerbes over a space $M$ are topologically classified by the Dixmier-Douady class which is an element of $mathrm{H}^3(M,mathbb{Z}).$ However, there is a finer description in terms of local differential forms of degrees $d=0,1,2,3$ and the case of the magnetic translations for $n=3$ the 2-form part is the magnetic field $B$ with non zero divergence. In this paper we study a quantum field theoretic construction in terms of $n$-component fermions on a real line or a unit circle. The non associativity arises when trying to lift the translation group action on the 1-particle system to the second quantized system.
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 this paper, we introduce the analytical method for the eigenvalue problem using a transfer matrix to quantitatively evaluate localization by deriving the time-averaged limit distribution and reveal the condition of strong trapping.
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 generating the time evolution of the system in the absence of direct measurements is assumed to be given by the sum of a term commuting with $mathcal{N}$ and a small perturbation not commuting with $mathcal{N}$. The system is subject to repeated direct (projective) measurements using a single instrument whose action on the state of the system commutes with $mathcal{N}$. If the Hamiltonian commutes with the observable $mathcal{N}$ (i.e., if the perturbation vanishes) the state of the system approaches an eigenstate of $mathcal{N}$, as the number of direct measurements tends to $infty$. If the perturbation term in the Hamiltonian does textit{not} commute with $mathcal{N}$ the system exhibits jumps between different eigenstates of $mathcal{N}$. We determine the rate of these jumps to leading order in the strength of the perturbation and show that if time is re-scaled appropriately a maximum likelihood estimate of $mathcal{N}$ approaches a Markovian jump process on the spectrum of $mathcal{N}$, as the strength of the perturbation tends to $0$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
