Related papers: Conformal Quantum Mechanics and Sine-Square Deform…
We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated…
Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a…
We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of…
The role of curvature in relation with Lie algebra contractions of the pseudo-ortogonal algebras so(p,q) is fully described by considering some associated symmetrical homogeneous spaces of constant curvature within a Cayley-Klein framework.…
Deformation quantization and geometric quantization on K\"ahler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum…
We study the map between two descriptions of the $T\bar{T}$ deformation of conformal field theory (CFT): One is the defining description as a deformation of CFT by the $T\bar{T}$-operator. The other is an alternative description as the…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
We define a strict deformation quantization which is compatible with any Hamiltonian with local spin interaction (e.g. the Heisenberg Hamiltonian) for a spin chain. This is a generalization of previous results known for mean-field theories.…
In this paper it is studied the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of…
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show…
Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate…
We study conformal quantum mechanics by first considering the perturbative $S$-matrix in various dimensions. The model has two couplings and we study perturbatively the degree of ultraviolet divergences arising in the interplay between the…
A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $\Lambda$ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The…
We consider the problem of bosonizing supersymmetric quantum mechanics (SSQM) and some of its variants, i.e., of realizing them in terms of only boson-like operators without fermion-like ones. In the SSQM case, this is realized in terms of…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we…
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…