Related papers: Normalized non-redundant vector tomographic portra…
We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual…
We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of…
Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used.…
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum…
We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all…
When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is expressed in terms of the well known Fano statistical tensor parameters. Employing the multiaxial representation [1], wherein a spin-j density matrix is shown to be…
In this paper, we develop a formalism describing in a relativistic way a system which consists of a classical and a quantum part being coupled. The formalism models one particle with spin 1/2 and it is a possible relativistic extension of…
To every binary linear [n,k]-code C we associate a quantum state ("codeket") belonging to the n-th tensor power of the 2-dimensional complex Hilbert space associated to the spin 1/2 particle. We completely characterize the expectation…
Determining the spin of any new particle and measuring its couplings to other particles and/or itself are crucial in reconstructing the structure of any quantum field theory containing the particle. A general helicity formalism is employed…
Usually the only difference between relativistic quantization and standard one is that the Lagrangian of the system under consideration should be Lorentz invariant. The standard approaches are logically incomplete and produce solutions with…
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…
The interpretation of quantum mechanics due to Lande' is applied to the connection between wave mechanics and matrix mechanics. The connection between the differential eigenvalue equation and the matrix eigenvalue equation for an operator…
We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…
We develop a technique to directly study spinons (emergent spin S = 1/2 particles) in quantum spin models in any number of dimensions. The size of a spinon wave packet and of a bound pair (a triplon) are defined in terms of wave-function…
We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description…
The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many…
In this paper the method of the relativistically-invariant effective tensor representation of Lagrangian decomposition and the amplitudes of the two-photon interaction with hadrons on photon energy is proposed. In the frames…
In the context of quantum tomography, we recently introduced a quantity called a partial determinant \cite{jackson2015detecting}. PDs (partial determinants) are explicit functions of the collected data which are sensitive to the presence of…