Related papers: Alternative derivation of the relativistic three-p…
We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…
We present a necessary and sufficient condition for three qutrit density matrices to be the one-particle reduced density matrices of a pure three-qutrit quantum state. The condition consists of seven classes of inequalities satisfied by the…
The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived, using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related…
In this paper we address the problem of the quantization of the perfect relativistic fluids formulated in terms of the K\"{a}hler parametrization. This fluid model describes a large set of interesting systems such as the power law energy…
The issue of non-perturbative background independent quantization of matrix models is addressed. The analysis is carried out by considering a simple matrix model which is a matrix extension of ordinary mechanics reduced to 0 dimension. It…
This is the third article in our series of articles exploring connections between dynamical systems of St\"ackel-type and of Painlev\'e-type. In this article we present a method of deforming of minimally quantized quasi-St\"ackel…
Recently proposed quantization in field theory based on an analogue of Hamiltonian formulation which treats space and time on equal footing (the so-called De Donder-Weyl theory) is applied to General Relativity in metric variables. We…
We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the…
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and…
The global symmetry data of a $D$-dimensional absolute quantum field theory can sometimes be packaged in terms of a $(D+1)$-dimensional bulk system obtained by extending along an interval, with a relative QFT$_D$ at one end and suitable…
It is possible that relativistic symmetries become deformed in the semiclassical regime of quantum gravity. Mathematically, such deformations lead to the noncommutativity of spacetime geometry and non-vanishing curvature of momentum space.…
The U(1)$^3$ model for 3+1 Euclidian signature general relativity is an interacting, generally covariant field theory with two physical polarisations that shares many features of Lorentzian general relativity. In particular, it displays a…
We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the…
Qubit regularization provides a rich framework to explore quantum field theories. The freedom to choose how the important symmetries of the theory are embedded in the qubit regularization scheme allows us to construct new lattice models…
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
An approximate quantum-mechanical two-body equation for spinless particles incorporating relativistic kinematics is derived. The derivation is based on the relativistic energy-momentum relation $mc^{2}+\epsilon =…
A higher-order dispersive equation is introduced as a candidate for the governing equation of a field theory. A new class of solutions of the three-dimensional field equation are considered, which are not localized functions in the sense of…
In this paper we discuss a new approach to the quasinormal-mode problem in general relativity. By combining a characteristic formulation of the perturbation equations with the integration of a suitable phase-function for a complex valued…
S matrix principles and symmetries impose constraints on three-particle scattering amplitudes, which can be formulated as a class of integral equations for their partial wave projections. However, these amplitudes are typically expressed in…
Usual approaches to quantisation of a 3-Toda lead to numerical calculations requiring many steps that can be time consuming to insure their reliability. In order to reduce as much as possible the numerical part of the EKB quantisation…