Related papers: Mini review of Poincar\'e invariant quantum theory
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…
Given a Hamiltonian system on a fiber bundle, there is a Poisson covariant formulation of the Hamilton equations. When a Lie group G acts freely, properly, preserving the fibers of the bundle and the Hamiltonian density is G-invariant, we…
The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…
The role of Poincar\'e covariant space-time translations is investigated in the case of the pseudoscalar-meson charge form factors. It is shown that this role extends beyond the standard energy-momentum conservation, which is accounted for…
Loop quantum gravity (LQG) is a quantization program for gravity based on the principles of QFT and general covariance of general relativity. Quantum states of LQG describe gravitational excitations based on graphs embedded in a spatial…
We construct Kaluza--Klein-type models with a de Sitter or Minkowski bundle in the de Sitter or Poincar\'e gauge theory of gravity, respectively. A manifestly gauge-invariant formalism has been given. The gravitational dynamics is…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
A class of interacting classical random fields is constructed using deformed *-algebras of creation and annihilation operators. The fields constructed are classical random field versions of "Lie fields". A vacuum vector is used to construct…
We present a discrete model theory similar in structure to ordinary quantum mechanics, but based on a finite field instead of complex amplitudes. The interpretation of this theory involves only the "modal" concepts of possibility and…
We consider a scalar Yukawa-like model in the framework of partially reduced quantum field theory. The reduced Lagrangian of the model consists of free scalar field terms and nonlocal current interaction term. Hamiltonian expressions for…
We present a bicovariant differential calculus on the quantum Poincare group in two dimensions. Gravity theories on quantum groups are discussed.
We provide a space-time covariant Hamiltonian treatment for a finite-range gravitational theory. The Kuchar approach is used to demonstrate the bimetric picture of space-time in its most transparent form. This Hamiltonian formalism is…
In this article we study abstract and embedded invariants of reduced curve germs via topological techniques. One of the most important numerical analytic invariants of an abstract curve is its delta invariant. Our primary goal is to develop…
We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian…
The Poincar\'e-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such systems. We prove a version of the Poincar\'e-Bendixson…
We define a new algebraic extension of the Poincar\'e symmetry; this algebra is used to implement a field theoretical model. Free Lagrangians are explicitly constructed; several discussions regarding degrees of freedom, compatibility with…
This paper constructs relativistic quantum mechanical models of particles satisfying cluster properties and the spectral condition which do not conserve particle number. The treatment of particle production is limited to systems with a…
We investigate higher-order geometric $k$-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our…
We discuss the scattering equivalence of the generalized Bakamjian-Thomas construction of dynamical representations of the Poincar\'e group in all of Dirac's forms of dynamics. The equivalence was established by Sokolov in the context of…
In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear…