Related papers: Lie Groups and Propagators Exemplified
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
Renormalized versions of cosmological perturbation theory have been very successful in recent years in describing the evolution of structure formation in the weakly non-linear regime. The concept of multi-point propagators has been…
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…
Recently it was introduced a negation of a probability distribution. The need for such negation arises when a knowledge-based system can use the terms like NOT HIGH, where HIGH is represented by a probability distribution (pd). For example,…
There is no known exact expression for the propagator of a non-relativistic particle colliding with a hard sphere. De Prunel\'e (2008 {\it J.~Phys.~A:~Math.~Theor.} {\bf 41} 255305) derived a partial wave expansion of the propagator and…
Necessary and sufficient conditions for the exponentiation of finite-dimensional real Lie algebras of linear operators on complete Hausdorff locally convex spaces are obtained, focused on the equicontinuous case - in particular, necessary…
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
Group-theoretical analysis of arbitrary polarization devices is performed, based on the theory of the Lorentz group. In effective "non-relativistic" Mueller case, described by 3-dimensional orthogonal matrices, results of the one…
It is possible to define a general initial state for a quantum field by introducing a contribution to the action defined at an initial-time boundary. The propagator for this theory is composed of two parts, one associated with the free…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
Hadronic resonance propagators which take into account the analytical properties of decay processes are built in terms of the dispersion relation technique. Such propagators can describe multi-component systems, for example, those when…
We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie…
We present three methods for calculating the Feynman propagator for the non-relativistic harmonic oscillator. The first method was employed by Schwinger a half a century ago, but has rarely been used in non-relativistic problems since. Also…
Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization for simple single-particle systems, in this…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
Using noncommutative deformed canonical commutation relations, a model describing a noncommutative complex scalar field theory is considered. Using the path integral formalism, the noncommutative free and exact propagators are calculated to…
For one dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, the semi-classical approximation to be exact. For velocity…
In this article, we introduce the concepts of excision and idealization for a multiplicative Lie algebra (also for a Lie algebra), which provides two new multiplicative Lie algebras (or Lie algebras) from a given multiplicative Lie algebra…
Analytical functions for the propagators of QCD, including a set of chiral quarks, are derived by a one-loop massive expansion in the Landau gauge, and are studied in Minkowski space, yielding a direct proof of positivity violation and…
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion…