Related papers: Lie Groups and Propagators Exemplified
The propagator of the discrete Schr\"odinger equation is computed and its properties are revealed through a Feynman path summation in discrete space. Initial data problems such as diffraction in discrete space and continuous time are…
Most discussions of propagators in Lee-Wick theories focus on the presence of two massive complex conjugate poles in the propagator. We show that there is in fact only one pole near the physical region, or in another representation three…
Characterising the propagation of particles in an external non-Abelian field only in terms of invariants constructed from its field tensor is not always sufficient, especially, in many analytically tractable and phenomenologically…
It is well known that n x n upper-triangular real matrices with 1's on the diagonal form a nilpotent Lie group with an interesting family of non-isotropic dilations and corresponding geometry, as in [9]. Here we look at p-adic versions of…
The radiation arising under uniform motion of non-relativistic charged particle by (or through) perfectly conducting sphere is considered. The rigorous results are obtained using the method of images known from electrostatics.
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…
A systematic loop expansion is formulated in terms of full propagators and vertices. It is based on an expansion of the general solution of an exact non-perturbative flow equation.
We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…
We characterize, up to Lie isomorphism, the real Lie groups that are definable in an o-minimal expansion of the real field.
Proof systems for the Relativized Propositional Calculus are defined and compared.
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…
A quantum mechanical description of particle propagation on the discrete spacetime of a causal set is presented. The model involves a discrete path integral in which trajectories within the causal set are summed over to obtain a particle…
We produce a connected real Lie group that, as a first order structure in the group language, interprets the real field expanded with a predicate for the integers. Moreover, the domain of our interpretation is definable in the group.
We present a derivation of the propagator for a particle in the presence of the step and delta function potentials. These propagators are known, but we present a direct path integral derivation, based on the path decomposition expansion and…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
An improved formulation of the one-step model of photoemission from crystal surfaces is proposed which overcomes different limitations of the original theory. Considering the results of an electronic-structure calculation, the electronic…
We develop a field theory approach to light propagation in a gas of resonant atoms taking into account vector character of light and atom-atom interactions. Within this approach, we calculate the propagator of the electric field for both…
We show that the general method of Lie algebra expansions can be applied to re-construct several algebras and related actions for non-relativistic gravity that have occurred in the recent literature. We explain the method and illustrate its…
Let $L$ be a free Lie algebra over a field $k$, $I$ a non-trivial proper ideal of $L$, $n>1$ an integer. The multiplicator $H_2(L/I^n,k)$ of $L/I^n$ is not finitely generated, and so in particular, $L/I^n$ is not finitely presented, even…