Related papers: Lie Groups and Propagators Exemplified
The free propagator for the scalar $\lambda \phi^4$--theory is calculated exactly up to the second derivative of a background field. Using this propagator I compute the one--loop effective action, which then contains all powers of the field…
I calculate characters of certain representations of loop groups based on non simply connected Lie groups. This gives a generalization of the Kac-Weyl character formula.
Simulations are made of a probe particle diffusing through a complex fluid. Probe particle motions are described by the Mori-Zwanzig equation and Mori's orthogonal hierarchy of random forces scheme, subject to the approximation that the…
In this article we study a transport-diffusion equation in the framework of the stratified Lie groups. For this equation we will study the existence of the solutions, a maximum principle, a positivity principle and H\"older regularity.
Let $\R$ be an alternative ring containing a nontrivial idempotent and $\D$ be a multiplicative Lie-type derivation from $\R$ into itself. Under certain assumptions on $\R$, we prove that $\D$ is almost additive. Let $p_n(x_1, x_2, \cdots,…
The J-matrix method of scattering is used to obtain analytic expressions for the phase shift of two classes of relativistic exponential-type separable potentials whose radial component is either of the general form r^(n-1)exp(-r) or…
We introduce a few of the key ideas of statistical analysis using two real-world examples to illustrate how these ideas are used in practice.
In this work, we perform a comparison of the employ of distinct gluon propagators with the experimental data in diffractive processes, $pp$ elastic scattering and light meson photo-production. The gluon propagators are calculated through…
We present a direct path integral derivation of the propagator in the presence of a step potential. The derivation makes use of the Path Decomposition Expansion (PDX), and also of the definition of the propagator as a limit of lattice…
We investigate the computational efficiency of two stochastic based alternatives to the Sequential Propagator Method used in Lattice QCD calculations of heavy-light semileptonic form factors. In the first method, we replace the sequential…
The propagators of unstable particles are considered in the framework of the convolution representation. Spectral function was found for a special case when the propagator of scalar unstable particle has Breight-Wigner form. The expressions…
We apply an extension of a new method of group classification to a family of nonlinear wave equations labelled by two arbitrary functions, each depending on its own argument. The results obtained confirm the efficiency of the proposed…
We classify and construct all irreducible positive energy representations of the loop group of a compact, connected and simple Lie group and show that they admit an intertwining action of Diff(S^{1}).
We present a formula for the degree of the discriminant of irreducible representations of a Lie group, in terms of the roots of the group and the highest weight of the representation. The proof uses equivariant cohomology techniques,…
Working on the approximation of low frequency, we present the light cone conditions for a class of theories constructed with the two gauge invariants of the Maxwell field without making use of average over polarization states. Different…
Gauge fields are special in the sense that they are invariant under gauge transformations and \emph{``ipso facto''} they lead to problems when we try quantizing them straightforwardly. To circumvent this problem we need to specify a gauge…
A fully algebraic approach to reconstructing one-dimensional reflectionless potentials is described. A simple and easily applicable general formula is derived, using the methods of the theory of determinants. In particular, useful…
We apply the Thermal Field Theory methods to study the propagation of photons in a plasma layer, that is a plasma in which the electrons are confined to a two-dimensional plane sheet. We calculate the photon self-energy and determine the…
Axions can be described by a relativistic field theory with a real scalar field $\phi$ whose self-interaction potential is a periodic function of $\phi$. Low-energy axions, such as those produced in the early universe by the vacuum…
We calculate extensions between certain irreducible admissible representations of p-adic groups.