Related papers: Lie Groups and Propagators Exemplified
We study the nonlinear propagator, a key ingredient in renormalized perturbation theory (RPT) that allows a well-controlled extension of perturbation theory into the nonlinear regime. We show that it can be thought as measuring the memory…
We have obtained the exact expression of the diffusion propagator in the time-dependent anharmonic potential $V(x,t)={1/2}a(t)x^2+b\ln x$. The underlying Euclidean metric of the problem allows us to obtain analytical solutions for a whole…
We study the propagator of a colored scalar particle in the background of a non-abelian gauge field using the worldline formalism. It is obtained by considering the open worldline of a scalar particle with extra degrees of freedom needed to…
This paper proposes a Poisson formula for the wave propagator of the Schwarzschild--de Sitter (SdS) metric. That is done by proving a Poisson formula relating wave propagators and scattering resonances for a class of non-compactly supported…
We develop a simple method to obtain approximate analytical expressions for the period of a particle moving in a given potential. The method is inspired to the Linear Delta Expansion (LDE) and it is applied to a large class of potentials.…
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The…
We explain that general differential calculus and Lie theory have a common foundation: Lie Calculus is differential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher…
We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…
This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class $2$. We also present a method for determining a multiplicative Lie algebra structure on a group that serves as an extension of one Lie…
I make three conceptual points regarding multigrid methods for computing propagators in lattice gauge theory: 1) The class of operators handled by the algorithm must be stable under coarsening. 2) Problems related by symmetry should have…
A projection operator technique for solution of relativistic wave equation on non-compact group has been proposed. This technique was applied to the construction of wave equations for charged vector boson in a potential field. The equations…
Employing a kinetic framework, we calculate all transport coefficients for relativistic dissipative (second-order) hydrodynamics for arbitrary particle masses in the 14-moment approximation. Taking the non-relativistic limit, it is shown…
An extensive number of numerical computations of energy 1/$N$ series using a recursive Taylor series method are presented in this paper. The series are computed to a high order of approximation and their behaviour on increasing the order of…
For a rational prime $p\neq 2$, we compute the sequence of ramification groups of a Galois, radical and finite extension $L/F$ where $F/\mathbb{Q}_p$ is an unramified finite extension. First, we compute it in the case where the exponent of…
Gauging of space translations for nonrelativistic point particles in one dimension leads to general coordinate transformations with fixed Newtonian time. The minimal gauge invariant extension of the particle velocity requires the…
In the e-print is discussed a few steps to introducing of "vocabulary" of relativistic physics in quantum theory of information and computation (QTI&C). The behavior of a few simple quantum systems those are used as models in QTI&C is…
It is of interest in a variety of contexts, and in particular in the arrival time problem, to consider the quantum state obtained through unitary evolution of an initial state regularly interspersed with periodic projections onto the…
The scalar and vector potentials of the acceleration field and the pressure field are calculated for the first time for a rotating relativistic uniform system, and the dependence of the potentials on the angular velocity is found. These…
The velocity basis of the Poincare group is used in the direct product space of two irreducible unitary representations of the Poincare group. The velocity basis with total angular momentum j will be used for the definition of relativistic…
We construct Lie algebras arising from commutators of the harmonic Hamiltonian and the perturbed anharmonic Hamiltonian. From there we form a very specific element of the associated Lie group and transform the unperturbed Hamiltonian into…