• Corpus ID: 238583148

Non-perturbative Quantum Propagators in Bounded Spaces

  title={Non-perturbative Quantum Propagators in Bounded Spaces},
  author={J. P. Edwards and V'ictor A. Gonz'alez-Dom'inguez and Idrish Huet and Maria Anabel Trejo},
We outline a new approach to calculating the quantum mechanical propagator in the presence of geometrically non-trivial Dirichlet boundary conditions based upon a generalisation of an integral transform of the propagator studied in previous work (the so-called “hit function”), and a convergent sequence of Padé approximants. In this paper the generalised hit function is defined as a many-point propagator and we describe its relation to the sum over trajectories in the Feynman path integral. We… 

Figures from this paper


Applications of the worldline Monte Carlo formalism in quantum mechanics
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte
Propagator from nonperturbative worldline dynamics
We use the worldline representation for correlation functions together with numerical path integral methods to extract nonperturbative information about the propagator to all orders in the coupling
February 1994 δ ′-Function Perturbations and Neumann Boundary-Conditions by Path Integration
δ-function perturbations and Neumann boundary conditions are incorporated into the path integral formalism. The starting point is the consideration of the path integral representation for the one
Worldline approach to quantum field theories on flat manifolds with boundaries
We study a worldline approach to quantum field theories on flat manifolds with boundaries. We consider the concrete case of a scalar field propagating on + × D−1 which leads us to study the
Perturbative quantum field theory in the string-inspired formalism
Abstract We review the status and present range of applications of the “string-inspired” approach to perturbative quantum field theory. This formalism offers the possibility of computing effective
δ-function perturbations and boundary problems by path integration
A wide class of boundary problems in quantum mechanics is discussed by using path integrals. This includes motion in half-spaces, radial boxes, rings, and moving boundaries. As a preparation the
Worldline formalism for a confined scalar field
Abstract The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first
Scalar heat kernel with boundary in the worldline formalism
The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this
Casimir effect on the worldline
We develop a method to compute the Casimir effect for arbitrary geometries. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with
Path integral of the relativistic point particle in Minkowski space
In this article, we analyze the fundamental global and local symmetries involved in the action for the free relativistic point particle in Minkowski space. Moreover, we identify a hidden local