Boundary conditions: The path integral approach

Path-integral for Quadratic Hamiltonian Systems and Boundary Conditions

A path-integral representation for the kernel of the evolution operator of general Hamiltonian systems is reviewed. We study the models with bosonic and fermionic degrees of freedom. A general scheme for introducing boundary conditions in the path-integral is given. We calculate the path-integral for the systems with quadratic first class constraints and present an explicit formula for the heat...

Boundary conditions in an integral approach to scattering.

Scattering of electromagnetic radiation by an object of arbitrary shape or a structured surface, infinite in extent, is considered. When radiation is incident on an interface separating vacuum from a material medium, a current density is induced in the bulk and a surface current density may appear on the boundary surface. The electromagnetic field is then the sum of the incident field and the f...

Path integrals and boundary conditions

The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange formalism preserves relativistic covariance which makes the Feynman method very convenient to achieve the renormalization of field theories both in perturbative...

Quantum Phenomenology with the Path Integral Approach

A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the cases of a harmonic oscillator, a bistable potential and two coupled systems, briefly illustrating their applications. PACS: 03.65.Bz, 06.30.-k, 74.50.+r

Second-Order Boundary Value Problem with Integral Boundary Conditions