No-Boundary Proposal as a Path Integral with Robin Boundary Conditions

Straight Quantum Waveguide with Robin Boundary Conditions⋆

Abstract. We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we localize the essential spectrum and derive a sufficient condition which guarantees the existence of bound states. Further properties of the associated...

Higher order multi-point fractional boundary value problems with integral boundary conditions

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Cosmological Perturbations from the No Boundary Euclidean Path Integral

We compute, from first principles, the quantum fluctuations about instanton saddle points of the Euclidean path integral for Einstein gravity coupled to a scalar field. The Euclidean two-point correlator is analytically continued into the Lorentzian region where it describes the quantum mechanical vacuum fluctuations in the state described by no boundary proposal initial conditions. We concentr...

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...

Second-Order Boundary Value Problem with Integral Boundary Conditions