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In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory…
We consider the quantum dynamics of a free nonrelativistic particle moving in a cavity and we analyze the effect of a rapid switching between two different boundary conditions. We show that this procedure induces, in the limit of infinitely…
The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum…
On the path towards quantum gravity, we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). This paper aims…
The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new…
We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called $ST$-form can be further reduced up to a form more effective in certain applications: In particular, in identifying the number of…
The boundary-value problem on semi-axis for one class operator-differential equations of the fourth order, the main part of which has the multiple characteristic is investigated in this paper in Sobolev type weighted space. Correctness and…
The electromagnetic interaction is characterised by discrete states for bound systems in contrast to continuous states for unbound systems. The difference merely arises because the characteristic equations do not exhibit the same behaviour…
The boundary values of the time-component of the gauge potential form externally specifiable data characterizing a gauge theory. We point out some consequences such as reduced symmetries, bulk currents for manifolds with disjoint boundaries…
In this paper we argue that boundary condition may run with energy scale. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin.…
For a very general class of unbounded self-adjoint operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
The Poincar\'e-covariant quantum-field-theoretic description of bound states by the homogeneous Bethe-Salpeter equation usually exhibits an intrinsic complexity that can be attenuated by allowing this formalism to undergo various…
In the framework of spatially extended dynamical systems, we present three examples in which the presence of walls lead to dynamic behavior qualitatively different from the one obtained in an infinite domain or under periodic boundary…
We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms…
Quantum physics on manifolds with boundary brings novel aspects due to boundary conditions. One important feature is the appearance of localised negative eigenmodes for the Laplacian on the boundary. These can potentially lead to…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
A framework associating quantum cosmological boundary conditions to minisuperspace hidden symmetries has been introduced in \cite{7}. The scope of the application was, notwithstanding the novelty, restrictive because it lacked a discussion…
We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and…