Related papers: Boundary conditions as constraints
In the context of quantum field theory, an anomaly exists when a theory has a classical symmetry which is not a symmetry of the quantum theory. This short exposition aims at introducing a new point of view, which is that the proper setting…
We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…
Open quantum systems are traditionally described by decomposing the total Hilbert space into a system and an external environment, linked by an explicit interaction Hamiltonian. We propose an alternative framework in which the environment…
Non-holonomic constraints, both in the Lagragian and Hamiltonian formalism, are discussed from the geometrical viewpoint of implicit differential equations. A precise statement of both problems is presented remarking the similarities and…
We show that after mapping each element of a set of second class constraints to the surface of the other ones, half of them form a subset of abelian first class constraints. The explicit form of the map is obtained considering the most…
Dynamical systems, described by Lagrangians with first- and second-class constraints, are investigated. In the Dirac approach to the generalized Hamiltonian formalism, the classification and separation of the first- and second-class…
We consider a general second-order elliptic differential operator on a domain with a cylindrical end. We impose Dirichlet boundary conditions on the boundary with the exception of a small set, where we impose Neumann boundary conditions.…
We study some geometric and potential theoretic properties of nodal domains of solutions to certain uniformly elliptic equations. In particular, we establish corkscrew conditions, Carleson type estimates and boundary Harnack inequalities on…
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics…
A persistent challenge in numerical relativity is the correct specification of boundary conditions. In this work we consider a many parameter family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein…
We compute the boundary entropies for the allowed boundary conditions of the SU(2)-invariant principal chiral model at level k=1. We used the reflection factors determined in a previous work. As a by-product we obtain some miscellaneous…
Relativistic quantum field theory offers, in form of the homogeneous Bethe-Salpeter framework, a (Poincar\'e-covariant) description of bound states in terms of their underlying theory's fundamental degrees of freedom. In view of the…
In this paper we present a model which can produce boundary confining condition on Dirac field interacting with Abelian or non Abelian gauge fields. The constraint is generated by a scalar field. This kind of model can be the foundation for…
Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…
Even a first approximation of bound states requires contributions of all powers in the coupling. This means that the concept of "lowest order bound state" needs to be defined. In these lectures I discuss the "Born" (no loop, lowest order in…
We analyse the boundary structure of General Relativity in the coframe formalism in the case of a lightlike boundary, i.e., when the restriction of the induced Lorentzian metric to the boundary is degenerate. We describe the associated…
We get deeper understanding of the role played by boundary conditions in quantum field theory, by studying the structure of a scalar massless quantum field theory bounded by two one dimensional planar crystal plates. The system can also be…
We consider how the problem of determining normal forms for a specific class of nonholonomic systems leads to various interesting and concrete bridges between two apparently unrelated themes. Various ideas that traditionally pertain to the…
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…