Related papers: Boundary conditions as constraints
In the Dirac approach to the generalized Hamiltonian formalism, dynamical systems with first- and second-class constraints are investigated. The classification and separation of constraints into the first- and second-class ones are…
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.…
The Hamiltonian description of mechanical or field models defined by singular Lagrangians plays a central role in physics. A number of methods are known for this purpose, the most popular of them being the one developed by Dirac. Here, we…
We study the isospectrality problem for a relativistic free quantum particle, described by the Dirac Hamiltonian, confined in a one-dimensional ring with a junction. We analyze all the self-adjoint extensions of the Hamiltonian in terms of…
The necessary and sufficient conditions are established for the second-class constraint surface to be (an almost) K\"ahler manifold. The deformation quantisation for such systems is scetched resulting in the Wick-type symbols for the…
A systematic way of generating sets of local boundary conditions on the gauge fields in a path integral is presented. These boundary conditions are suitable for one--loop effective action calculations on manifolds with boundary and for…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
These are pedagogical notes on the Hamiltonian formulation of constrained dynamical systems. All the examples are finite dimensional, field theories are not covered, and the notes could be used by students for a preliminary study before the…
We investigate the role of external constraints in quantum field theory using the path integral formalism. We begin by reviewing the quantization of constrained systems and extend the analysis to cases where constraints are added to the…
In this paper, we present a review of the canonical structure of field theories defined on manifolds with time-like boundaries. The notion of differentiable generator is shown to be a requirement coming from the consistency of the…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we…
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian…
For two dimensional Schroedinger Hamiltonians we formulate boundary conditions that split the Hilbert space according to the chirality of the eigenstates on the boundary. With magnetic fields, and in particular, for Quantum Hall Systems,…
We compute the boundary terms and junction conditions for Horndeski's panoptic class of scalar-tensor theories, and write the bulk and boundary equations of motion in explicitly second order form. We consider a number of special subclasses,…
This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential…
A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary…
There is a review of the physical theories needing Dirac-Bergmann theory of constraints at the Hamiltonian level due to the existence of gauge symmetries. It contains: i) the treatment of systems of point particles in special relativity…
A multisymplectic setting for classical field theories subjected to non-holonomic constraints is presented. The infinite dimensional setting in the space of Cauchy data is also given.
The purpose of this talk is to sketch some recent progress which has been made in calculating non-perturbatively the reflection factors for the sinh-Gordon model restricted to a half-line by integrable boundary conditions. The essential…
We present the Lagrangian whose corresponding action is the trace K action for General Relativity. Although this Lagrangian is second order in the derivatives, it has no second order time derivatives and its behaviour at space infinity in…