Related papers: Boundary Poisson structure and quantization
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among…
Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The main result of the paper is a construction of a highly…
We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures…
Boundary operators and boundary ground states in sine-Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators.We also obtain the form-factors of this model.
Localization properties of scalar single particle states are analyzed by explicit calculational examples with a focus on the massless case. Problems arising from the non-existence of relativistic particle position operators respecting the…
Interaction of branes in presence of internal gauge fields is considered by using the boundary state formalism. This approach enables us to consider the problems that are not easily accessible to the canonical approach via open strings. The…
A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary is realized. In beam physics,…
In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally, boundary values can appear as additive…
In this paper we examine various approaches to the notion of Poisson manifold in the context of Banach manifolds. Existing definitions are presented and differences between them are explored and illustrated with examples.
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
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…
Consistent boundary Poisson structures for open string theory coupled to background $B$-field are considered using the new approach proposed in hep-th/0111005. It is found that there are infinitely many consistent Poisson structures, each…
We address an apparent conflict between the traditional canonical quantization framework of quantum theory and the spatially restricted quantum dynamics, when the translation invariance of the otherwise free quantum system is broken by…
The purpose of this paper is two-fold. First, we would like to get rid of common assumption that causal set is bounded and attempt to model its scalar field action under the assumption that it isn't. Secondly, we would like to propose…
Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical…
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the…
A simple formalism for exploring quantum scattering and possible bound states in an arbitrary symmetric and localized potential in a unified way is presented. The symmetric square barrier and well potentials are used for illustrating the…
The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which…