We provide a systematic study on the possibility of supersymmetry (SUSY) for one dimensional quantum mechanical systems consisting of a pair of lines R or intervals [−l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) fa...

We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the c...

In manifolds with spatial boundary, BRST formalism can be used to quantize gauge theories. We show that, in a U(1) gauge theory, only a subset of all the boundary conditions allowed by the self-adjointness of the Hamiltonian preserves BRST symmetry. Hence, the theory can be quantized using BRST formalism only when that subset of boundary conditions is considered. We also show that for such boun...

We notice that, when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits a singular behaviour associated with restructuring of classical trajectories. The system with the crypto-Hermitian Hamiltonian H = (p + z)/2 − igz and hy...

In this paper we discussed the self-adjointness of the Maxwell’s equations with variable coefficients ε and μ. Three different Lagrangian are attained. By the Legendre transformation, a multisymplectic Bridge’s (Hamilton) form is obtained. Based on the multisymplectic structure, the multisymplectic conservation law of the system is derived and a nine-point Preissman multisymplectic scheme which...

Strong and Markov uniqueness problems in L for Dirichlet operators on rigged Hilbert spaces are studied. An analytic approach based on a–priori estimates is used. The extension of the problem to the L-setting is discussed. As a direct application essential self–adjointness and strong uniqueness in L is proved for the generator (with initial domain the bounded smooth cylinder functions) of the s...

The present paper introduces a mixed stress-displacement method for linear elasticity, as an extension of the work performed by Christiansen [15] for computational relativity. Moreover, we establish self-adjointness in a special sense and perform numerical simulations to assess the relevance of the method, including comparison with the recent TDNNS [30, 34] mixed formulation. Extensions to high...

The possibility of composite systems arising out of a point charge interacting with a Nielsen-Olesen vortex in 2+1-dimensions is investigated. It is shown that classical bounded orbits are possible for certain ranges of parameters. Long lived metastable states are shown to exist, in a semi-classical approach, from the study of the effective potential. Loss of self-adjointness of the Hamiltonian...