Related papers: Rigged Hilbert Space Resonances and Time Asymmetri…
The Higgs mechanism is reconsidered in the canonical Weyl gauge formulation of quantized gauge theories, using an approach in which redundant degrees of freedom are eliminated. As a consequence, its symmetry aspects appear in a different…
In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $\mathcal H_{xt}=L^2(\mathcal M_{xt})$, with time as the sole evolution parameter. The momentum-energy representation $\phi(k,E)$ is…
We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution…
Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…
Effective mass Klein-Gordon equation for the asymmetric Hulth{\'e}n potential is solved in terms of hypergeometric functions. Results are obtained for the scattering and bound states with the position dependent mass and constant mass, as a…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
The description of bumps in scattering cross-sections by Breit-Wigner amplitudes led in the framework of the mathematical Physics to its formulation as the so-called Resonance-Decay Problem. It consists of a spectraltheoretical component…
Motivated by recent work connecting Higgs phases to symmetry protected topological (SPT) phases, we investigate the interplay of gauge redundancy and global symmetry in lattice gauge theories with Higgs fields in the presence of a boundary.…
Scattering resonances play a central role in collision processes in physics and chemistry. They help building an intuitive understanding of the collision dynamics due to the spatial localization of the scattering wavefunctions. For…
In this paper we show how the quantum mechanics of the inverted harmonic oscillator can be mapped to the quantum mechanics of a particle in a super-critical inverse square potential. We demonstrate this by relating both of these systems to…
As a toy model for the microscopic description of matter in de Sitter space, we consider a Hamiltonian acting on the spin-j representation of SU(2). This is a model with a finite-dimensional Hilbert space, from which quasinormal modes…
The main purpose of this paper is to review the progress that has taken place so far in the search for a single unifying principle that harmonizes (i) the wave and particle natures of matter and radiation, both at the quantum and the…
Classical mechanics admits multiple equivalent formulations, from Newton's equations to the variational Lagrange-Hamilton framework and the scalar Hamilton-Jacobi (HJ) theory. In the HJ formulation, classical ensembles evolve through the…
We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
The Feshbach-type reduction of the Hilbert space to the physically most relevant "model" subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed PT symmetric modification. The…
We investigate the ratchet current that appears in a kicked Hamiltonian system when the period of the kicks corresponds to the regime of quantum resonance. In the classical analogue, a spatial-temporal symmetry should be broken to obtain a…
The geometric argument of the general relativity principle can be carried out on (unstable) Riemann space-time just inspired by nonlinear representation of supersymmetry(NLSUSY), where tangent space is specified by Grassmann degrees of…
It is well known that the observed Higgs mass is more naturally explained in the NMSSM than in the MSSM. Without any violation of this success, there are variants on the NMSSM which can lead to new phenomenologies. In this study we propose…
Symmetry plays a fundamentally important role in physics. In this work, we find a conservation law, $S^{\dagger}(H_{c}^{\dagger})S(H_{c})=I$, which is valid for any non-Hermitian scattering center $H_c$. As a result, the reflections and…