SUSY transformation of the Green function and a trace formula

Green's functions for reflectionless potentials and addition of boundstates to powerlaw potentials to find Supersymmetric partners

Green's functions for reflectionless potentials are constructed and analyzed. Green's functions for power law potentials, their Super Symmetric partners and sum rules for eigenvalues are examined. The SUSY partner potentials to power law potentials which have an additional bound state at $E=0$ are constructed.

Pseudospin symmetry in nuclear structure and its supersymmetric representation

The quasi-degeneracy between the single-particle states $(n,\,l,\,j=l+1/2)$ and $(n-1,\,l+2,\,j=l+3/2)$ indicates a special and hidden symmetry in atomic nuclei---the so-called pseudospin symmetry (PSS)---which is an important concept in both spherical and deformed nuclei. A number of phenomena in nuclear structure have been successfully interpreted directly or implicitly by this symmetry, including nuclear superdeformed configurations, identical bands, quantized alignment, pseudospin partner bands, and so on. Since the PSS was recognized as a relativistic symmetry in 1990s, there have been co…

Many-Body Contributions to Green's Functions and Casimir Energies

The multiple scattering formalism is used to extract irreducible N-body parts of Green's functions and Casimir energies describing the interaction of N objects that are not necessarily mutually disjoint. The irreducible N-body scattering matrix is expressed in terms of single-body transition matrices. The irreducible N-body Casimir energy is the trace of the corresponding irreducible N-body part of the Green's function. This formalism requires the solution of a set of linear integral equations. The irreducible three-body Green's function and the corresponding Casimir energy of a massless scala…

A massless scalar field in Robertson-Walker spacetimes: Adiabatic regularization and Green's function

We study adiabatic regularization of a coupling massless scalar field in general spatially flat Robertson-Walker (RW) spacetimes. For the conformally-coupling, the 0th-order regularized power spectrum and 0th-order regularized stress tensor are zero, and no trace anomaly exists in general RW spacetimes. This is a new result which extents those found in de Sitter space. For the minimally-coupling, the regularized spectra are also zero in the radiation-dominant stage, the matter-dominant stage, and de Sitter space as well. The vanishing of these adiabatically regularized spectra are also confirm…

Unitary equivalence between the Green's function and Schrödinger approaches for quantum graphs

In a previous work [Andrade \textit{et al.}, Phys. Rep. \textbf{647}, 1 (2016)], it was shown that the exact Green's function (GF) for an arbitrarily large (although finite) quantum graph is given as a sum over scattering paths, where local quantum effects are taken into account through the reflection and transmission scattering amplitudes. To deal with general graphs, two simplifying procedures were developed: regrouping of paths into families of paths and the separation of a large graph into subgraphs. However, for less symmetrical graphs with complicated topologies as, for instance, random …

超越Born-Oppenheimer格林函数理论：绝对与关系

Beyond Born-Oppenheimer Green's function theories: absolute and relational

本文提出一种关系性的约化格林函数理论，以解决超越Born-Oppenheimer近似下的库仑多体问题，强调可观测量的相对性定义，并阐明声子等实体可在关系理论中自然解释。