5,357 research outputs found
Muonium spectrum beyond the nonrelativistic limit
A generalization of the Gell-Mann-Low theorem is applied to the
antimuon-electron system. The bound state spectrum is extracted numerically. As
a result, fine and hyperfine structure are reproduced correctly near the
nonrelativistic limit (and for arbitrary masses). We compare the spectrum for
the relativistic value alpha = 0.3 with corresponding calculations in
light-front quantization.Comment: 6 pages, LaTeX, 2 figures, uses aipxfm.sty. Talk delivered at the XI
Mexican Workshop on Particles and Fields, Tuxtla Gutierrez, Mexico, November
7-12, 2007; to be published in the proceeding
A nonrelativistic limit for AdS perturbations
The familiar nonrelativistic limit converts the
Klein-Gordon equation in Minkowski spacetime to the free Schroedinger equation,
and the Einstein-massive-scalar system without a cosmological constant to the
Schroedinger-Newton (SN) equation. In this paper, motivated by the problem of
stability of Anti-de Sitter (AdS) spacetime, we examine how this limit is
affected by the presence of a negative cosmological constant .
Assuming for consistency that the product tends to a negative
constant as , we show that the corresponding
nonrelativistic limit is given by the SN system with an external harmonic
potential which we call the Schrodinger-Newton-Hooke (SNH) system. We then
derive the resonant approximation which captures the dynamics of small
amplitude spherically symmetric solutions of the SNH system. This resonant
system turns out to be much simpler than its general-relativistic version,
which makes it amenable to analytic methods. Specifically, in four spatial
dimensions, we show that the resonant system possesses a three-dimensional
invariant subspace on which the dynamics is completely integrable and hence can
be solved analytically. The evolution of the two-lowest-mode initial data (an
extensively studied case for the original general-relativistic system), in
particular, is described by this family of solutions.Comment: v3: slightly expanded published versio
Ground States for a Stationary Mean-Field Model for a Nucleon
In this paper we consider a variational problem related to a model for a
nucleon interacting with the and mesons in the atomic
nucleus. The model is relativistic, and we study it in a nuclear physics
nonrelativistic limit, which is of a very different nature than the
nonrelativistic limit in the atomic physics. Ground states are shown to exist
for a large class of values for the parameters of the problem, which are
determined by the values of some physical constants
The non-relativistic limit of (central-extended) Poincare group and some consequences for quantum actualization
The nonrelativistic limit of the centrally extended Poincar\'e group is
considered and their consequences in the modal Hamiltonian interpretation of
quantum mechanics are discussed [ O. Lombardi and M. Castagnino, Stud. Hist.
Philos. Mod. Phys 39, 380 (2008) ; J. Phys, Conf. Ser. 128, 012014 (2008) ].
Through the assumption that in quantum field theory the Casimir operators of
the Poincar\'e group actualize, the nonrelativistic limit of the latter group
yields to the actualization of the Casimir operators of the Galilei group,
which is in agreement with the actualization rule of previous versions of modal
Hamiltonian interpretation [ Ardenghi et al., Found. Phys. (submitted)
Symmetry Breaking of Relativistic Multiconfiguration Methods in the Nonrelativistic Limit
The multiconfiguration Dirac-Fock method allows to calculate the state of
relativistic electrons in atoms or molecules. This method has been known for a
long time to provide certain wrong predictions in the nonrelativistic limit. We
study in full mathematical details the nonlinear model obtained in the
nonrelativistic limit for Be-like atoms. We show that the method with sp+pd
configurations in the J=1 sector leads to a symmetry breaking phenomenon in the
sense that the ground state is never an eigenvector of L^2 or S^2. We thereby
complement and clarify some previous studies.Comment: Final version, to appear in Nonlinearity. Nonlinearity (2010) in
pres
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