We performed angle-resolved photoemission spectroscopy (ARPES) studies of the electronic structure of the nematic phase in LaFeAsO. Degeneracy breaking between the dxz and dyz hole bands near the {Gamma} and M point is observed in the nematic phase.
Different temperature dependent band splitting behaviors are observed at the {Gamma} and M points. The energy of the band splitting near the M point decreases as the temperature decreases while it has little temperature dependence near the {Gamma} point. The nematic nature of the band shift near the M point is confirmed through a detwin experiment using a piezo device. Since a momentum dependent splitting behavior has been observed in other iron based superconductors, our observation confirms that the behavior is a universal one among iron based superconductors.
Two-photon states produce enough symmetry needed for Diracs construction of the two-oscillator system which produces the Lie algebra for the O(3,2) space-time symmetry. This O(3,2) group can be contracted to the inhomogeneous Lorentz group which, acc
ording to Dirac, serves as the basic space-time symmetry for quantum mechanics in the Lorentz-covariant world. Since the harmonic oscillator serves as the language of Heisenbergs uncertainty relations, it is right to say that the symmetry of the Lorentz-covariant world, with Einsteins $E = mc^2$, is derivable from Heisenbergs uncertainty relations.
The aim of this research paper is to obtain explicit expressions of (i) $ {}_1F_1 left[begin{array}{c} alpha 2alpha + i end{array} ; x right]. {}_1F_1left[ begin{array}{c} beta 2beta + j end{array} ; x right]$ (ii) ${}_1F_1 left[ begin{array}{c
} alpha 2alpha - i end{array} ; x right] . {}_1F_1 left[ begin{array}{c} beta 2beta - j end{array} ; x right]$ (iii) ${}_1F_1 left[ begin{array}{c} alpha 2alpha + i end{array} ; x right] . {}_1F_1 left[begin{array}{c} beta 2beta - j end{array} ; x right]$ in the most general form for any $i,j=0,1,2,ldots$ For $i=j=0$, we recover well known and useful identity due to Bailey. The results are derived with the help of a well known Baileys formula involving products of generalized hypergeometric series and generalization of Kummers second transformation formulas available in the literature. A few interesting new as well as known special cases have also been given.
We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model is used t
o resolve a discontinuity problem in option pricing.
In this note we state (with minor corrections) and give an alternative proof of a very general hypergeometric transformation formula due to Slater. As an application, we obtain a new hypergeometric transformation formula for a ${}_5F_4(-1)$ series wi
th one pair of parameters differing by unity expressed as a linear combination of two ${}_3F_2(1)$ series.
It is noted that the Poincare sphere for polarization optics contains the symmetries of the Lorentz group. The sphere is thus capable of describing the internal space-time symmetries dictated by Wigners little groups. For massive particles, the littl
e group is like the three-dimensional rotation group, while it is like the two-dimensional Euclidean group for massless particles. It is shown that the Poincare sphere, in addition, has a symmetry parameter corresponding to reducing the particle mass from a positive value to zero. The Poincare sphere thus the gives one unified picture of Wigners little groups for massive and massless particles.
The aim in this note is to provide a generalization of an interesting entry in Ramanujans Notebooks that relate sums involving the derivatives of a function Phi(t) evaluated at 0 and 1. The generalization obtained is derived with the help of expressi
ons for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recently obtained in Kim et al. [Two results for the terminating 3F2(2) with applications, Bull. Korean Math. Soc. 49 (2012) pp. 621{633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.
Expressions for the summation of a new series involving the Laguerre polynomials are obtained in terms of generalized hypergeometric functions. These results provide alternative, and in some cases simpler, expressions to those recently obtained in the literature.
One hundred years ago, in 1908, Hermann Minkowski completed his proof that Maxwells equations are covariant under Lorentz transformations. During this process, he introduced a four-dimensional space called the Minkowskian space. In 1949, P. A. M. Dir
ac showed the Minkowskian space can be handled with the light-cone coordinate system with squeeze transformations. While the squeeze is one of the fundamental mathematical operations in optical sciences, it could serve useful purposes in two-level systems. Some possibilities are considered in this report. It is shown possible to cross the light-cone boundary in optical and two-level systems while it is not possible in Einsteins theory of relativity.
The beam transfer matrix, often called the $ABCD$ matrix, is a two-by-two matrix with unit determinant, and with three independent parameters. It is noted that this matrix cannot always be diagonalized. It can however be brought by rotation to a matr
ix with equal diagonal elements. This equi-diagonal matrix can then be squeeze-transformed to a rotation, to a squeeze, or to one of the two shear matrices. It is noted that these one-parameter matrices constitute the basic elements of the Wigners little group for space-time symmetries of elementary particles. Thus every $ABCD$ matrix can be written as a similarity transformation of one of the Wigner matrices, while the transformation matrix is a rotation preceded by a squeeze. This mathematical property enables us to compute scattering processes in periodic systems. Laser cavities and multilayer optics are discussed in detail. For both cases, it is shown possible to write the one-cycle transfer matrix as a similarity transformation of one of the Wigner matrices. It is thus possible to calculate the $ABCD$ matrix for an arbitrary number of cycles.
