TRANSVERSE MERCATOR EQUATIONS OBTAINED FROM A SPHERICAL BASIS

Survey Review ◽  
1989 ◽  
Vol 30 (233) ◽  
pp. 125-133 ◽  
Author(s):  
B. R. Bowring
Keyword(s):  
Spherical Basis

First (fuzzy) Hopf map from irreps of SU(2)

Open Physics ◽  
2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Hossein Fakhri ◽  
Mehdi Lotfizadeh
Keyword(s):  
Vector Bundles ◽  
Hopf Fibration ◽  
Complex Vector ◽  
Spherical Basis ◽  
Hopf Map ◽  
One To One

AbstractUsing the spherical basis of the spin-ν operator, together with an appropriate normalized complex (2ν +1)-spinor on S 3 we obtain spin-ν representation of the U(1) Hopf fibration S 3 → S 2 as well as its associated fuzzy version. Also, to realize the first Hopf map via the spherical basis of the spin-1 operator with even winding numbers, we present an appropriate normalized complex three-spinor. We put the winding numbers in one-to-one correspondence with the monopole charges corresponding to different associated complex vector bundles.

DISCUSSION OF A KNOWN SPHERICAL BASIS FOR DIRAC WAVE FUNCTIONS

2013 ◽  
Vol 28 (08) ◽  
pp. 1350022
Author(s):  
WERNER SCHEID
Keyword(s):  
Boundary Condition ◽  
Dirac Equation ◽  
Bound States ◽  
Wave Functions ◽  
Expectation Values ◽  
Original Boundary ◽  
Mit Bag Model ◽  
Slight Extension ◽  
Spherical Basis ◽  
Coulomb Potentials

The paper considers the free spherical Dirac equation with a boundary condition at r = R which is a slight extension of the original boundary condition of the MIT bag model. We discuss the basis states and apply them for a diagonalization of Coulomb potentials. The obtained results agree quite well with the lowest bound states with κ = -1, +1 and -2 and their expectation values [Formula: see text]. There appear basis states with energies -mc2 < E < mc2 under certain circumstances of the boundary condition. These states are concentrated at the boundary.

scholarly journals Some Connections between the Spherical and Parabolic Bases on the Cone Expressed in terms of the Macdonald Function

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
I. A. Shilin ◽  
Junesang Choi
Keyword(s):  
Linear Operator ◽  
Hypergeometric Functions ◽  
Legendre Function ◽  
Integral Formula ◽  
Macdonald Function ◽  
Representation Space ◽  
Legendre Functions ◽  
Matrix Elements ◽  
The Matrix ◽  
Spherical Basis

Computing the matrix elements of the linear operator, which transforms the spherical basis ofSO(3,1)-representation space into the hyperbolic basis, very recently, Shilin and Choi (2013) presented an integral formula involving the product of two Legendre functions of the first kind expressed in terms of 4F3-hypergeometric function and, using the general Mehler-Fock transform, another integral formula for the Legendre function of the first kind. In the sequel, we investigate the pairwise connections between the spherical, hyperbolic, and parabolic bases. Using the above connections, we give an interesting series involving the Gauss hypergeometric functions expressed in terms of the Macdonald function.

THE BOSONIC SIGMA MODEL ON A TOROIDAL SURFACE

2004 ◽  
Vol 19 (16) ◽  
pp. 2713-2720
Author(s):  
D. G. C. McKEON
Keyword(s):  
Riemannian Manifold ◽  
Sigma Model ◽  
Three Dimensional ◽  
The Other ◽  
Target Space ◽  
Dimensional Euclidean Space ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Toroidal Surface ◽  
Spherical Basis

The nonlinear sigma model with a two-dimensional basis space and an n-dimensional target space is considered. Two different basis spaces are considered; the first is an 0(2)×0(2) subspace of the 0(2,2) projective space related to the Minkowski basis space, and the other is a toroidal space embedded into three-dimensional Euclidean space, characterized by radii R and r. The target space is taken to be an arbitrarily curved Riemannian manifold. One-loop dependence on the renormalization induced scale μ is shown in the toroidal basis space to be the same as in a flat or spherical basis space.

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