Engineering topics
Curtright, Thomas L.
Publications and source records attributed to Curtright, Thomas L..
More on rotations as spin matrix polynomials
Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful framework to meet this challenge. Central factorial numbers play a key role in the theoretical development. Explicit polynomial coefficients for rotations expressed either as exponentials or as rational Cayley transforms are considered here. Structural features of the results are discussed and compared, and large j limits of the coefficients are examined.
A Compact Formula for Rotations as Spin Matrix Polynomials
Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. Here, the simple explicit result exhibits connections between group theory, combinatorics, and Fourier analysis, especially in the large spin limit. Salient intuitive features of the formula are illustrated and discussed.
Branched Hamiltonians and supersymmetry
Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles. In conclusion, a basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail.