Papers by Thomas Curtright
Systems built out of N-body interactions, beyond 2-body interactions, are formulated on the plane... more Systems built out of N-body interactions, beyond 2-body interactions, are formulated on the plane, and investigated classically and quantum mechanically (in phase space). Their Wigner Functions—the density matrices in phase-space quantization—are given and analyzed. In this brief note, we consider systems of N particles on a plane, interacting through N-body potentials, over and above more familiar 2-body potentials. Below, we provide the compact generating function, G(a,a ∗,b,b ∗;z,z ∗,p,p ∗ ) = 1 1 |a|
Physics Letters A, 2017
The number of times spin s appears in the Kronecker product of n spin j representations is comput... more The number of times spin s appears in the Kronecker product of n spin j representations is computed, and the large n asymptotic behavior of the result is obtained. Applications are briefly sketched.
AIP Conference Proceedings, 2003
We relate classical and quantum Dirac and Nambu brackets. At the classical level, we use the rela... more We relate classical and quantum Dirac and Nambu brackets. At the classical level, we use the relations between the two brackets to gain some insight into the Jacobi identity for Dirac brackets, among other things. At the quantum level, we suggest that the Nambu bracket is the preferred method for introducing constraints, although at the expense of some unorthodox behavior, which we describe in detail.
Journal of Physics A: Mathematical and Theoretical, 2014
Recent results for rotations expressed as polynomials of spin matrices are derived here by elemen... more Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an alternate derivation. The central factorial numbers play key roles in both derivations.
Branes, Strings, and Odd Quantum Nambu Brackets
Quantum Theory and Symmetries - Proceedings of the 3rd International Symposium, 2004
Lecture Notes in Physics
This is a pedagogical digest of results reported in [Curtright, Fairlie, & Zachos 1997], and an e... more This is a pedagogical digest of results reported in [Curtright, Fairlie, & Zachos 1997], and an explicit implementation of Euler's construction for the solution of the Poisson Bracket dual Nahm equation. But it does not cover 9 and 10-dimensional systems, and subsequent progress on them [Fairlie 1997]. Cubic interactions are considered in 3 and 7 space dimensions, respectively, for bosonic membranes in Poisson Bracket form. Their symmetries and vacuum configurations are explored. Their associated first order equations are transformed to Nahm's equations, and are hence seen to be integrable, for the 3-dimensional case, by virtue of the explicit Lax pair provided. Most constructions introduced also apply to matrix commutator or Moyal Bracket analogs.
Physical Review D, 1986
%'e explore the classical dynamics of strings with rigidity, i.e. , with terms added to the strin... more %'e explore the classical dynamics of strings with rigidity, i.e. , with terms added to the string action which depend on the extrinsic curvature of the world sheet. %e study classical solutions of the string equations of motion using both analytical and numerical methods, and we determine the leading Regge trajectories J(E2) for a set of classical rotating string configurations. %e observe that for open strings the dominant classical solutions are identical to those for the conventional Nambu string, and correspondingly give linear trajectories. However, for closed strings we find new solutions that include finite-energy, static configurations, and that give trajectories which are nonlinear as the lowest-energy solution is approached, but become linear asymptotically as J(E')~ao.
Progress of Theoretical Physics Supplement, 1999
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicate... more In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple-indeed, classical-for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published in Refs. 1) and 2).
Physics Letters B, 1997
Cubic interactions are considered in 3 and 7 space dimensions, respectively, for bosonic membrane... more Cubic interactions are considered in 3 and 7 space dimensions, respectively, for bosonic membranes in Poisson Bracket form. Their symmetries and vacuum configurations are discussed. Their associated first order equations are transformed to Nahm's equations, and are hence seen to be integrable, for the 3-dimensional case, by virtue of the explicit Lax pair provided. The constructions introduced also apply to commutator or Moyal Bracket analogues.
Physics Letters B, 2009
We consider several ternary algebras relevant to physics. We compare and contrast the quantal ver...
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Papers by Thomas Curtright