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Canonical transformation
About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.
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TL;DR: In this paper, a discrete symplectic map and its continuous symplectic analog are derived for forward magnetic field line trajectories in natural canonical coordinates based on these, and the magnetic footprint on the inboard collector plate in the DIII-D is calculated.
Abstract: Any canonical transformation of Hamiltonian equations is symplectic, and any area-preserving transformation in 2D is a symplectomorphism. Based on these, a discrete symplectic map and its continuous symplectic analog are derived for forward magnetic field line trajectories in natural canonical coordinates. The unperturbed axisymmetric Hamiltonian for magnetic field lines is constructed from the experimental data in the DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The equilibrium Hamiltonian is a highly accurate, analytic, and realistic representation of the magnetic geometry of the DIII-D. These symplectic mathematical maps are used to calculate the magnetic footprint on the inboard collector plate in the DIII-D. Internal statistical topological noise and field errors are irreducible and ubiquitous in magnetic confinement schemes for fusion. It is important to know the stochasticity and magnetic footprint from noise and error fields. The estimates of the spectrum and mode amplitude...
11 citations
TL;DR: In this paper, a canonical transformation of the Hamiltonian is proposed to distinguish fast and slow variables, and the canonical coordinates of a collective mode are naturally introduced to explain the stability of these structures.
Abstract: The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low-energy initial conditions. The aim of this paper is to show in a detailed manner how these structures arise and to explain their stability. By a convenient canonical transformation we rewrite the Hamiltonian in such a way that fast and slow variables are singled out and the canonical coordinates of a collective mode are naturally introduced. If, initially, enough energy is put in this mode, its decay can be extremely slow. However, both analytical arguments and numerical simulations suggest that these structures eventually decay to the spatially uniform equilibrium state, although this can happen on impressively long time scales. Finally, we heuristically introduce a one-particle time-dependent Hamiltonian that well reproduces most of the observed phenomenology.
11 citations
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TL;DR: In this article, the authors examined the electric-magnetic duality for a U(1) gauge theory on a general four manifold which generates the SL(2, Z) group.
Abstract: We examine the electric-magnetic duality for a U(1) gauge theory on a general four manifold which generates the SL(2, Z) group. The partition functions for such a theory transforms as a modular form of specific weight. However, in the canonical approach, we show that S-duality for the abelian theory, like T-duality, is generated by a canonical transformation leading to a modular invariant partition function.
11 citations
TL;DR: In this article, the canonical formulation of the Poincare BFCG theory in terms of the spatial 2-connection and its canonical conjugate momenta was found. But the canonical transformation relating the two was not discussed.
Abstract: We find the canonical formulation of the Poincare BFCG theory in terms of the spatial 2-connection and its canonically conjugate momenta. We show that the Poincare BFCG action is dynamically equivalent to the BF action for the Poincare group and we find the canonical transformation relating the two. We study the canonical quantization of the Poincare BFCG theory by passing to the Poincare-connection basis. The quantization in the 2-connection basis can be then achieved by performing a Fourier transform. We also briefly discuss how to approach the problem of constructing a basis of spin-foam states, which are the categorical generalization of the spin-network states from loop quantum gravity.
11 citations
TL;DR: In this article, a collective-variable theory for nonlinear coherent excitations based on Dirac's formalism of constrained Hamiltonian systems is proposed. No approximations are involved in this theory in the sense that they are able to formulate equations of motion for a new set of variables, including the collective variables themselves, which are equivalent to the original set of Hamilton's equation of motion.
11 citations