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Symplectic vector space

About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.


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Journal ArticleDOI
01 Feb 2004
TL;DR: In this paper, an alternative approach to embed second class systems using Wess-Zumino (WZ) variables is proposed, which is developed within the symplectic framework.
Abstract: An alternative approach to embed second class systems using the Wess-Zumino (WZ) variables is proposed[1]. This is developed within the symplectic framework[2,3].

12 citations

Journal ArticleDOI
TL;DR: In the following, an alternate symplectic packing problem is explored where the target and domains are 2n-dimensional manifolds which have first homology group equal to Zn and the embeddings induce isomorphisms of firsthomology.
Abstract: Finding optimal packings of a symplectic manifold with symplectic embeddings of balls is a well known problem. In the following, an alternate symplectic packing problem is explored where the target and domains are 2n-dimensional manifolds which have first homology group equal to Zn and the embeddings induce isomorphisms of first homology. When the target and domains are Tn × V and Tn × U in the cotangent bundle of the torus, all such symplectic packings give rise to packings of V by copies of U under GL(n, Z) and translations. For arbitrary dimensions, symplectic packing invariants are computed when packing a small number of objects. In dimensions 4 and 6, computer algorithms are used to calculate the invariants associated to packing a larger number of objects. These alternate and classic symplectic packing invariants have interesting similarities and differences.

12 citations

Book ChapterDOI
15 Jun 2012
TL;DR: High-order symplectic schemes for stochastic Hamiltonian systems preserving Hamiltonian functions are presented, based on the generating function method, and it is demonstrated numerically that the symp eclectic schemes are effective for long time simulations.
Abstract: We present high-order symplectic schemes for stochastic Hamiltonian systems preserving Hamiltonian functions. The approach is based on the generating function method, and we show that for the stochastic Hamiltonian systems, the coefficients of the generating function are invariant under permutations. As a consequence, the high-order symplectic schemes have a simpler form than the explicit Taylor expansion schemes with the same order. Moreover, we demonstrate numerically that the symplectic schemes are effective for long time simulations.

12 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed a model for the quantization of gravity by working in a bundle $E$ where they realized the Hamilton constraint as the Wheeler-DeWitt equation, but the corresponding operator only acts in the fibers and not in the base space.
Abstract: In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not in the base space. Therefore, we now discard the Wheeler-DeWitt equation and express the Hamilton constraint differently, either with the help of the Hamilton equations or by employing a geometric evolution equation. There are two modifications possible which both are equivalent to the Hamilton constraint and which lead to two new models. In the first model we obtain a hyperbolic operator that acts in the fibers as well as in the base space and we can construct a symplectic vector space and a Weyl system. d In the second model the resulting equation is a wave equation in $\so \times (0,\infty)$ valid in points $(x,t,\xi)$ in $E$ and we look for solutions for each fixed $\xi$. This set of equations contains as a special case the equation of a quantized cosmological Friedmann universe without matter but with a cosmological constant, when we look for solutions which only depend on $t$. Moreover, in case $\so$ is compact we prove a spectral resolution of the equation.

12 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present theorems of decomposition by symplectic twist maps and existence of periodic orbits for optical Hamiltonian systems of T ∗ T n. The novelty of these results lies in the fact that no explicit asymptotic condition is imposed on the system.

12 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202310
202221
202113
20208
201910
201818