Gauge fields in the separation of rotations andinternal motions in the n-body problem

Littlejohn, Robert G.; Reinsch, Matthias

doi:10.1103/revmodphys.69.213

Cited by 291 publications

(285 citation statements)

References 72 publications

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“…Previous treatments of the latter problem within a gauge-invariant approach have been given in [4] and references therein. A gauge theory of rotations and internal motions of deformable bodies, including classical and quantum N -body systems, is developed in [7] (see also [8]) from a point of view different from ours. Non-gauge-invariant treatments can be found, e.g., in [5] in the context of nuclear physics, and in [9,10] in molecular physics.…”

Section: Introductionmentioning

confidence: 99%

Rotating frames and gauge invariance in three-dimensional many-body quantum systems

Bouzas¹,

Mendez-Gamboa²

2004

J. Phys. A: Math. Gen.

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We study the quantization of many-body systems in three dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear gauge conditions, and discuss their Gribov ambiguities and commutator algebra. We construct the momentum operators, inner-product and Hamiltonian in those gauges, for systems with and without translation invariance. The analogy with the quantization of non-Abelian Yang-Mills theories in noncovariant gauges is emphasized. Our results are applied to quasi-rigid systems in the Eckart frame.

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Section: Introductionmentioning

confidence: 99%

Rotating frames and gauge invariance in three-dimensional many-body quantum systems

Bouzas¹,

Mendez-Gamboa²

2004

J. Phys. A: Math. Gen.

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“…Our approach to systematic reduction of dimension is based on the framework of geometric mechanics [1,2] and hyperspherical coordinates [3]. In the hyperspherical coordinates, one can express the internal motions of an n-atom system in terms of the three gyration radii and the (3n − 9) hyperangular variables.…”

Section: Collective Coordinates and Dynamical Reaction Barriermentioning

confidence: 99%

Collective coordinates and the mechanism for conformational transitions of complex molecules

Yanao

Koon

Marsden

et al. 2007

Proc Appl Math and Mech

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Reduction of dimensionality is crucial for the deeper understanding of the mechanism for large-amplitude conformational transitions of complex molecules. By taking up a six-atom cluster as an illustrative example, we present a general methodology to understand conformational transitions of molecules in terms of the low-dimensional dynamics of molecular gyration radii. The dynamics of gyration radii is generally governed by the interplay between the ordinary potential force and a dynamical force called the internal centrifugal force. We show that the internal centrifugal force can be more important than the original potential barrier and gives rise to a new dynamical barrier that truly dominates the conformational transitions of the system. This kind of dynamical effect should be crucially important in a wide class of molecular reaction dynamics.

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“…A geometric viewpoint, complementing the analytic viewpoint focused on forces and dynamics, generated fundamental insight into the n-body problem, specifically on the interaction between internal motions (vibrations) and spatial rotations [9]. In this paper, a similar geometric approach is developed to analyse data on biological collective motion and for future applications to technological synthesis of such motion (in robots for instance).…”

Section: Introductionmentioning

confidence: 99%

Geometric decompositions of collective motion

Mischiati

Krishnaprasad

2017

Proc. R. Soc. A.

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Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots.

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Gauge fields in the separation of rotations andinternal motions in the n-body problem

Cited by 291 publications

References 72 publications

Rotating frames and gauge invariance in three-dimensional many-body quantum systems

Rotating frames and gauge invariance in three-dimensional many-body quantum systems

Collective coordinates and the mechanism for conformational transitions of complex molecules

Geometric decompositions of collective motion

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