Yang-Mills Fields

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Robert Otto Bauer - One of the best experts on this subject based on the ideXlab platform.

  • Yang-Mills Fields and stochastic parallel transport in small geodesic balls
    Stochastic Processes and their Applications, 2000
    Co-Authors: Robert Otto Bauer
    Abstract:

    We develop a new method to obtain stochastic characterizations of Yang–Mills Fields. Our main tool is the Ito-equation for the stochastic parallel transport. We estimate the drift terms in a small ball of radius e and find that for a general connection the average rotation is of order e3 but that for a Yang–Mills connections the average rotation is of order e4. Using a Doob h-transform we give a new proof of the stochastic characterization of Yang–Mills Fields by S. Stafford. Varying the starting point of the Brownian motion we obtain an unconditioned version of this result. By considering the horizontal Laplace equation we then apply our result to obtain a new analytic characterization of Yang–Mills Fields.

  • Characterizing Yang–Mills Fields by Stochastic Parallel Transport
    Journal of Functional Analysis, 1998
    Co-Authors: Robert Otto Bauer
    Abstract:

    Abstract We give a new stochastic approach to Yang–Mills Fields on vector bundles by studying the derivative of the stochastic parallel transport in the vector bundle under a variation of connection. We establish martingale criterions for variations transversal to the gauge orbit and for Yang–Mills Fields using variations induced by the flow of vector Fields of gradient type on the base manifold. In dimension four we link the local Yang–Mills action to the quadratic variation of the derivative process defined by scalings of the driving Brownian motion in a coordinate chart.

Zhen-rong Zhou - One of the best experts on this subject based on the ideXlab platform.

  • Energy gaps for Yang–Mills Fields
    Journal of Mathematical Analysis and Applications, 2016
    Co-Authors: Zhen-rong Zhou
    Abstract:

    Abstract In this paper, we establish two analytical lemmas, and then use them to investigate energy gaps of YMFs (Yang–Mills Fields) over some Riemannian manifolds. The L p -energy gaps ( p ≥ n / 2 ) for YMFs of the unit sphere S n are obtained. As a consequence, we get an L ∞ -energy gap which coincides the result in [2] . The L n 2 -energy gaps of YMFs over the Euclidean space R n and the hyperbolic space H n are also arrived.

  • Inequalities of Simons type and gaps for Yang–Mills Fields
    Annals of Global Analysis and Geometry, 2015
    Co-Authors: Zhen-rong Zhou
    Abstract:

    In this paper, we establish an inequality of Simons type for Yang–Mills Fields, and obtain a gap property, which generalize the results obtained in Bourguignon and Lawson (Comm Math Phys 79(2):189–230, 1981).

  • Stabilities of F-Yang-Mills Fields on submanifolds
    Archivum Mathematicum, 2013
    Co-Authors: Gao-yang Jia, Zhen-rong Zhou
    Abstract:

    In this paper, we define an $F$-Yang-Mills functional, and hence $F$-Yang-Mills Fields. The first and the second variational formulas are calculated, and the stabilities of $F$-Yang-Mills Fields on some submanifolds of the Euclidean spaces and the spheres are investigated, and hence the theories of Yang-Mills Fields are generalized in this paper.

  • On Gap Properties and Instabilities of p-Yang-Mills Fields
    Canadian Journal of Mathematics, 2007
    Co-Authors: Qun Chen, Zhen-rong Zhou
    Abstract:

    We consider the p-Yang-Mills functional (p ≥ 2) defined as YM p(∇) := 1 p R M k R ∇k p. We call critical points of YM p( � ) the p-Yang-Mills connections, and the associated curvature R ∇ the p-Yang-Mills Fields. In this paper, we prove gap properties and instability theorems for p-Yang-Mills Fields over submanifolds in R n+k and S n+k .

Vincent Moncrief - One of the best experts on this subject based on the ideXlab platform.

  • Hyperboloidal Einstein-matter evolution and tails for scalar and Yang–Mills Fields
    Classical and Quantum Gravity, 2013
    Co-Authors: Oliver Rinne, Vincent Moncrief
    Abstract:

    We show how matter can be included in a constrained ADM-like formulation of the Einstein equations on constant mean curvature surfaces. Previous results on the regularity of the equations at future null infinity are unaffected by the addition of matter with a trace-free energy–momentum tensor. Two examples are studied in detail, namely a conformally coupled scalar field and a Yang–Mills field. We first derive the equations under no symmetry assumptions and then reduce them to spherical symmetry. Both sectors (gravitational and sphaleron) of the spherically symmetric Yang–Mills field are included. We implement this scheme numerically in order to study late-time tails of scalar and Yang–Mills Fields coupled to the Einstein equations. We are able to evolve spacetimes that disperse to flat space, accrete onto a given black hole or collapse to a black hole from regular initial data. The sphaleron sector of Yang–Mills is found to exhibit some nontrivial gauge dynamics.

  • Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills Fields
    Classical and Quantum Gravity, 2010
    Co-Authors: Oliver Rinne, Vincent Moncrief
    Abstract:

    We show how matter can be included in a constrained ADM-like formulation of the Einstein equations on constant mean curvature surfaces. Previous results on the regularity of the equations at future null infinity are unaffected by the addition of matter with tracefree energy-momentum tensor. Two examples are studied in detail, a conformally coupled scalar field and a Yang-Mills field. We first derive the equations under no symmetry assumptions and then reduce them to spherical symmetry. Both sectors (gravitational and sphaleron) of the spherically symmetric Yang-Mills field are included. We implement this scheme numerically in order to study late-time tails of scalar and Yang-Mills Fields coupled to the Einstein equations. We are able to evolve spacetimes that disperse to flat space, accrete onto a given black hole or collapse to a black hole from regular initial data. The sphaleron sector of Yang-Mills is found to exhibit some nontrivial gauge dynamics.

Anton Thalmaier - One of the best experts on this subject based on the ideXlab platform.

  • Yang-Mills Fields and random holonomy along Brownian bridges
    The Annals of Probability, 2003
    Co-Authors: Marc Arnaudon, Anton Thalmaier
    Abstract:

    We characterize Yang--Mills connections in vector bundles in terms of covariant derivatives of stochastic parallel transport along variations of Brownian bridges on the base manifold. In particular, we prove that a connection in a vector bundle E is Yang--Mills if and only if the covariant derivative of parallel transport along Brownian bridges (in the direction of their drift) is a local martingale, when transported back to the starting point. We present a Taylor expansion up to order 3 for stochastic parallel transport in E along small rescaled Brownian bridges and prove that the connection in E is Yang--Mills if and only if all drift terms in the expansion (up to order 3) vanish or, equivalently, if and only if the average rotation of parallel transport along small bridges and loops is of order 4.

Oliver Rinne - One of the best experts on this subject based on the ideXlab platform.

  • Hyperboloidal Einstein-matter evolution and tails for scalar and Yang–Mills Fields
    Classical and Quantum Gravity, 2013
    Co-Authors: Oliver Rinne, Vincent Moncrief
    Abstract:

    We show how matter can be included in a constrained ADM-like formulation of the Einstein equations on constant mean curvature surfaces. Previous results on the regularity of the equations at future null infinity are unaffected by the addition of matter with a trace-free energy–momentum tensor. Two examples are studied in detail, namely a conformally coupled scalar field and a Yang–Mills field. We first derive the equations under no symmetry assumptions and then reduce them to spherical symmetry. Both sectors (gravitational and sphaleron) of the spherically symmetric Yang–Mills field are included. We implement this scheme numerically in order to study late-time tails of scalar and Yang–Mills Fields coupled to the Einstein equations. We are able to evolve spacetimes that disperse to flat space, accrete onto a given black hole or collapse to a black hole from regular initial data. The sphaleron sector of Yang–Mills is found to exhibit some nontrivial gauge dynamics.

  • Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills Fields
    Classical and Quantum Gravity, 2010
    Co-Authors: Oliver Rinne, Vincent Moncrief
    Abstract:

    We show how matter can be included in a constrained ADM-like formulation of the Einstein equations on constant mean curvature surfaces. Previous results on the regularity of the equations at future null infinity are unaffected by the addition of matter with tracefree energy-momentum tensor. Two examples are studied in detail, a conformally coupled scalar field and a Yang-Mills field. We first derive the equations under no symmetry assumptions and then reduce them to spherical symmetry. Both sectors (gravitational and sphaleron) of the spherically symmetric Yang-Mills field are included. We implement this scheme numerically in order to study late-time tails of scalar and Yang-Mills Fields coupled to the Einstein equations. We are able to evolve spacetimes that disperse to flat space, accrete onto a given black hole or collapse to a black hole from regular initial data. The sphaleron sector of Yang-Mills is found to exhibit some nontrivial gauge dynamics.