Talk detail

Participant	Pietrzyk, Monika
Institution	School of Physics and Astronomy, University of St Andrews - North Haugh - St Andrews - Fife, Scotland - United Kingdom

Session	ES2	Accepted		Order	Time
Talk	Oral abstract	Title	Polysymplectic integrator for short pulse equation and numerical GR
Coauthors
Abstract	Multisympectic formalism is based on a generalization of the variational Poincar\'e-Cartan form to the multiple integral variational problems describing classical field theories. First application to General Relativity can be found in the book by De Donder (1935) and most recent ones are in the papers on multisymplectic treatment of gravity by Vey (2015), precanonical quantization of gravity by Kanatchikov (2012,2013) and covariant Hamilton-Jacobi theory for gravity by Horava (1991). While the first two authors elaborate on a generalization of the Dirac theory of constraints using different variations of the multisymplectic formalism and a generalization of the Poisson bracket to this framework introduced by Kanatchikov (1993), their analysis is not yet complete. Here I will fill one of the gaps, namely, I will show how a generalized Dirac analysis of constraints within the vielbein first order (Palatini) formulation of GR leads to the representation of Einstein-Palatini equations in terms of the generalized Dirac brackets with the so-called De Donder--Weyl Hamiltonian function, which is defined from the Eisntein-Palatini Lagrangian for the vielbein gravity. The formulation can be useful both for the precanonical quantization of gravity put forward by Kanatchikov (2012, 2013) and for the construction of multisymplectic numerical integrators whose superior robustness and speed have been observed in our earlier numerical experiments using the Short Pulse Equation in nonlinear optics. References. 1. Th. De Donder, The\'eorie invariantive du calcul des variations, Paris 1930. 2. D.Vey, Multisymplectic formulation of vielbein gravity. De Donder-Weyl formulation, Hamiltonian (n-1)-form, CQG 32, 095005, 2015. 3. I. Kanatchikov, De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity, arXiv:1302.2610. 4. I. Kanatchikov, On precanonical quantization of gravity in spin connection variable, arXiv:1212.6963. 5. P. Horava, On a covariant Hamilton-Jacobi framework for the Einstein-Maxwell theory, CQG 8, 2069 (1991). 6. I. Kanatchikov, On Field Theoretic Generalizations of a Poisson Algebra, Rep. Math. Phys. 40, 225 (1997). 7. M. Pietrzyk, Multisymplectic integrator for General Relativity, work in progress.
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