Poisson algebras for non-linear field theories in the Cahiers topos - INSPIRE

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Poisson algebras for non-linear field theories in the Cahiers topos

Feb 1, 2016

30 pages

Published in:

Annales Henri Poincare 18 (2017) 4, 1435-1464

Published: Nov 17, 2016

e-Print:

1602.00708 [math-ph]

DOI:

10.1007/s00023-016-0533-2

Report number:

EMPG-16-03

View in:

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Abstract: (Springer)

We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework, the solution space of the field equation carries a natural smooth structure and, following Zuckerman’s ideas, we can endow it with a presymplectic current. We formulate the Hamiltonian vector field equation in this setting and show that it selects a family of observables which forms a Poisson algebra. Our approach provides a clean splitting between geometric and algebraic aspects of the construction of a Poisson algebra, which are sufficient to guarantee existence, and analytical aspects that are crucial to analyze its properties.

Note:

v2: 24 pages; compatible with version to appear in Annales Henri Poincare

algebra: Poisson
field theory: nonlinear
field theory: scalar
differential geometry
field equations
model: topological

References(15)

Figures(0)

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