• Corpus ID: 117719308

Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories

@article{Gotay2004MomentumMA,
  title={Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories},
  author={Mark J. Gotay and James Allen Isenberg and Jerrold E. Marsden},
  journal={arXiv: Mathematical Physics},
  year={2004}
}
With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulation of classical field theories. The canonical formluation works with fields defined as time-evolving cross sections of bundles over a Cauchy surface, rather than as sections of bundles over spacetime as in the covariant formulation. In Chapter 5 we begin to relate these approaches to classical field theory; in… 

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References

SHOWING 1-10 OF 40 REFERENCES

The initial value problem and the dynamical formulation of general relativity

In this chapter we discuss some of the interrelationships between the initial value problem, the canonical formalism, linearization stability and the space of gravitational degrees of freedom. In the

The well‐posedness of (N=1) classical supergravity

In this paper we investigate whether classical (N=1) supergravity has a well‐posed locally causal Cauchy problem. We define well‐posedness to mean that any choice of initial data (from an appropriate

Stress-Energy-Momentum Tensors and the Belinfante-Rosenfeld Formula

We present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory. The stress-energy-momentum tensor T ^μ

Exactly soluble diffeomorphism invariant theories

A class of diffeomorphism invariant theories is described for which the Hilbert space of quantum states can be explicitly constructed. These theories can be formulated in any dimension and include

Closed forms on symplectic fibre bundles

A bundle of symplectic manifolds is a differentiable fibre bundle F--~ E-% B whose structure group (not necessarily a Lie group) preserves a symplectic structure on F. The vertical subbundle V=Ker

Stratified symplectic spaces and reduction

Let (M, w) be a Hamiltonian G-space with proper momentum map J: M -> g*. It is well-known that if zero is a regular value of J and G acts freely on the level set J '(0), then the reduced space MO =