Classical Field Theories from Hamiltonian Constraint: Local Symmetries and Static Gauge Fields

@article{Zatloukal2016ClassicalFT,
  title={Classical Field Theories from Hamiltonian Constraint: Local Symmetries and Static Gauge Fields},
  author={V{\'a}clav Zatloukal},
  journal={Advances in Applied Clifford Algebras},
  year={2016},
  volume={28},
  pages={1-27}
}
  • V. Zatloukal
  • Published 9 November 2016
  • Physics
  • Advances in Applied Clifford Algebras
We consider the Hamiltonian constraint formulation of classical field theories, which treats spacetime and the space of fields symmetrically, and utilizes the concept of momentum multivector. The gauge field is introduced to compensate for non-invariance of the Hamiltonian under local transformations. It is a position-dependent linear mapping, which couples to the Hamiltonian by acting on the momentum multivector. We investigate symmetries of the ensuing gauged Hamiltonian, and propose a… 
1 Citations

Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time

The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical

References

SHOWING 1-10 OF 33 REFERENCES

Classical field theories from Hamiltonian constraint: Symmetries and conservation laws

We discuss the relation between symmetries and conservation laws in the realm of classical field theories based on the Hamiltonian constraint. In this approach, spacetime positions and field values

Classical field theories from Hamiltonian constraint: Canonical equations of motion and local Hamilton-Jacobi theory

Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics

Covariant Hamiltonian Field Theory

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler–Lagrange field equations,

Finite dimensional Hamiltonian formalism for gauge and quantum field theories

We discuss in this article the canonical structure of classical field theory in finite dimensions within the pataplectic Hamiltonian formulation, where we put forward the role of Legendre

Gravity, gauge theories and geometric algebra

  • A. LasenbyC. DoranS. Gull
  • Physics
    Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1998
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent

Gauge Theory Gravity with Geometric Calculus

A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein’s principles of equivalence and general relativity are replaced by gauge principles

Multivector fields and connections: Setting Lagrangian equations in field theories

The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle J1E → E → M , it is shown that integrable multivector fields in E are equivalent to

Variational Problems in Differential Geometry: Multisymplectic formalism and the covariant phase space

In most attempts for building the mathematical foundations of Quantum Fields Theory (QFT) two classical ways have been explored. The first one is often referred to as the Feynman integral or

Multivector Fields and Connections. Setting Lagrangian Equations in Field Theories

The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle $J^1E\to E\to M$, it is shown that integrable multivector fields in $E$ are equivalent to