Related papers: Polysymplectic Hamiltonian formalism and some quan…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
Using a massless scalar field as a clock variable, the Legendre transform of the group field theory Lagrangian gives a relational Hamiltonian. In the classical theory, it is natural to define 'equal relational time' Poisson brackets, where…
We describe the symplectic reduction construction for the physical phase space in gauge theory and apply it for the BF theory. Symplectic reduction theorem allows us to rewrite the same phase space as a quotient by the gauge group action,…
The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
In $n$-dimensional classical field theory one studies maps from $n$-dimensional manifolds in such a way that classical mechanics is recovered for $n=1$. In previous papers we have shown that the standard polysymplectic framework in which…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
We determine a precise necessary and sufficient condition for completeness of the Hamiltonian vector field associated to a homogeneous cubic polynomial on a symplectic plane.
We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…
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…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
A realistic axiomatic formulation of Galilean Quantum Field Theories is presented, from which the most important theorems of the theory can be deduced. In comparison with others formulations, the formal aspect has been improved by the use…
We develop Hamiltonian formalism for Lagrange Multiplier Modified Gravity. We further calculate the Poisson brackets between constraints and we show that they coincide with the algebra of constraints in Hamiltonian formulation of General…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…
A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic…
This paper defines a symplectic form on the infinite dimensional Fr\'echet manifold of framed curves of fixed length over a simply connected Riemannian manifold of constant curvature. The paper then considers Hamiltonian systems generated…
A covariant description of the canonical theory for interacting classical fields is developed on a space-like hypersurface. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in…
We discuss a covariant setting for Hamiltonian formalism in a relativistic field theory and we use this to obtain again the properties of Hamilton principal functional in Newtonian mechanics, relativistic mechanics, Klein-Gordon,…