Related papers: Covariant canonical quantization
The De Donder-Weyl (DW) Hamiltonian theory of fields treats space and time variables on equal footing. Its quantization, called precanonical quantization, leads to a hypercomplex generalization of quantum formalism to field theory as it…
It has been suggested that the chiral symmetry can be implemented only in classical Lagrangians containing higher covariant derivatives of odd order. Contrary to this belief, it is shown that one can construct an exactly soluble…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
We generalize Koopman-von Neumann classical mechanics to poly-symplectic fields and recover De Donder-Weyl theory. Comparing with Dirac's Hamiltonian density inspires a new Hamiltonian formulation with a canonical momentum field that is…
A quantization of field theory based on the DeDonder-Weyl covariant Hamiltonian formulation is discussed. A hypercomplex extension of quantum mechanics, in which the space-time Clifford algebra replaces that of the complex numbers, appears…
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 review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches…
We introduce a phase space with spinorial momenta, corresponding to fermionic derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is a generalisation of the covariant De Donder-Weyl Hamiltonian formulation on this…
We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the…
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved…
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
The prequantization map for a Poisson-Gerstenhaber algebra of dynamical variables represented by differential forms within the polysymplectic formulation of the De Donder--Weyl covariant Hamiltonian field theory is presented and the…
This paper gives a brief overview of the manifestly covariant canonical gauge gravity (CCGG) that is rooted in the De Donder-Weyl Hamiltonian formulation of relativistic field theories, and the proven methodology of the canonical…
Particle localization within quantum field theory is revisited. Canonical quantization of a free scalar field theory is performed in a manifestly Lorentz covariant way with respect to an arbitrary 3-surface $\Sigma$, which is the…
A covariant Hamiltonian formulation generalizing De Donder-Weyl mechanics is constructed with field strengths as velocity fields. Since the teleparallel equivalents to general relativity are quadratic in field strengths, the field-strength…
A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a…
We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of…
The functional Schr\"odinger representation of a scalar field on an $n$-dimensional static space-time background is argued to be a singular limiting case of the hypercomplex quantum theory of the same system obtained by the precanonical…
We present a quantization of the Hamiltonian and diffeomorphism constraint of canonical quantum gravity in the spin network representation. The novelty consists in considering a space of wavefunctions based on the Vassiliev knot invariants.…
We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…