相关论文: Quantisation, Representation and Reduction; How Sh…

In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…

One of the hardest problems to tackle in the dynamics of canonical approaches to quantum gravity is that of the Hamiltonian constraint. We investigate said problem in the context of formal geometric quantization. We study the implications…

We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3--geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the…

We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…

A relativistic Hamiltonian mechanical system is seen as a conservative Dirac constraint system on the cotangent bundle of a pseudo-Riemannian manifold. We provide geometric quantization of this cotangent bundle where the quantum constraint…

The basic features of the complex canonical formulation of general relativity and the recent developments in the quantum gravity program based on it are reviewed. The exposition is intended to be complementary to the review articles…

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…

A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation…

For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…

We study a generalized version of the Hamiltonian constraint operator in nonperturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU(2) representations in the regularization of the operator, in…

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 review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…

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 canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…

The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other…

Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…

Last years a certain attention was attracted to the statement that Hamiltonian formulations of General Relativity, in which different parametrizations of gravitational variables were used, may not be related by a canonical transformation.…

Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities.…

We show in this article how the usual hamiltonian formalism of General Relativity should be modified in order to allow the inclusion of the Euclidean classical solutions of Einstein's equations. We study the effect that the dynamical change…