相关论文: Geometric Momentum: the Proper Momentum for a Free…
Fermions are coupled to the Einstein-Cartan system in the canonical formulation, including the cosmological, the Barbero-Immirzi, and the non-minimal coupling constants. The resulting ten first-class constraints generate gauge…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford Algebra. The momentum…
For a particle moves on a 2D surface f(x)=0 embedded in 3D Euclidean space, the geometric momentum and potential are simultaneously admissible within the Dirac canonical quantization scheme for constrained motion. In our approach, not the…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
A geometric potential $V_C$ depending on the mean and Gaussian curvatures of a surface $\Sigma$ arises when confining a particle initially in a three-dimensional space $\Omega$ onto $\Sigma$ when the particle Hamiltonian $H_\Omega$ is taken…
An isolated classical chaotic system, when driven by the slow change of several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations we show that…
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a…
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
A summary is given of some results and perspectives of the hamiltonian ADM approach to 2+1 dimensional gravity. After recalling the classical results for closed universes in absence of matter we go over the the case in which matter is…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a binary system of complex relations…
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…
The coupled angular momentum is an integrable system with two degrees of freedom which is fundamental in physics and the theory of integrable systems. It is obtained by coupling two angular momenta. We construct a $p$-adic analog of this…
In this paper we present some results obtained in a previous paper about the Cartan's approach to Riemannian normal coordinates and our conformal transformations among pseudo-Riemannian manifolds. We also review the classical and the…
In two-dimensional space-time, point particles can experience a geometric, dimension-specific gravity force, which modifies the usual geodesic equation of motion and provides a link between the cosmological constant and the vacuum…