arXiv subjects

Merced Montesinos

Publications and source records attributed to Merced Montesinos.

62 records · Page 4Linked to original sources

arXiv2001

Relational evolution of the degrees of freedom of generally covariant quantum theories

We study the classical and quantum dynamics of generally covariant theories with vanishing a Hamiltonian and with a finite number of degrees of freedom. In particular, the geometric meaning of the full solution of the relational evolution of the degrees of freedom is displayed, which means the determination of the total number of evolving constants of motion required. Also a method to find evolving constants is proposed. The generalized Heinsenberg picture needs M time variables, as opposed to the Heisenberg picture of standard quantum mechanics where one time variable t is enough. As an application, we study the parameterized harmonic oscillator and the SL(2,R) model with one physical degree of freedom that mimics the constraint structure of general relativity where a Schrodinger equation emerges in its quantum dynamics.

gr-qc↗

arXiv2001

Statistical mechanics of generally covariant quantum theories: A Boltzmann-like approach

We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of energy and external time. We consider a composite system formed by a large number of identical components, and apply Boltzmann's ideas and the fundamental postulates of ordinary statistical physics. The thermodynamical parameters are determined by the properties of the thermalizing interaction. We apply these ideas to a simple example, in which the component system has one physical degree of freedom and mimics the constraint algebra of general relativity.

gr-qc↗

arXiv2000

Gauge invariance of complex general relativity

In this paper it is implemented how to make compatible the boundary conditions and the gauge fixing conditions for complex general relativity written in terms of Ashtekar variables using the Henneaux-Teitelboim-Vergara approach. Moreover, it is found that at first order in the gauge parameters, the Hamiltonian action is (on shell) fully gauge-invariant under the gauge symmetry generated by the first class constraints in the case when spacetime $\cal M$ has the topology ${\cal M}= R \times Σ$ and $Σ$ has no boundary. Thus, the statement that the constraints linear in the momenta do not contribute to the boundary terms is right, but only in the case when $Σ$ has no boundary.

gr-qc↗

arXiv1999

Minimal coupling and Feynman's proof

The non quantum relativistic version of the proof of Feynman for the Maxwell equations is discussed in a framework with a minimum number of hypotheses required. From the present point of view it is clear that the classical equations of motion corresponding to the gauge field interactions can be deduced from the minimal coupling rule, and we claim here resides the essence of the proof of Feynman.

quant-ph↗

arXiv1999

Exact solutions of n-level systems and gauge theories

We find a relationship between unitary transformations of the dynamics of quantum systems with time-dependent Hamiltonians and gauge theories. In particular, we show that the nonrelativistic dynamics of spin-$\frac12$ particles in a magnetic field $B^i (t)$ can be formulated in a natural way as an SU(2) gauge theory, with the magnetic field $B^i(t)$ playing the role of the gauge potential A^i. The present approach can also be applied to systems of n levels with time-dependent potentials, U(n) being the gauge group. This geometric interpretation provides a powerful method to find exact solutions of the Schrödinger equation. The root of the present approach rests in the Hermiticity property of the Hamiltonian operators involved. In addition, the relationship with true gauge symmetries of n-level quantum systems is discussed.

quant-ph↗

arXiv1999

SL(2,R) model with two Hamiltonian constraints

We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one Hamiltonian constraint associated with each space point. We solve the classical and quantum dynamics of the model, which turns out to be governed by an SL(2,R) gauge symmetry, local in time. In classical theory, we solve the equations of motion, find a SO(2,2) algebra of Dirac observables, find the gauge transformations for the Lagrangian and canonical variables and for the Lagrange multipliers. In quantum theory, we find the physical states, the quantum observables, and the physical inner product, which is determined by the reality conditions. In addition, we construct the classical and quantum evolving constants of the system. The model illustrates how to describe physical gauge-invariant relative evolution when coordinate time evolution is a gauge.

gr-qc↗

arXiv1998

The fermionic contribution to the spectrum of the area operator in nonperturbative quantum gravity

The role of fermionic matter in the spectrum of the area operator is analyzed using the Baez--Krasnov framework for quantum fermions and gravity. The result is that the fermionic contribution to the area of a surface $S$ is equivalent to the contribution of purely gravitational spin network's edges tangent to $S$. Therefore, the spectrum of the area operator is the same as in the pure gravity case.

gr-qc↗

arXiv1998

Exact inflationary solutions

We present a new class of exact inflationary solutions for the evolution of a universe with spatial curvature, filled with a perfect fluid, a scalar field with potential $V_{\pm}(ϕ)=λ(ϕ^2\pmδ^2)^2$ and a cosmological constant $Λ$. With the $V_+(ϕ)$ potential and a negative cosmological constant, the scale factor experiments a graceful exit. We give a brief discussion about the physical meaning of the solutions.

gr-qc↗