scholarly journals RESTORING TIME DEPENDENCE INTO QUANTUM COSMOLOGY

2012 ◽  
Vol 21 (11) ◽  
pp. 1242011 ◽  
Author(s):  
AHARON DAVIDSON ◽  
BEN YELLIN
Keyword(s):  
Quantum Theory ◽  
Time Dependence ◽  
Quantum Cosmology ◽  
Scale Factor ◽  
Time Dependent ◽  
Hamiltonian Constraint ◽  
Canonical Variables ◽  
Explicit Time Dependence ◽  
Dirac Brackets ◽  
Lapse Function

Mini superspace cosmology treats the scale factor a(t), the lapse function n(t) and an optional dilation field ϕ(t) as canonical variables. While pre-fixing n(t) means losing the Hamiltonian constraint, pre-fixing a(t) is serendipitously harmless at this level. This suggests an alternative to the Hartle–Hawking approach, where the pre-fixed a(t) and its derivatives are treated as explicit functions of time, leaving n(t) and a now mandatory ϕ(t) to serve as canonical variables. The naive gauge pre-fix a(t) = const . is clearly forbidden, causing evolution to freeze altogether; so pre-fixing the scale factor, say a(t) = t, necessarily introduces explicit time dependence into the Lagrangian. Invoking Dirac's prescription for dealing with constraints, we construct the corresponding mini superspace time-dependent total Hamiltonian and calculate the Dirac brackets, characterized by {n, ϕ}D ≠ 0, which are promoted to commutation relations in the quantum theory.

scholarly journals MINISUPERSPACES: OBSERVABLES AND QUANTIZATION

1993 ◽  
Vol 02 (01) ◽  
pp. 15-50 ◽  
Author(s):  
ABHAY ASHTEKAR ◽  
RANJEET TATE ◽  
CLAES UGGLA
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
Canonical Transformation ◽  
Parameter Family ◽  
Hamiltonian Constraint ◽  
Canonical Coordinates ◽  
Quantum Theories ◽  
Canonical Variables ◽  
Unitary Transformations ◽  
Homogeneous Cosmologies

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 expressions of Dirac observables, i.e. phase-space functions which commute weakly with the constraint. This, in turn, enables us to carry out a general quantization program to completion. We are also able to address the issue of time through “deparametrization” and discuss physical questions such as the fate of initial singularities in the quantum theory. We find that they persist in the quantum theory in spite of the fact that the evolution is implemented by a one-parameter family of unitary transformations. Finally, certain of these models admit conditional symmetries which are explicit already prior to the canonical transformation. These can be used to pass to the quantum theory following an independent avenue. The two quantum theories — based, respectively, on Dirac observables in the new canonical variables and conditional symmetries in the original ADM variables — are compared and shown to be equivalent.

scholarly journals Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator

2019 ◽  
Vol 35 (08) ◽  
pp. 2050041 ◽  
Author(s):  
Andreas Fring ◽  
Thomas Frith
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependence ◽  
Time Dependent ◽  
Two Dimensional ◽  
Coupling Term ◽  
Coupled Oscillator ◽  
Explicit Time Dependence ◽  
Independent Model

We provide a time-dependent Dyson map and metric for the two-dimensional harmonic oscillator with a non-Hermitian ixy coupling term. This particular time-independent model exhibits spontaneously broken [Formula: see text]-symmetry and becomes unphysical in the broken regime, with the spectrum becoming partially complex. By introducing an explicit time dependence into the Dyson map, we provide a time-dependent metric that renders the model consistent across the unbroken and broken regimes.

THE CAUSAL INTERPRETATION OF QUANTUM MECHANICS AND THE SINGULARITY PROBLEM AND TIME ISSUE IN QUANTUM COSMOLOGY

1998 ◽  
Vol 07 (02) ◽  
pp. 201-213 ◽  
Author(s):  
J. ACACIO DE BARROS ◽  
N. PINTO-NETO
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Cosmology ◽  
Interpretation Of Quantum Mechanics ◽  
Causal Interpretation ◽  
Slow Time ◽  
Singularity Problem ◽  
Classical Singularity ◽  
Lapse Function ◽  
Time Issue

We apply the causal interpretation of quantum mechanics to homogeneous quantum cosmology and show that the quantum theory is independent of any time-gauge choice and there is no issue of time. We exemplify this result by studying a particular minisuperspace model where the quantum potential driven by a prescribed quantum state prevents the formation of the classical singularity, independently on the choice of the lapse function. Hence, within the framework of the causal interpretation of quantum cosmology, the fast-slow-time gauge conjecture is incorrect for homogeneous minisuperspace models.

TIME-DEPENDENT SOLUTIONS OF 5D VACUUM EINSTEIN EQUATIONS WITH COSMOLOGICAL CONSTANT

2011 ◽  
Vol 26 (22) ◽  
pp. 1673-1679 ◽  
Author(s):  
TAE HOON LEE
Keyword(s):  
Cosmological Constant ◽  
Time Dependence ◽  
Scale Factor ◽  
Einstein Equations ◽  
Time Dependent ◽  
Vacuum Field ◽  
Field Equations ◽  
Vacuum Einstein Equations ◽  
Dimensional Gravity

We solve vacuum field equations in five-dimensional gravity with cosmological constant to determine the time-dependence of the Robertson–Walker scale factor. We discuss its cosmological implications.

scholarly journals Supersymmetric minisuperspace models in self-dual loop quantum cosmology

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
K. Eder ◽  
H. Sahlmann
Keyword(s):  
Quantum Theory ◽  
Quantum Cosmology ◽  
Natural State ◽  
Loop Quantum Cosmology ◽  
Hamiltonian Constraint ◽  
Dual Variables ◽  
Left And Right ◽  
Constraint Algebra ◽  
Gravitino Field ◽  
Supersymmetric Approach

Abstract In this paper, we study a class of symmetry reduced models of $$ \mathcal{N} $$ N = 1 super- gravity using self-dual variables. It is based on a particular Ansatz for the gravitino field as proposed by D’Eath et al. We show that the essential part of the constraint algebra in the classical theory closes. In particular, the (graded) Poisson bracket between the left and right supersymmetry constraint reproduces the Hamiltonian constraint.For the quantum theory, we apply techniques from the manifestly supersymmetric approach to loop quantum supergravity, which yields a graded analog of the holonomy-flux algebra and a natural state space.We implement the remaining constraints in the quantum theory. For a certain subclass of these models, we show explicitly that the (graded) commutator of the supersymmetry constraints exactly reproduces the classical Poisson relations. In particular, the trace of the commutator of left and right supersymmetry constraints reproduces the Hamilton constraint operator. Finally, we consider the dynamics of the theory and compare it to a quantization using standard variables and standard minisuperspace techniques.

scholarly journals Renormalization Group Approach to Pandemics as a Time-Dependent SIR Model

2021 ◽  
Vol 8 ◽  
Author(s):  
Michele Della Morte ◽  
Francesco Sannino
Keyword(s):  
Renormalization Group ◽  
Time Dependence ◽  
Recovery Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Cumulative Number ◽  
Group Approach ◽  
Renormalization Group Approach

We generalise the epidemic Renormalization Group framework while connecting it to a SIR model with time-dependent coefficients. We then confront the model with COVID-19 in Denmark, Germany, Italy and France and show that the approach works rather well in reproducing the data. We also show that a better understanding of the time dependence of the recovery rate would require extending the model to take into account the number of deaths whenever these are over 15% of the cumulative number of infected cases.

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