Quantum cosmological intertwining: Factor ordering and boundary conditions from hidden symmetries

Abstract

We explore the implications of hidden symmetries present in a particular quantum cosmological setting, extending the results reported in [1,2]. In more detail, our case study is constituted by a spatially closed Friedmann-Lemaître-Robertson-Walker universe, in the presence of a conformally coupled scalar field. The su(1, 1) hidden symmetries of this model, together with the Hamiltonian constraint, lead to the gauge invariance of its corresponding Bargmann indices. We subsequently show that some factor-ordering choices can be related to the allowed spectrum of Bargmann indices and hence, to the hidden symmetries. Moreover, the presence of those hidden symmetries also implies a set of appropriate boundary conditions to choose from. In summary, our results suggest that factor ordering and boundary conditions can be intertwined when a quantum cosmological model has hidden symmetries.

Prospecting black hole thermodynamics with fractional quantum mechanics

“…where a prime symbol, , denotes the derivative of ψ(x) with respect to x. As pointed out by Tipler [74][75][76][77], the constant γ (with dimension of length) would be a new fundamental constant of theory. To avoid such, we set it to be zero.…”

Shape Invariant Potentials in Supersymmetric Quantum Cosmology

“…Secondly, these algebraic/group theory procedures (within the concrete use of algebras such as SO(2, 1) or SO(3)), have a striking resemblance to the approach and descriptive language used in [13,14,15,16]; a review of this idea is found in [17]. Therein, it was pointed that intertwining boundary conditions, the algebra of constraints and hidden symmetries in quantum cosmology could be quite fruitful.…”

“…Therein, it was pointed that intertwining boundary conditions, the algebra of constraints and hidden symmetries in quantum cosmology could be quite fruitful. Specifically, group/algebraic properties within ladder operators, either from angular momentum or from within the explicit presence of specific matter fields (and their properties), determined a partition of wave functions and boundary conditions, according to the Bargmann index [13,14,15,16]. Moreover, we proposed in [17] to extend this framework towards SIP, which could include well known analytically solvable cosmological cases.…”

Quantum cosmology: The (supersymmetric) door

“…Nevertheless, other boundary conditions can be put forward with well known results, which have been widely investigated in the literature, including consistency and potential observational features. It would be interesting to find some algebraic support for them, along the lines discussed in this review (and [1][2][3][4][5] ), but the statements defining the main boundary conditions are more of a 'topological' nature for the minisuperspaces involved and hence it is not obvious whether this can be achieved. Moreover, singularities of a differential nature can be present in a given cosmology and a discussion involving them as well as conditions on Ψ and admissible boundary conditions by means of the algebra of constraints is indeed quite worthy to venture into, namely within the context of hidden symmetries and 'beyond' (e.g., supersymmetry).…”