New Hamiltonian analysis of Regge-Teitelboim minisuperspace cosmology

Abstract

A new Hamiltonian formulation of the minisuperspace cosmology following from the geodetic brane gravity model introduced by Regge and Teitelboim is presented. The model is considered in the framework of higher derivative theories which facilitates Hamiltonian formulation. The analysis is done using the equivalent first-order approach. The gauge generator containing the exact number of gauge parameters is constructed. Equivalence between the gauge and reparametrization symmetries has been demonstrated. Complete gauge fixed computations have been provided and formal quantization is done indicating the Wheeler DeWitt equation. Compatibility with existing results is shown.

BRST symmetry for Regge–Teitelboim-based minisuperspace models

“…A Hamiltonian analysis of this minisuperspace model has already been performed in different ways and quantization was further explored in [4][5][6][7][8][9]. Particularly, in [4] the same model with the higher derivative term was analyzed without neglecting the surface term. There the authors have explored the reparammetrization symmetries of the model exploiting the first order formalism developed earlier in [10].…”

“…Section 4 is our main contribution which we devoted to the exploration of the BRST symmetries. In this section we calculated the BRST transformation using the same gauges as considered in [4]. Also, we calculate the BRST charge and the Jacobian of the path integral under FFBRST symmetry, in Sect.…”

“…The existence of the primary first-class constraint is in conformity with one independent gauge symmetry, which is in the course of the calculation identified as reparametrization invariance. To canonically quantize the model two gauges were proposed in [4]. We considered the same gauge-fixing conditions to find their implications in the BRST symmetries.…”

“…With a Friedmann-Rebertson-Lamaitre-Walker (FRLW) background we construct the minisuperspace version of the EH action which is analogous to the minisuperspace version of the Regge-Teitelboim (RT) model [3]. A Hamiltonian analysis of this minisuperspace model has already been performed in different ways and quantization was further explored in [4][5][6][7][8][9]. Particularly, in [4] the same model with the higher derivative term was analyzed without neglecting the surface term.…”

A first-class approach of higher derivative Maxwell–Chern–Simons–Proca model

“…As the second term in the action (1) contains higher derivative terms ∂ λ ∂ λ A μ , the canonical analysis will be done by a variant of Ostrogradsky method [46][47][48][49][50][51] developed in Ref. [52], based on an equivalent first order formalism [53,54] and applied to a number of particle and field theoretic models [52,[55][56][57]. The Hamiltonian analysis of a higher derivative extension of a theory displays a constraints set with a more complicated structure than the constraints set of the usual theory (where the Lagrangian is a function of the fields and their first derivatives only).…”