TY - JOUR
T1 - Polymer quantization, stability and higher-order time derivative terms
AU - Cumsille, Patricio
AU - Reyes, Carlos M.
AU - Ossandon, Sebastian
AU - Reyes, Camilo
N1 - Publisher Copyright:
© 2016 World Scientific Publishing Company.
PY - 2016/3/30
Y1 - 2016/3/30
N2 - The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais-Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.
AB - The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais-Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.
KW - Higher time derivatives
KW - polymer quantization
KW - stability
UR - http://www.scopus.com/inward/record.url?scp=84962277705&partnerID=8YFLogxK
U2 - 10.1142/S0217751X16500408
DO - 10.1142/S0217751X16500408
M3 - Article
AN - SCOPUS:84962277705
VL - 31
JO - International Journal of Modern Physics A
JF - International Journal of Modern Physics A
SN - 0217-751X
IS - 9
M1 - 1650040
ER -