Quantization of spacetime based on a spacetime interval operator

Abstract

Motivated by both concepts of R.J. Adler's recent work on utilizing Clifford algebra as the linear line element ds = γµ dX µ , and the fermionization of the cylindrical worldsheet Polyakov action, we introduce a new type of spacetime quantization that is fully covariant. The theory is based on the reinterpretation of Adler's linear line element as ds = γµ λγ µ , where λ is the characteristic length of the theory. We name this new operator as "spacetime interval operator", and argue that it can be regarded as a natural extension to the one-forms in the U (su(2)) non-commutative geometry. By treating Fourier momentum as the particle momentum, the generalized uncertainty principle of the U (su(2)) non-commutative geometry, as an approximation to the generalized uncertainty principle of our theory, is derived, and is shown to have a lowest order correction term of the order p 2 similar to that of Snyder's. The holography nature of the theory is demonstrated, and the predicted fuzziness of the geodesic is shown to be much smaller than conceivable astrophysical bounds.

Pair production in Reissner-Nordström-Anti de Sitter black holes *

“…It was shown that the abovementioned relation also holds for a charged scalar field [11] and for a charged spinor field [4], both in a four-dimensional near extremal RN black hole.…”

“…Usually the equation of motions (EoMs) of quantum fields in a general black hole background is difficult to solve analytically in full spacetime. However, when the symmetry of the spacetime geometry is enhanced under some conditions, the problem becomes manageable; for this reason, in a series of recent studies, the spontaneous pair production of charged particles has been systematically studied in near extremal charged black holes, including the RN black hole [3][4][5] and the Kerr-Newman (KN) black hole [6,7], in which the near horizon geometry is enhanced into AdS 2 or warped AdS 3 in the near extremal limit. Owing to the enhanced near horizon symmetry, the explicit forms of the pair production rate and other 2-point correlation functions have been obtained and their holographic descriptions have been found based on the RN/CFT [8][9][10][11][12][13] and KN/CFTs dualities [14][15][16].…”

A generic unitary black-hole evaporation model based on first principles

“…where j is the spherical Bessel of the 1st kind and d is, as defined previously, the dimension of the configuration space for the positive-mass subsystem. This is typical for fields in a non-commutative space [35][36][37][38], which hints at the existence of a microscopically discrete horizon [39,40], despite the semi-classical nature of our analysis.…”

Generalized Holographic Principle, Gauge Invariance and the Emergence of Gravity à la Wilczek

“…Almost one hundred years of attempts to quantize gravity suggest that physical perspective may be responsible for this failure (Garay, 1995). While continuing to seek an UV-complete theory of either General Relativity (GR) or one of its possible extensions (Polchinski, 1998;Rovelli, 2004;Modesto, 2012;Modesto and Rachwal, 2014), an alternative option is to look at gravity as an emergent phenomenon (Jacobson, 1995;Barcelo et al, 2005;Van Raamsdonk, 2010;Verlinde, 2011;Swingle and Van Raamsdonk, 2014;Chiang et al, 2016;Oh et al, 2018). Among many possible instantiations of this simple idea stands a paradigm of emergence that aims at recovering gravity via its analogical similarity with Yang-Mills gauge theories.…”