Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · gr-qc/9602031

Free Quantum Fields on the Poincare' Group

M. Toller
View original source ↗Read source document ↗Export metadata ↓

Abstract

A class of free quantum fields defined on the Poincare' group, is described by means of their two-point vacuum expectation values. They are not equivalent to fields defined on the Minkowski spacetime and they are "elementary" in the sense that they describe particles that transform according to irreducible unitary representations of the symmetry group, given by the product of the Poincare' group and of the group SL(2, C) considered as an internal symmetry group. Some of these fields describe particles with positive mass and arbitrary spin and particles with zero mass and arbitrary helicity or with an infinite helicity spectrum. In each case the allowed SL(2, C) internal quantum numbers are specified. The properties of local commutativity and the limit in which one recovers the usual field theories in Minkowski spacetime are discussed. By means of a superposition of elementary fields, one obtains an example of a field that present a broken symmetry with respect to the group Sp(4, R), that survives in the short-distance limit. Finally, the interaction with an accelerated external source is studied and and it is shown that, in some theories, the average number of particles emitted per unit of proper time diverges when the acceleration exceeds a finite critical value.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. Toller. 1996-02-14. Free Quantum Fields on the Poincare' Group. https://doi.org/10.1063/1.531537

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

An upper bound on the minimum orbital period of black holes

Previous research has focused on establishing lower bounds on the minimum orbital period of black holes. In this work, we explore the complementary question of whether an upper bound exists for the minimum orbital period of black holes. We investigate the minimum orbital periods of three types of black holes: Schwarzschild, Reissner-Nordström and Kerr-Newman black holes. We find that the minimum orbital period of these black holes is bounded by an upper limit $T_{min} \leqslant 6\sqrt{3}πM$, where $M$ is the black hole mass. Our results suggest that this upper bound on the minimum orbital period may be a general property in black hole spacetimes.

gr-qc↗
arXiv2026

Bounds on the minimum orbital period in the background of 5-dimensional charged black holes

In this paper, we study the upper and lower bounds on the minimum orbital period of 5-dimensional charged black holes. Our results indicate that the upper bound of the minimum orbital period corresponds to non-charged black holes, while the lower bound is achieved in the case of maximally charged black holes. We further establish precise analytical expressions for the upper and lower bounds of the minimum orbital period. Our findings provide valuable insights into 5-dimensional charged black holes and help constrain theoretical gravity models.

gr-qc↗
arXiv2026

Analysis of minimum orbital periods around d-dimensional charged black holes

This paper investigates the bounds on the minimum orbital period for test objects around d-dimensional charged black holes in asymptotically flat spacetimes. We derive the exact critical radius and the minimum orbital period. We then prove analytically that the minimum orbital period decreases strictly as the charge of the black hole increases. Thus, the upper limit is reached for an uncharged black hole, while the lower limit is attained for a maximally charged one, and the two bounds take the closed form $\frac{2π(d-2)}{d-3}[(d-2)M]^{\frac{1}{d-3}}\leqslant T_{min} \leqslant 2π\sqrt{\frac{d-1}{d-3}}\,[(d-1)M]^{\frac{1}{d-3}}$. Since the minimum period equals $2π$ times the shadow radius, the upper bound is equivalently a universal upper bound on the shadow radius. These results improve our understanding of dynamics around d-dimensional black holes and impose constraints on candidate gravity theories.

gr-qc↗