<i>Spinors and Space-Time, Volume I: Two-Spinor Calculus and Relativistic Fields</i>

Penrose, Roger; Rindler, Wolfgang; Goldberg, Joshua N.

doi:10.1063/1.2814899

Cited by 342 publications

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“…More general considerations on the transformation properties of (spin weighted) spherical harmonics under Lorentz transformations can be found in [17,18,19]. For later use, let us denote the standard, globally well-defined BMS algebra on the sphere by bms glob 4 .…”

Section: Globally Well-defined Symmetry Algebramentioning

confidence: 99%

BMS charge algebra

Barnich

Troessaert

2011

J. High Energ. Phys.

408

745

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ABSTRACT. The surface charges associated with the symmetries of asymptotically flat four dimensional spacetimes at null infinity are constructed. They realize the symmetry algebra in general only up to a field-dependent central extension that satisfies a suitably generalized cocycle condition. This extension vanishes when using the globally well defined BMS algebra. For the Kerr black hole and the enlarged BMS algebra with both supertranslations and superrotations, some of the supertranslations charges diverge whereas there are no divergences for the superrotation charges. The central extension is proportional to the rotation parameter and involves divergent integrals on the sphere.

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Section: Globally Well-defined Symmetry Algebramentioning

confidence: 99%

BMS charge algebra

Barnich

Troessaert

2011

J. High Energ. Phys.

408

745

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“…Of the two dimensions, one represents time and the other is used for listing several systems (such as a, b, app 1 , app 2 , etc.). This notation is based on a similar diagram notation developed by Penrose and Rindler [41] for the tensors of general relativity.…”

Section: F Diagram Notationmentioning

confidence: 99%

The Quantum Formalism and the GRW Formalism

Tumulka

Zanghı̀

2012

J Stat Phys

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The Ghirardi-Rimini-Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world. PACS: 03.65.Ta. Key words: quantum theory without observers; Ghirardi-RiminiWeber (GRW) theory of spontaneous wave function collapse; empirical predictions; quantum measurement theory; predicted deviations from quantum mechanics; primitive ontology; limitations to knowledge; positive-operator-valued measure (POVM); completely positive superoperator. *

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“…Tensors are indicated using the abstract index notation (see, for example, [18] or [20]). Enclosure of indices in square brackets or parentheses indicates complete skew-symmetrization or complete symmetrization over tensor factors corresponding to the enclosed indices.…”

Section: Preliminariesmentioning

confidence: 99%

Remarks on symplectic sectional curvature

Fox

2017

Differential Geometry and its Applications

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Abstract. In [11], I. M. Gelfand, V. Retakh, and M. Shubin defined the symplectic sectional curvature of a torsion-free connection preserving a symplectic form. The present article defines the corresponding notion of constant symplectic sectional curvature and characterizes this notion in terms of the curvature tensor of the symplectic connection and its covariant derivatives. Some relations between various more general conditions on the symplectic sectional curvature and the geometry of the symplectic connection or that induced on a symplectic submanifold are explored as well.

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Spinors and Space-Time, Volume I: Two-Spinor Calculus and Relativistic Fields

Cited by 342 publications

References 0 publications

BMS charge algebra

BMS charge algebra

The Quantum Formalism and the GRW Formalism

Remarks on symplectic sectional curvature

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