Formalism
Definition
Spacetime configurations
Properties
Spacetimes
black hole spacetimes | vanishing angular momentum | positive angular momentum |
---|---|---|
vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
Quantum theory
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
superalgebra and (synthetic ) supergeometry
fields and particles in particle physics
and in the standard model of particle physics:
matter field fermions (spinors, Dirac fields)
flavors of fundamental fermions in the standard model of particle physics: | |||
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generation of fermions | 1st generation | 2nd generation | 3d generation |
quarks () | |||
up-type | up quark () | charm quark () | top quark () |
down-type | down quark () | strange quark () | bottom quark () |
leptons | |||
charged | electron | muon | tauon |
neutral | electron neutrino | muon neutrino | tau neutrino |
bound states: | |||
mesons | light mesons: pion () ρ-meson () ω-meson () f1-meson a1-meson | strange-mesons: ϕ-meson (), kaon, K*-meson (, ) eta-meson () charmed heavy mesons: D-meson (, , ) J/ψ-meson () | bottom heavy mesons: B-meson () ϒ-meson () |
baryons | nucleons: proton neutron |
(also: antiparticles)
hadrons (bound states of the above quarks)
minimally extended supersymmetric standard model
bosinos:
dark matter candidates
Exotica
In quantum field theory the term gravitino refers to the superpartner of the graviton, a Rarita-Schwinger field of spin that appears in supergravity.
In supergravity a field history is a connection on super spacetime locally given by a super Lie algebra-valued differential form
on spacetime with values in the super Poincaré Lie algebra. Its components in the spin representation is the gravitino field.
The name derives from the fact that the other two components are identified in gravity with the graviton field.
The Rarita-Scwinger-like equation of motion for the gravitino in D=11 N=1 supergravity is (on any chart)
(due to Cremmer, Julia & Scherk 1978, p. 411, cf. Castellani, D’Auria & Fré 1991, §III.8, p. 910),
where
are the bosonic frame field components of the gravitino field strength:
So for each value of the indices this is a smooth function from the chart to the real vector space underlying the irreducible real representation of ,
is the skew-symmetrized product of Clifford algebra basis elements in the irreducible real representation of ,
here acting pointwise on the component spinors of ,
the Einstein summation convention implies summation over repeated indices.
(implications of 11d gravitino equation)
We have the following implications of the gravitino equation (1) in D=11 supergravity:
Equation (2) follows immediately by Clifford contraction:
Equation (3) follows by the contraction
and using that the second summand vanishes by assumption (1).
For equation (4) we compute as follows:
where in the second and fourth step we used (3).
For (5) we consider this contraction:
where in the second step we used (4).
See also
Classification of possible long-range forces, hence of scattering processes of massless fields, by classification of suitably factorizing and decaying Poincaré-invariant S-matrices depending on particle spin, leading to uniqueness statements about Maxwell/photon-, Yang-Mills/gluon-, gravity/graviton- and supergravity/gravitino-interactions:
Steven Weinberg, Feynman Rules for Any Spin. 2. Massless Particles, Phys. Rev. 134 (1964) B882 (doi:10.1103/PhysRev.134.B882)
Steven Weinberg, Photons and Gravitons in -Matrix Theory: Derivation of Charge Conservationand Equality of Gravitational and Inertial Mass, Phys. Rev. 135 (1964) B1049 (doi:10.1103/PhysRev.135.B1049)
Steven Weinberg, Photons and Gravitons in Perturbation Theory: Derivation of Maxwell’s and Einstein’s Equations,” Phys. Rev. 138 (1965) B988 (doi:10.1103/PhysRev.138.B988)
Paolo Benincasa, Freddy Cachazo, Consistency Conditions on the S-Matrix of Massless Particles (arXiv:0705.4305)
David A. McGady, Laurentiu Rodina, Higher-spin massless S-matrices in four-dimensions, Phys. Rev. D 90, 084048 (2014) (arXiv:1311.2938, doi:10.1103/PhysRevD.90.084048)
Review:
Claus Kiefer, section 2.1.3 of: Quantum Gravity, Oxford University Press 2007 (doi:10.1093/acprof:oso/9780199585205.001.0001, cds:1509512)
Daniel Baumann, What long-range forces are allowed?, 2019 (pdf)
Discussion of the gravitino as a dark matter candidate:
A proposal for super-heavy gravitinos as dark matter, by embedding D=4 N=8 supergravity into E10-U-duality-invariant M-theory:
Krzysztof A. Meissner, Hermann Nicolai: Standard Model Fermions and Infinite-Dimensional R-Symmetries, Phys. Rev. Lett. 121 091601 (2018) [arXiv:1804.09606, doi:10.1103/PhysRevLett.121.091601]
Krzysztof A. Meissner, Hermann Nicolai, Planck Mass Charged Gravitino Dark Matter, Phys. Rev. D 100, 035001 (2019) (arXiv:1809.01441)
following the proposal towards the end of
Murray Gell-Mann, introductory talk at Shelter Island II, 1983 (pdf)
in: Shelter Island II: Proceedings of the 1983 Shelter Island Conference on Quantum Field Theory and the Fundamental Problems of Physics. MIT Press. pp. 301–343. ISBN 0-262-10031-2.
Further discussion:
Krzysztof A. Meissner, Hermann Nicolai, Supermassive gravitinos and giant primordial black holes (arXiv:2007.11889)
Krzysztof A. Meissner, Hermann Nicolai, Evidence for a stable supermassive gravitino with charge ? [arXiv:2303.09131]
Adrianna Kruk, Michał Lesiuk, Krzysztof A. Meissner, Hermann Nicolai: Signatures of supermassive charged gravitinos in liquid scintillator detectors [arXiv:2407.04883]
Last revised on October 27, 2024 at 10:30:35. See the history of this page for a list of all contributions to it.