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Title: On consistent kinetic and derivative interactions for gravitons

Abstract

The only known fully ghost-free and consistent Lorentz-invariant kinetic term for a graviton (or indeed for any spin-2 field) is the Einstein-Hilbert term. Here we propose and investigate a new candidate family of kinetic interactions and their extensions to derivative interactions involving several spin-2 fields. These new terms generically break diffeomorphism invariance(s) and as a result can lead to the propagation of 5 degrees of freedom for a single spin-2 field — analogous to ghost-free Massive Gravity. We discuss under what circumstances these new terms can be used to build healthy effective field theories and in the process establish the ‘Jordan’ and ‘Einstein’ frame pictures for Massive-, Bi- and Multi-Gravity.

Authors:
 [1]
  1. Astrophysics, University of Oxford, DWB, Keble Road, Oxford, OX1 3RH (United Kingdom)
Publication Date:
Sponsoring Org.:
SCOAP3, CERN, Geneva (Switzerland)
OSTI Identifier:
22454538
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 04; Other Information: PUBLISHER-ID: JCAP04(2015)025; OAI: oai:repo.scoap3.org:9941; Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DEGREES OF FREEDOM; FIELD THEORIES; GRAVITONS; INTERACTIONS; LORENTZ INVARIANCE; NONLUMINOUS MATTER; SPIN

Citation Formats

Noller, Johannes. On consistent kinetic and derivative interactions for gravitons. United States: N. p., 2015. Web. doi:10.1088/1475-7516/2015/04/025.
Noller, Johannes. On consistent kinetic and derivative interactions for gravitons. United States. doi:10.1088/1475-7516/2015/04/025.
Noller, Johannes. Fri . "On consistent kinetic and derivative interactions for gravitons". United States. doi:10.1088/1475-7516/2015/04/025.
@article{osti_22454538,
title = {On consistent kinetic and derivative interactions for gravitons},
author = {Noller, Johannes},
abstractNote = {The only known fully ghost-free and consistent Lorentz-invariant kinetic term for a graviton (or indeed for any spin-2 field) is the Einstein-Hilbert term. Here we propose and investigate a new candidate family of kinetic interactions and their extensions to derivative interactions involving several spin-2 fields. These new terms generically break diffeomorphism invariance(s) and as a result can lead to the propagation of 5 degrees of freedom for a single spin-2 field — analogous to ghost-free Massive Gravity. We discuss under what circumstances these new terms can be used to build healthy effective field theories and in the process establish the ‘Jordan’ and ‘Einstein’ frame pictures for Massive-, Bi- and Multi-Gravity.},
doi = {10.1088/1475-7516/2015/04/025},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 04,
volume = 2015,
place = {United States},
year = {Fri Apr 17 00:00:00 EDT 2015},
month = {Fri Apr 17 00:00:00 EDT 2015}
}
  • The only known fully ghost-free and consistent Lorentz-invariant kinetic term for a graviton (or indeed for any spin-2 field) is the Einstein-Hilbert term. Here we propose and investigate a new candidate family of kinetic interactions and their extensions to derivative interactions involving several spin-2 fields. These new terms generically break diffeomorphism invariance(s) and as a result can lead to the propagation of 5 degrees of freedom for a single spin-2 field—analogous to ghost-free Massive Gravity. We discuss under what circumstances these new terms can be used to build healthy effective field theories and in the process establish the 'Jordan' andmore » 'Einstein' frame pictures for Massive-, Bi- and Multi-Gravity.« less
  • The consistent couplings that can be added to a 'free' theory whose Lagrangian action is written as the sum between the linearized Weyl action and that of a massless Majorana spinor are constructed by means of deforming the solution to the classical master equation.
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  • We develop a self-consistent method to solve the basic equation for the self-energy correction of the Hubbard model obtained previously. The term ..pi..(..delta..) involving second functional derivatives is neglected, and the quantities < N/sub R sigma/(t) > and < C/sub R sigma//sup dagger/(t) C/sub R'' sigma/(t) > are initially assumed to be independent of the external fields epsilon(sigma) and epsilon(sigma-bar). Under these restrictions, the complete self-energy correction is shown to be expanded in powers of epsilon (sigma) and epsilon (sigma-bar) in the form ..sigma../sub R R prime sigma/(tt') = xi/sub 0/(RR'sigma-bart) delta/sub tt'/ + ..sigma../sub n//sub 0/ ..sigma../sub R primemore » prime/ ..sigma../sub R prime prime prime/ xi/sup( n)/ (RR';R''R''') epsilon (R''R'''sigmat) delta/sub t t prime/, where xi/sub 0/ consists of all possible terms linear in epsilon (sigma-bar), while xi/sup( n)/ is made up of all possible terms of the nth degree in epsilon (sigma-bar). Equations for xi/sub 0/ and xi/sup( n)/ are solved exactly and the resulting series is summed analytically, yielding a compact and complete analytic solution for the restricted equation results. The part which is linear in epsilon is shown to be equal to the perturbation result obtained in the previous paper;the claim that the perturbation result is exact through terms linear in epsilon is thus confirmed. The method is extended and the effect of delta < N >/deltaepsilon and delta< C/sup dagger/C > /deltaepsilon is included. The effect is found to eliminate the difficulty that the value of one of the terms in the self-energy correction is abnormally overestimated in the previous result in the split-band, half-filled limit.« less
  • Proofs from different theoretical frameworks, namely, the Hohenbergh-Kohn theorems, the Kohn-Sham scheme, and the first-order density matrix representation, have been presented in this paper to show that the functional derivative of the noninteracting kinetic energy density functional can uniquely be expressed as the negative of the Kohn-Sham effective potential, arbitrary only to an additive orbital-independent constant. Key points leading to the current result as well as confusion about the quantity in the literature are briefly discussed.