Julian Schwinger--Recollections from many decades
I present some reminiscences, both personal and scientific, over a lifetime of admiration of, and friendship with, one of the Grandmasters of our subject.
physics.hist-ph↗
arXiv subjects
S. Deser
Publications and source records attributed to S. Deser.
Higher curvature gravities, unlike GR, cannot be bootstrapped from their (usual) linearizations
We show that higher curvature order gravities, in particular the propagating quadratic curvature models, cannot be derived by self-coupling from their linear, flat space, forms, except through an unphysical version of linearization; only GR can. Separately, we comment on an early version of the self-coupling bootstrap.
gr-qc↗
Truth, Beauty and Supergravity
I use Supergravity as a test case to study the role and uses of elegance/simplicity in formulating and evaluating physical models, whose sole criterion is of course truth: an observationally verified description of Nature within a certain range of scales.
physics.hist-ph↗
One-loop gravity divergences in D>4 cannot all be removed
Unlike the one-loop QG divergences in D=4, which can all be transformed away, those in arbitrary higher (even) dimension cannot.
gr-qc↗
Massive to gauge field reduction and gravitational wave zone information
We show explicitly that massive, Abelian, vector, just like (properly defined) massive tensor, fields limit smoothly to their massless, gauge, versions: they emit only maximal helicity radiation and mediate Coulomb and (special relativistic) Newtonian, forces between their (conserved) sources. Our main motivation, though, is to show that the recent gravitational wave detection probably cannot directly rule out very long-range gravity: Even though the waves were emitted in a strong field regime, their being detected in the weak field wave zone means the above equivalences apply. There remains the, not unlikely, possibility that no strong field generation of radiation in massive models can reproduce the observed ring-down patterns. Separately, the smooth linear limiting behaviors show that the discontinuity lies not in the mass alone, but rather in Abelian versus non-Abelian, Yang-Mills and General Relativity, regimes, whose respective massive versions are known to be non-physical.
gr-qc↗
Non-linear duality invariant partially massless models?
We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Our models mimic Dirac-Born-Infeld theory but it is unclear whether they are Lagrangian.
hep-th↗
Renormalizability Properties of Supergravity
The possible local counterterms to supergravity are investigated to all loop orders. Supersymmetry implies that (1) supergravity-matter coupling is one-loop nonrenormalizable, with a specific counterterm; (2) pure supergravity is renormalizable at both one and two loops; (3) it fails at three loops; (4) extended supergravity models may avoid the three-loop catastrophe, and have no dangerous local counterterms to any order. In that case, the nonleading divergences could be removed by field redefinitions, which would establish renormalizability for these systems.
hep-th↗
Propagation peculiarities of mean field massive gravity
Massive gravity (mGR) describes a dynamical "metric" on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its "mean field theory". Analyzing mean field massive gravity propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita--Schwinger (RS) theory. The fiducial and mGR mean field background metrics in the mean field mGR model correspond to the RS Minkowski metric and external EM field. The common implications in both systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories. Although both can still be considered as predictive effective models in the weak regime, their lower helicities exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. This "crystal-like" phenomenon of differing helicities having differing propagation speeds in both mean field mGR and mGR is a peculiar feature of these models.
hep-th↗
Bel-Robinson as stress-tensor gradients and their extensions to massive spin (0,1,2)
We show that the Bel-Robinson (BR) tensor is - generically, as well as in its original GR setting - an autonomously conserved part of the, manifestly conserved, double gradient of a system's stress-tensor. This suggests its natural extension from GR to matter models, first to (known) massless scalars and vectors, then to massive ones, including tensors. These massive versions are to be expected, given that they arise upon KK reduction of massless D+1 ones. We exhibit the resulting spin (0, 1, 2) "massive" BR.
gr-qc↗
The legacy of ADM
This tribute to the memory of my old friend and collaborator, Richard Arnowitt, focuses on the history, results and physical significance of the Arnowitt-Deser-Misner formulation of General Relativity, starting from its birth in 1958-9 through its completion, in a series of over a dozen papers, in 1962-3. A few of its later applications are also reviewed.
gr-qc↗
Self-Interaction and Gauge Invariance
A simple unified closed form derivation of the non-linearities of the Einstein, Yang-Mills and spinless (e.g., chiral) meson systems is given. For the first two, the non-linearities are required by locality and consistency; in all cases, they are determined by the conserved currents associated with the initial (linear) gauge invariance of the first kind. Use of first-order formalism leads uniformly to a simple cubic self-interaction.
gr-qc↗
Covariant constraints for generic massive gravity and analysis of its characteristics
We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates five degrees of freedom; this is also verified by a new and streamlined Hamiltonian description. The constraint's covariant expression permits computation of the model's caustics. Although new features such as the dynamical Riemann tensor appear in the characteristic matrix, the model still exhibits the pathologies uncovered in earlier work: superluminality and likely acausalities.
hep-th↗
Problems of Massive Gravities
The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring explicit solutions. We review this method and its application to massive gravity theories to show the limitations of these models' physical viability: Among their problems are loss of unique evolution, superluminal signals, matter coupling inconsistencies and micro-acausality (propagation of signals around local closed timelike/causal curves). We extend previous no-go results to the entire three-parameter range of massive gravity theories. It is also argued that bimetric models suffer a similar fate.
hep-th↗
Duality invariance of $s \ge 3/2$ fermions in AdS
We show that in D=4 AdS, $s\ge 3/2$ partially massless (PM) fermions retain the duality invariances of their flat space massless counterparts. They have tuned ratios $ {m^2}/{M^2}\ne 0$ that turn them into sums of effectively massless unconstrained helicity $\pm(s,\cdots,\frac{3}{2})$ excitations, shorn of the lowest (non-dual)\helicity $\pm \frac{1}{2}$-rung and -more generally- of succeeding higher rung as well. Each helicity mode is separately duality invariant, like its flat space counterpart.
hep-th↗
Unconstrained canonical action for, and positive energy of, massive spin 2
Filling a much-needed gap, we exhibit the D=4 Fierz-Pauli (FP) massive s=2 action, and its--manifestly positive--energy, in terms of its 2s+1=5 unconstrained helicity (2,1,0) excitations, after reducing and diagonalizing the troublesome helicity-0 sector.
gr-qc↗
Non-Einstein source effects in massive gravity
We exhibit novel effects (absent in GR) of sources in massive gravity. First, we show that removing its ghost mode forces a field-current identity: The metric's trace is locally proportional to that of its stress tensor; a point source implies a metric singularity enhanced by the square of the graviton's range. Second, exterior solutions acquire spatial stress hair--their metric components depend on the interior T_ij. Also, in contrast to naive expectations, the Newtonian potential of a source is now determined by both its spatial stress and mass. Our explicit results are obtained at linear, Fierz-Pauli, level, but qualitatively persist nonlinearly.
gr-qc↗
Superluminal Propagation and Acausality of Nonlinear Massive Gravity
Massive gravity is an old idea: trading geometry for mass. Much effort has been expended on establishing a healthy model, culminating in the current ghost-free version. We summarize here our recent findings -- that it is still untenable -- because it is locally acausal: CTC solutions can be constructed in a small neighborhood of any event.
hep-th↗
Observational Viability and Stability of Nonlocal Cosmology
We show that a class of nonlocal gravity models, proposed to explain current cosmic acceleration without dark energy, passes two major tests: First, they can be defined so as not to alter the, observationally correct, general relativity predictions for gravitationally bound systems. Second, they are stable, ghost-free, with no additional excitations beyond those of general relativity. In this they differ from their, ghostful, localized versions. The systems' initial value constraints are the same as in general relativity, and our nonlocal modifications never convert the original gravitons into ghosts.
astro-ph.CO↗