There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Superstring theoryをめぐって(放談室)

We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali-Gabadadze-Porrati model, cascading gravity and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware-Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally we present alternative and related models of massive gravity such as new massive gravity, Lorentz-violating massive gravity and non-local massive gravity.

Massive Gravity

Beyond the cosmological standard model

In this article, using the language of jet space, we propose a functional class space for pseudo-local functionals. We test this functional class proposal in a number of examples ranging from string-field-theory to AdS/CFT dualities. Implications of the locality proposal at the quartic order are also discussed.

Pseudo-local Theories: A Functional Class Proposal

The spectrum of Prokushkin--Vasiliev Theory is puzzling in light of the Gaberdiel--Gopakumar conjecture because it generically contains an additional sector besides higher-spin gauge and scalar fields. We find the unique truncation of the theory avoiding this problem to order 2 in perturbations around AdS$_3$. The second-order backreaction on the physical gauge sector induced by the scalars is computed explicitly. The cubic action for the physical fields is determined completely. We comment on a different higher-spin theory without such additional fields at $\lambda=1$.

/pdf/higher-spins-and-matter-interacting-in-dimension-three-1v1xsgh7o2.pdf

Higher Spins and Matter Interacting in Dimension Three

We present a no-go result on consistent interactions among higher-spin gauge fields in AdS$_{d+1}$ space-times. We show that crossing symmetry with higher-spin gauge fields in the spectrum necessitates the presence of pathological $1/\Box$ non-localities in the bulk. This suggests the breakdown of the field theory picture for interacting higher-spin gauge theories at the classical level.

Higher spin gauge theories and bulk locality: a no-go result

We determine the Feynman rules for the minimal type A higher-spin gauge theory on AdSd+1 at cubic order. In particular, we establish the quantum action at cubic order in de Donder gauge, including ghosts. We also give the full de Donder gauge propagators of higher-spin gauge fields and their ghosts. This provides all ingredients needed to quantise the theory at cubic order.

/pdf/feynman-rules-for-higher-spin-gauge-fields-on-ads-d-1-3ygikfc7v8.pdf

Feynman rules for higher-spin gauge fields on AdS d+1

We determine the Feynman rules for the minimal type A higher-spin gauge theory on AdS$_{d+1}$ at cubic order. In particular, we establish the quantum action at cubic order in de Donder gauge, including ghosts. We also give the full de Donder gauge propagators of higher-spin gauge fields and their ghosts. This provides all ingredients needed to quantise the theory at cubic order.

/pdf/feynman-rules-for-higher-spin-gauge-fields-on-ads-d-1-4nzrt70dr9.pdf

Massimo Taronna

Papers

Pseudo-local Theories: A Functional Class Proposal

Higher Spins and Matter Interacting in Dimension Three

Higher spin gauge theories and bulk locality: a no-go result

Feynman rules for higher-spin gauge fields on AdS d+1

Feynman rules for higher-spin gauge fields on AdS$_{d+1}$