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

This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes. The lectures may be viewed online at this https URL. Please send typos or corrections to strominger@physics.this http URL.

Lectures on the Infrared Structure of Gravity and Gauge Theory

A lecture is given on a paper by P Kulish and L. D. Faddeev Theor. Math. Phys. 4, 153 (1970). The motivations and results are briefly described. (JFP)

Asymptotic condition and infrared divergences in quantum electrodynamics

Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

Tabletop experiments for quantum gravity: a user’s manual

We explore the spacetime structure near nonextremal horizons in any spacetime dimension greater than two and discover a wealth of novel results: (i) Different boundary conditions are specified by a functional of the dynamical variables, describing inequivalent interactions at the horizon with a thermal bath. (ii) The near horizon algebra of a set of boundary conditions, labeled by a parameter $s$, is given by the semidirect sum of diffeomorphisms at the horizon with ``spin-$s$ supertranslations.'' For $s=1$ we obtain the first explicit near horizon realization of the Bondi-Metzner-Sachs algebra. (iii) For another choice, we find a nonlinear extension of the Heisenberg algebra, generalizing recent results in three spacetime dimensions. This algebra allows us to recover the aforementioned (linear) ones as composites. (iv) These examples allow us to equip not only black holes, but also cosmological horizons with soft hair. We also discuss implications of soft hair for black hole thermodynamics and entropy.

https://link.aps.org/pdf/10.1103/PhysRevLett.124.041601

Spacetime Structure near Generic Horizons and Soft Hair

We discuss information-theoretic properties of low-energy photons and gravitons in the S matrix. Given an incoming n-particle momentum eigenstate, we demonstrate that unobserved soft photons decohere nearly all outgoing momentum superpositions of charged particles, while the universality of gravity implies that soft gravitons decohere nearly all outgoing momentum superpositions of all the hard particles. Using this decoherence, we compute the entanglement entropy of the soft bosons and show that it is infrared-finite when the leading divergences are resummed in the manner of Bloch and Nordsieck.

/pdf/infrared-quantum-information-445ri7f046.pdf

Infrared Quantum Information.

We study information-theoretic aspects of the infrared sector of quantum electrodynamics, using the dressed-state approach pioneered by Chung, Kibble, Faddeev-Kulish, and others. In this formalism QED has an IR-finite S-matrix describing the scattering of electrons dressed by coherent states of photons. We show that measurements sensitive only to the outgoing electronic degrees of freedom will experience decoherence in the electron momentum basis due to unobservable photons in the dressing. We make some comments on possible refinements of the dressed-state formalism, and how these considerations relate to the black hole information paradox.

Dressed infrared quantum information

In order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this result in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.

/pdf/on-the-need-for-soft-dressing-2g8wlykqdv.pdf

On the need for soft dressing

In order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.

/pdf/on-the-need-for-soft-dressing-23babs14tl.pdf

We study relativistic scattering when one only has access to a subset of the particles, using the language of quantum measurement theory. We give an exact, non-perturbative formula for the von Neumann entanglement entropy of an apparatus particle scattered off an arbitrary set of system particles, in either the elastic or inelastic regime, and show how to evaluate it perturbatively. We give general formulas for the late-time expectation values of apparatus observables. Some simple example applications are included: in particular, a protocol to verify preparation of coherent superpositions of spatially localized system states using position-space information in the outgoing apparatus state, at lowest order in perturbation theory in a weak apparatus-system coupling.

Laurent Chaurette

Papers

Infrared Quantum Information.

Dressed infrared quantum information

On the need for soft dressing

On the need for soft dressing

Scattering with partial information