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Results for “QFT and Causality”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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9 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Reviving QFT in ( 2 + 1 )-dimensional de Sitter spacetime

We consider a conformally coupled scalar quantum field theory (QFT) on ( 2 + 1 )-dimensional static Einstein universe R × S 2 and write down the free theory Hilbert space. We explain that this theory is secretly a QFT in ( 2 + 1 )-dimensional de Sitter space because all the quantum observables experience “quantum revivals,” which naturally restricts the timelike R to the appropriate de Sitter time range. Our construction circumvents the causal obstruction to formulating QFT in de Sitter due to event horizons. There are not any in static Einstein. The “unitary gauge” description of the theory is realized by the zonal harmonics P ℓ ( n ^ · n ^ ′ ) . We verify that interactions with conformally invariant external sources are mediated only by these modes. Hence these modes comprise the complete basis of the “bulk” theory. When the theory is cut off in the UV, the basis dimension scales as the Bekenstein-Hawking formula. Published by the American Physical Society 2024

D’Amico, Guido (ORCID:0000000281831214)↗
DOE OSTI2022

What is the iε for the S-matrix?

Can the S-matrix be complexified in a way consistent with causality? Since the 1960's, the affirmative answer to this question has been well-understood for 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε -like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. In addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view, we illustrate all the points on explicit examples, both symbolically and numerically. Furthermore, to help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points.

Anomalous thresholds↗
DOE OSTI2021

Dispersion formulas in QFTs, CFTs and holography

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n -points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

New perspectives on QFT and gravity from quantum entanglement

The work accomplished by the PI as part of this award included studying the fundamental as- pects of quantum field theory (QFT) and the nature of space-time and gravity via the patterns of quantum entanglement present in these theories. By following these patterns the PI attacked basic questions on the nature of quantum gravity and found new constraints on the dynamical content of QFT. These topics find a natural home within the holographic dualiy, a deep mathemat- ical correspondence discovered in string theory where a gravitational system can be described by a quantum system without gravity. By studying the spatial distribution of quantum correlation, or entanglement, in various quantum systems the PI managed to directly observe the holographic emergence of quantum gravity within this mathematical framework. The PI also characterized the space-time structure that emerges via the duality. In achieving these aims the project shed light on the thermodynamic nature of gravity and had considerable impact on understanding of the uni- fication of gravity with quantum mechanics. Additionally, this work shed light on the structure of quantum entanglement in QFT and in so doing used powerful constraints satisfied by entanglement and it’s generalizations to place bounds on the basic data of the QFT. The project also related these bounds to causality constraints and quantum energy conditions in field theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

The structure of quantum singularities on a Cauchy horizon

Spacetime singularities pose a long-standing puzzle in quantum gravity. Unlike Schwarzschild, a generic family of black holes gives rise to a Cauchy horizon on which, even in the Hartle-Hawking state, quantum observables such as ⟨T μν ⟩ — the expectation value of the stress-energy tensor — can diverge, causing a breakdown of semiclassical gravity. Because they are diagnosed within quantum field theory (QFT) on a smooth background, these singularities may provide a better-controlled version of the spacetime singularity problem, and merit further study. Here, I highlight a mildness puzzle of Cauchy horizon singularities: the ⟨T μν ⟩ singularity is significantly milder than expected from symmetry and dimensional analysis. I address the puzzle in a simple spacetime ${\mathcal{W}}_P$, which arises universally near all black hole Cauchy horizons: the past of a codimension-two spacelike plane in flat spacetime. Specifically, I propose an extremely broad QFT construction in which, roughly speaking, Cauchy horizon singularities originate from operator insertions in the causal complement of the spacetime. The construction reproduces well-known outer horizon singularities (e.g., in the Boulware state), and remarkably, when applied to ${\mathcal{W}}_P$, gives rise to a universal mild singularity structure for robust singularities, ones whose leading singular behavior is state-independent. I make non-trivial predictions for all black hole Cauchy horizon singularities using this, and discuss extending the results beyond robust singularities and the strict near Cauchy horizon limit.

black holes↗
DOE OSTI2021

On completeness and generalized symmetries in quantum field theory

We review a notion of completeness in QFT arising from the analysis of basic properties of the set of operator algebras attached to regions. In words, this completeness asserts that the physical observable algebras produced by local degrees of freedom are the maximal ones compatible with causality. We elaborate on equivalent statements to this completeness principle such as the non-existence of generalized symmetries and the uniqueness of the net of algebras. We clarify that for non-complete theories, the existence of generalized symmetries is unavoidable and further that they always come in dual pairs with precisely the same “size”. Moreover, the dual symmetries are always broken together, be it explicitly or effectively. Finally, we comment on several issues raised in recent literature, such as the relationship between completeness and modular invariance, dense sets of charges, and absence of generalized symmetries in the bulk of holographic theories.

Astronomy & Astrophysics↗
DOE OSTI2026

From Quantum Time to Manifestly Covariant QFT: On the Need for a Quantum-Action-Based Quantization

In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT so that Lorentz covariance becomes manifest at the Hilbert-space level, rather than being hidden as in the standard canonical formulation. We address this question by proposing a second-quantized approach in which the elementary particle is the QT particle itself, leading naturally to the notion of spacetime field algebras and of quantum action. We show, however, that a naive many-body construction runs into inconsistencies. To pinpoint their origin we introduce a classical counterpart of the second-quantized formalism, spacetime classical mechanics (SCM), and prove a no-go theorem: Dirac quantization of SCM collapses back to standard QFT and therefore hides covariance. We circumvent this problem by presenting a quantum-action-based quantization that yields a spacetime version of quantum mechanics (SQM), making covariance manifest for (interacting) QFTs. Finally, we show that this resolution is tied to a genuine spacetime generalization of the notion of a quantum state, required by causality and closely connected to recent “states over time” proposals and, in dS/CFT–motivated settings, to microscopic notions of timelike entanglement and emergent time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Seeing the entanglement wedge

We study the problem of revealing the entanglement wedge using simple operations. We ask what operation a semiclassical observer can do to bring the entanglement wedge into causal contact with the boundary, via backreaction. In a generic perturbative class of states, we propose a unitary operation in the causal wedge whose backreaction brings all of the previously causally inaccessible ‘peninsula’ into causal contact with the boundary. This class of cases includes entanglement wedges associated to boundary sub-regions that are unions of disjoint spherical caps, and the protocol works to first order in the size of the peninsula. The unitary is closely related to the so-called Connes Cocycle flow, which is a unitary that is both well-defined in QFT and localised to a sub-region. Our construction requires a generalization of the work by Ceyhan & Faulkner to regions which are unions of disconnected spherical caps. We discuss this generalization in the appendix. We argue that this cocycle should be thought of as naturally generalizing the non-local coupling introduced in the work of Gao, Jafferis & Wall.

2D gravity↗
DOE OSTI2020

Holographic Space-Time and Quantum Information

The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a Lorentzian geometry. The Bekenstein-Hawking-Gibbons-’t Hooft-Jacobson-Fischler-Susskind-Bousso Covariant Entropy Principle, equates the logarithm of the dimension of the Hilbert space associated with a diamond to one quarter of the area of the diamond’s holographic screen, measured in Planck units. The most convincing argument for this principle is Jacobson’s derivation of Einstein’s equations as the hydrodynamic expression of this entropy law. In that context, the null energy condition (NEC) is seen to be the analog of the local law of entropy increase. The quantum version of Einstein’s relativity principle is a set of constraints on the mutual quantum information shared by causal diamonds along different time-like trajectories. The implementation of this constraint for trajectories in relative motion is the greatest unsolved problem in HST. The other key feature of HST is its claim that, for non-negative cosmological constant or causal diamonds much smaller than the asymptotic radius of curvature for negative c.c., the degrees of freedom localized in the bulk of a diamond are constrained states of variables defined on the holographic screen. This principle gives a simple explanation of otherwise puzzling features of BH entropy formulae, and resolves the firewall problem for black holes in Minkowski space. It motivates a covariant version of the CKN [1] bound on the regime of validity of quantum field theory (QFT) and a detailed picture of the way in which QFT emerges as an approximation to the exact theory

tensor network↗