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Universe
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Quantum Fields – From Fundamental Concepts to Phenomenological Questions
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Quantum Fields – From Fundamental Concepts to Phenomenological Questions

A special issue of Universe (ISSN 2218-1997).

Deadline for manuscript submissions: closed (17 February 2019) | Viewed by 27992

Special Issue Editors

Dr. Astrid Eichhorn

E-Mail Website
Guest Editor
Universitat Heidelberg, Heidelberg, Germany
Interests: approaches to quantum gravity; physics beyond the Standard Model
Dr. Roberto Percacci

E-Mail Website
Guest Editor
Scuola Internazionale di Studi Superiori Avanzati (SISSA), 34136 Trieste, Italy
Interests: quantum field theory; classical and quantum gravity; unified theories
Prof. Dr. Frank Saueressig

E-Mail Website
Guest Editor
Institute for Mathematics, Astrophysics, and Particle Physics, Radboud University Nijmegen, Astrophysics and Particle Physics (IMAPP), 6525 AJ Nijmegen, The Netherlands
Interests: quantum gravity; asymptotic safety; quantum field theory in curved space-time; black holes; theoretical cosmology; renormalization group techniques

Special Issue Information

Dear Colleagues,

This Special Issue collects contributions to the conference "Quantum Fields—from Fundamental Concepts to Phenomenological Questions” held at the Mainz Institute for Theoretical Physics (MITP), 26–28 September 2018. The focus of the Special Issue is the structure of quantum field theories and their observational consequences beyond the perturbative domain. Progress along this research frontier may be the key to answering fundamental questions related to the structure of space, time, and matter. Following the idea of “renormalizing the non-renormalizable”, this route may even allow for a unified description of all fundamental forces, including gravity, within the framework of quantum field theory. Various non-perturbative approaches will be covered, with special emphasis on functional methods. All papers in this Special Issue will be published free of charge.

Dr. Astrid Eichhorn
Prof. Dr. Roberto Percacci
Dr. Frank Saueressig
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum field theory
  • Non-perturbative methods
  • Resurgence
  • Functional integrals
  • Functional renormalization group equations
  • Quantum gravity
  • Asymptotic safety

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Published Papers (10 papers)

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Editorial

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6 pages, 209 KiB  
Editorial
Editorial for the Special Issue “Quantum Fields—From Fundamental Concepts to Phenomenological Questions”
by Astrid Eichhorn, Roberto Percacci and Frank Saueressig
Universe 2020, 6(12), 235; https://doi.org/10.3390/universe6120235 - 10 Dec 2020
Viewed by 1656
Abstract
Quantum field theory and Einstein’s theory of general relativity are extremely successful in predicting the outcome of particle physics and gravitational experiments [...] Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)

Research

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14 pages, 298 KiB  
Article
The Inflationary Mechanism in Asymptotically Safe Gravity
by Alessia Platania
Universe 2019, 5(8), 189; https://doi.org/10.3390/universe5080189 - 20 Aug 2019
Cited by 23 | Viewed by 2701
Abstract
According to the asymptotic safety conjecture, gravity is a renormalizable quantum field theory whose continuum limit is defined by an interacting fixed point of the renormalization group flow. In these proceedings, we review some implications of the existence of this nontrivial fixed point [...] Read more.
According to the asymptotic safety conjecture, gravity is a renormalizable quantum field theory whose continuum limit is defined by an interacting fixed point of the renormalization group flow. In these proceedings, we review some implications of the existence of this nontrivial fixed point in cosmological contexts. Specifically, we discuss a toy model exemplifying how the departure from the fixed-point regime can explain the approximate scale-invariance of the power spectrum of temperature fluctuations in the cosmic microwave background. Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)
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8 pages, 313 KiB  
Article
On the Structure of the Vacuum in Quantum Gravity: A View from the Asymptotic Safety Scenario
by Alfio Bonanno
Universe 2019, 5(8), 182; https://doi.org/10.3390/universe5080182 - 3 Aug 2019
Cited by 8 | Viewed by 2582
Abstract
Although the Asymptotic Safety scenario is one of the most promising approaches to quantum gravity, little attention has been devoted to the issue of the vacuum state. Higher derivative operators often appear on the ultraviolet critical surface around the non-Gaussian fixed point generating [...] Read more.
Although the Asymptotic Safety scenario is one of the most promising approaches to quantum gravity, little attention has been devoted to the issue of the vacuum state. Higher derivative operators often appear on the ultraviolet critical surface around the non-Gaussian fixed point generating additional degrees of freedom which can render the standard vacuum unstable. When this happens, translation and rotational symmetries can be spontaneously broken and a new set of symmetries can show up at the level of the effective action. In this work, it will be argued that a “kinetic condensate” characterizes the vacuum state of asymptotically safe quadratic gravity theories. If this scenario is realized in the full theory, the vacuum state of gravity is the gravitational analogous to the Savvidy vacuum in Quantum Chromo-Dynamics (QCD). Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)
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46 pages, 536 KiB  
Article
Holographic Formulation of 3D Metric Gravity with Finite Boundaries
by Seth K. Asante, Bianca Dittrich and Florian Hopfmueller
Universe 2019, 5(8), 181; https://doi.org/10.3390/universe5080181 - 31 Jul 2019
Cited by 7 | Viewed by 2914
Abstract
In this work we construct holographic boundary theories for linearized 3D gravity, for a general family of finite or quasi-local boundaries. These boundary theories are directly derived from the dynamics of 3D gravity by computing the effective action for a geometric boundary observable, [...] Read more.
In this work we construct holographic boundary theories for linearized 3D gravity, for a general family of finite or quasi-local boundaries. These boundary theories are directly derived from the dynamics of 3D gravity by computing the effective action for a geometric boundary observable, which measures the geodesic length from a given boundary point to some center in the bulk manifold. We identify the general form for these boundary theories and find that these are Liouville-like with a coupling to the boundary Ricci scalar. This is illustrated with various examples, which each offer interesting insights into the structure of holographic boundary theories. Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)
17 pages, 485 KiB  
Article
Anti-Newtonian Expansions and the Functional Renormalization Group
by Max Niedermaier
Universe 2019, 5(3), 85; https://doi.org/10.3390/universe5030085 - 21 Mar 2019
Cited by 8 | Viewed by 2778
Abstract
Anti-Newtonian expansions are introduced for scalar quantum field theories and classical gravity. They expand around a limiting theory that evolves only in time while the spatial points are dynamically decoupled. Higher orders of the expansion re-introduce spatial interactions and produce overlapping lightcones from [...] Read more.
Anti-Newtonian expansions are introduced for scalar quantum field theories and classical gravity. They expand around a limiting theory that evolves only in time while the spatial points are dynamically decoupled. Higher orders of the expansion re-introduce spatial interactions and produce overlapping lightcones from the limiting isolated world line evolution. In scalar quantum field theories, the limiting system consists of copies of a self-interacting quantum mechanical system. In a spatially discretized setting, a nonlinear “graph transform” arises that produces an in principle exact solution of the Functional Renormalization Group for the Legendre effective action. The quantum mechanical input data can be prepared from its 1 + 0 dimensional counterpart. In Einstein gravity, the anti-Newtonian limit has no dynamical spatial gradients, yet remains fully diffeomorphism invariant and propagates the original number of degrees of freedom. A canonical transformation (trivialization map) is constructed, in powers of a fractional inverse of Newton’s constant, that maps the ADM action into its anti-Newtonian limit. We outline the prospects of an associated trivializing flow in the quantum theory. Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)
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11 pages, 257 KiB  
Article
Dimension and Dimensional Reduction in Quantum Gravity
by Steven Carlip
Universe 2019, 5(3), 83; https://doi.org/10.3390/universe5030083 - 19 Mar 2019
Cited by 27 | Viewed by 3473
Abstract
If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. [...] Read more.
If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. I will review the evidence for this behavior, emphasizing the physical question of what one means by “dimension” in a quantum spacetime, and will discuss possible mechanisms that could explain the universality of this phenomenon. Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)
10 pages, 239 KiB  
Article
The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡
by Walter Dittrich
Universe 2019, 5(3), 79; https://doi.org/10.3390/universe5030079 - 14 Mar 2019
Cited by 3 | Viewed by 3338
Abstract
In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Riemann’s zeta function [...] Read more.
In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Riemann’s zeta function to regularize the otherwise infinite results of the so-called Heisenberg–Euler Lagrangian. As a spin-off, we also calculate some integrals that are useful in mathematics and physics. Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)

Review

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14 pages, 327 KiB  
Review
Multi-Critical Multi-Field Models: A CFT Approach to the Leading Order
by Gian Paolo Vacca, Alessandro Codello, Mahmoud Safari and Omar Zanusso
Universe 2019, 5(6), 151; https://doi.org/10.3390/universe5060151 - 13 Jun 2019
Cited by 12 | Viewed by 2541
Abstract
We present some general results for the multi-critical multi-field models in d > 2 recently obtained using conformal field theory (CFT) and Schwinger–Dyson methods at the perturbative level without assuming any symmetry. Results in the leading non trivial order are derived consistently for [...] Read more.
We present some general results for the multi-critical multi-field models in d > 2 recently obtained using conformal field theory (CFT) and Schwinger–Dyson methods at the perturbative level without assuming any symmetry. Results in the leading non trivial order are derived consistently for several conformal data in full agreement with functional perturbative renormalization group (RG) methods. Mechanisms like emergent (possibly approximate) symmetries can be naturally investigated in this framework. Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)
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16 pages, 298 KiB  
Review
Geometric Operators in the Einstein–Hilbert Truncation
by Maximilian Becker and Carlo Pagani
Universe 2019, 5(3), 75; https://doi.org/10.3390/universe5030075 - 11 Mar 2019
Cited by 7 | Viewed by 2428
Abstract
We review the study of the scaling properties of geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the use of such operators and how they can [...] Read more.
We review the study of the scaling properties of geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the use of such operators and how they can be embedded in the effective average action formalism. We report the anomalous dimension of the geometric operators in the Einstein–Hilbert truncation via different approximations by considering simple extensions of previous studies. Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)
21 pages, 317 KiB  
Review
Vacuum Effective Actions and Mass-Dependent Renormalization in Curved Space
by Sebastián A. Franchino-Viñas, Tibério de Paula Netto and Omar Zanusso
Universe 2019, 5(3), 67; https://doi.org/10.3390/universe5030067 - 28 Feb 2019
Cited by 16 | Viewed by 2620
Abstract
We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss [...] Read more.
We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton’s constant and the other gravitational couplings. Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)
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