We discuss the fate of the correspondence principle beyond quantum mechanics, specifically in quantum field theory and quantum gravity, in connection with the intrinsic limitations of the human ability to observe the external world. We conclude that the best correspondence principle is made of unitarity, locality, proper renormalizability (a refinement of strict renormalizability), combined with fundamental local symmetries and the requirement of having a finite number of fields. Quantum gravity is identified in an essentially unique way. The gauge interactions are uniquely identified in form. Instead, the matter sector remains basically unrestricted. The major prediction is the violation of causality at small distances.
OSF preprints | DOI: 10.31219/osf.io/d2nj7
PhilSci 15287 (v1: PhilSci 15048)
Preprints 2018, 2018110213 | DOI: 10.20944/preprints201811.0213.v1
We elaborate on the idea of fake particle and study its physical consequences. When a theory contains fakeons, the true classical limit is determined by the quantization and a subsequent process of “classicization”. One of the major predictions due to the fake particles is the violation of microcausality, which survives the classical limit. This fact gives hope to detect the violation experimentally. A fakeon of spin 2, together with a scalar field, is able to make quantum gravity renormalizable while preserving unitarity. We claim that the theory of quantum gravity emerging from this construction is the right one. By means of the classicization, we work out the corrections to the field equations of general relativity. We show that the finalized equations have, in simple terms, the form $\langle F\rangle =ma$, where $\langle F\rangle $ is an average that includes a little bit of “future”.
Class. and Quantum Grav. 36 (2019) 065010 | DOI: 10.1088/1361-6382/ab04c8
We investigate the properties of fakeons in quantum gravity at one loop. The theory is described by a graviton multiplet, which contains the fluctuation $h_{\mu \nu }$ of the metric, a massive scalar $\phi $ and the spin-2 fakeon $\chi _{\mu \nu }$. The fields $\phi $ and $\chi _{\mu \nu }$ are introduced explicitly at the level of the Lagrangian by means of standard procedures. We consider two options, where $\phi $ is quantized as a physical particle or a fakeon, and compute the absorptive part of the self-energy of the graviton multiplet. The width of $\chi _{\mu \nu }$, which is negative, shows that the theory predicts the violation of causality at energies larger than the fakeon mass. We address this issue and compare the results with those of the Stelle theory, where $\chi _{\mu \nu }$ is a ghost instead of a fakeon.
J. High Energy Phys. 11 (2018) 21 | DOI: 10.1007/JHEP11(2018)021
A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the free propagators that are due to the higher derivatives into fakeons. The classical Lagrangian contains the cosmological term, the Hilbert term, $
\sqrt{-g}R_{\mu \nu }R^{\mu \nu }$ and $\sqrt{-g}R^{2}$. In this paper, we compute the one-loop renormalization of the theory and the absorptive part of the graviton self energy. The results illustrate the mechanism that makes renormalizability compatible with unitarity. The fakeons disentangle the real part of the self energy from the imaginary part. The former obeys a renormalizable power counting, while the latter obeys the nonrenormalizable power counting of the low energy expansion and is consistent with unitarity in the limit of vanishing cosmological constant. The value of the absorptive part is related to the central charge $c$ of the matter fields coupled to gravity.
J. High Energ. Phys. 05 (2018) 27 | DOI: 10.1007/JHEP05(2018)027
The “fakeon” is a fake degree of freedom, i.e. a degree of freedom that does not belong to the physical spectrum, but propagates inside the Feynman diagrams. Fakeons can be used to make higher-derivative theories unitary. Moreover, they help us clarify how the Lee-Wick models work. In this paper we study the fakeon models, that is to say the theories that contain fake and physical degrees of freedom. We formulate them by (nonanalytically) Wick rotating their Euclidean versions. We investigate the properties of arbitrary Feynman diagrams and, among other things, prove that the fakeon models are perturbatively unitary to all orders. If standard power counting constraints are fulfilled, the models are also renormalizable. The S matrix is regionwise analytic. The amplitudes can be continued from the Euclidean region to the other regions by means of an unambiguous, but nonanalytic, operation, called average continuation. We compute the average continuation of typical amplitudes in four, three and two dimensions and show that its predictions agree with those of the nonanalytic Wick rotation. By reconciling renormalizability and unitarity in higher-derivative theories, the fakeon models are good candidates to explain quantum gravity.
J. High Energy Phys. 02 (2018) 141 | DOI: 10.1007/JHEP02(2018)141
We study the main options for a unitary and renormalizable, local quantum field theory of the gravitational interactions. The first model is a Lee-Wick superrenormalizable higher-derivative gravity, formulated as a nonanalytically Wick rotated Euclidean theory. We show that, under certain conditions, the $S$ matrix is unitary when the cosmological constant vanishes. The model is the simplest of its class. However, infinitely many similar options are allowed, which raises the issue of uniqueness. To deal with this problem, we propose a new quantization prescription, by doubling the unphysical poles of the higher-derivative propagators and turning them into Lee-Wick poles. The Lagrangian of the simplest theory of quantum gravity based on this idea is the linear combination of $R$, $R_{\mu \nu}R^{\mu \nu }$, $R^{2}$ and the cosmological term. Only the graviton propagates in the cutting equations and, when the cosmological constant vanishes, the $S$ matrix is unitary. The theory satisfies the locality of counterterms and is renormalizable by power counting. It is unique in the sense that it is the only one with a dimensionless gauge coupling.
J. High Energy Phys. 06 (2017) 086 | DOI: 10.1007/JHEP06(2017)086
We study the perturbative unitarity of the Lee-Wick models, formulated as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions and the values of a loop integral in the various regions are related to one another by a nonanalytic procedure. We show that the one-loop diagrams satisfy the expected, unitary cutting equations in each region: only the physical degrees of freedom propagate through the cuts. The goal can be achieved by working in suitable subsets of each region and proving that the cutting equations can be analytically continued as a whole. We make explicit calculations in the cases of the bubble and triangle diagrams and address the generality of our approach. We also show that the same higher-derivative models violate unitarity if they are formulated directly in Minkowski spacetime.
Phys. Rev. D 96 (2017) 045009 | DOI: 10.1103/PhysRevD.96.045009
The Lee-Wick models are higher-derivative theories that are claimed to be unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a new formulation of the models, to clarify several aspects that have remained quite mysterious, so far. Specifically, we define them as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions, which can be related to one another by a well defined, albeit nonanalytic procedure. Working in a generic Lorentz frame, the models are intrinsically equipped with the right recipe to treat the pinchings of the Lee-Wick poles, with no need of external ad hoc prescriptions. We describe these features in detail by calculating the one-loop bubble diagram and explaining how the key properties generalize to more complicated diagrams. The physical results of our formulation are different from those of the previous ones. The unusual behaviors of the physical amplitudes lead to interesting phenomenological predictions.
J. High Energy Phys. 06 (2017) 066 | DOI: 10.1007/JHEP06(2017)066
It is normally believed that viewing time as time, that is to say a real coordinate $t$ with a Minkowski metric, is equivalent to viewing it as a space coordinate $x^4$ (with a Euclidean metric) that is turned into imaginary values by means of the Wick rotation. Indeed, most quantum field theories, including the standard model, can be equivalently formulated directly in Minkowski spacetime or by Wick rotating their Euclidean versions.
However, in a recent paper it was shown that the two formulations are not always equivalent. In particular, they are not equivalent in a wide realm of quantum field theories that is relevant for the search of quantum gravity.
The two formulations differ so much that one of the two, the Minkowski one, is mathematically inconsistent, because it leads to nonlocal divergences that cannot be subtracted away. The only viable formulation of quantum field theory is thus the Wick rotation of a Euclidean theory.
This observation could have very broad consequences. Ultimately, it tells us that the environment of quantum field theory is not Minkowski spacetime, but a different kind of spacetime, which we may call Wick spacetime, that is to say the Wick rotated Euclidean space.
If we believe that quantum field theory is the correct framework to describe nature, as all experimental evidence suggests so far, the conclusion extends from quantum field theory to nature itself, i.e.
the universe does not live in Minkowski spacetime, but in Wick spacetime.
Said differently,
time is not time, but an imaginary space.
The cutting equations are diagrammatic identities that are used to prove perturbative unitarity in quantum field theory. In this paper, we derive algebraic, upgraded versions of them. Differently from the diagrammatic versions, the algebraic identities also holds for propagators with arbitrary, nonvanishing widths. In particular, the cut propagators do not need to vanish off shell. The new approach provides a framework to address unsolved problems of perturbative quantum field theory and a tool to investigate perturbative unitarity in higher-derivative theories that are relevant to the problem of quantum gravity, such as the Lee-Wick models and the fakeon models.
Ann. Phys. 394 (2018) 294 | DOI: 10.1016/j.aop.2018.04.034
Search this site
YouTube Channel
Quantum Gravity 
Book
14B1 D. Anselmi
Renormalization
Course on renormalization, taught in 2015.
Last update: September 15th 2023, 242 pages
The final (2023) edition is vaibable on Amazon:
Contents:
Preface
1. Functional integral
2. Renormalization
3. Renormalization group
4. Gauge symmetry
5. Canonical formalism
6. Quantum electrodynamics
7. Non-Abelian gauge field theories
Notation and useful formulas
References
The pdf file of the 2015 Edition is available here: PDF
Logo
Cite papers of this site as follows:
Auths, Title, 'year'A'num' Renorm
For example:
D. Anselmi, Master functional and proper formalism for quantum gauge field theory, 12A3 Renorm
Cite books as
Auths, Title, 'year'B'num' Renorm
Cite reviews as
Auths, Title, 'year'R'num' Renorm
Cite proceedings as
Auths, Title, 'year'P'num' Renorm
Cite theorems as
Auths, Title, Theorem 'year'T'num' Renorm
Cite exercises as
Auths, Title, Exercise 'year'E'num' Renorm
You may also want to add links as shown
