RENORMALIZATION

Quantum Field Theory and Quantum Gravity

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Course

19S1 D. Anselmi
Theories of gravitation

Program

Recent Papers

24A2 Damiano Anselmi
Quantum gravity with purely virtual particles from asymptotically local quantum field theory

We investigate the local limits of various classes of unitary, nonlocal quantum field theories. While it is easy to build nonlocal models with well-behaved asymptotics ... (read more)
24A1 Damiano Anselmi
Cosmological inhomogeneities, primordial black holes, and a hypothesis on the death of the universe

We study the impact of the expansion of the universe on a broad class of objects, including black holes, neutron stars, white dwarfs, and others. ... (read more)
23A3 Damiano Anselmi
Gauge theories and quantum gravity in a finite interval of time, on a compact space manifold

We study gauge theories and quantum gravity in a finite interval of time $ \tau $, on a compact space manifold $\Omega $. The initial, ... (read more)
23A2 Damiano Anselmi
Propagators and widths of physical and purely virtual particles in a finite interval of time

We study the free and dressed propagators of physical and purely virtual particles in a finite interval of time $τ$ and on a compact space ... (read more)
23A1 Damiano Anselmi
Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity

We provide a diagrammatic formulation of perturbative quantum field theory in a finite interval of time $τ$, on a compact space manifold $Ω$. We explain ... (read more)
22A5 Damiano Anselmi
A new quantization principle from a minimally non time-ordered product

We formulate a new quantization principle for perturbative quantum field theory, based on a minimally non time-ordered product, and show that it gives the theories ... (read more)
22A4 Damiano Anselmi
Purely virtual extension of quantum field theory for gauge invariant fields: quantum gravity

Quantum gravity is extended to include purely virtual “cloud sectors”, which allow us to define a complete set of point-dependent observables, including a gauge invariant ... (read more)
22A3 Damiano Anselmi
Purely virtual extension of quantum field theory for gauge invariant fields: Yang-Mills theory

We extend quantum field theory by including purely virtual “cloud” sectors, to define physical off-shell correlation functions of gauge invariant quark and gluon fields, without ... (read more)
22A2 Damiano Anselmi
Purely virtual particles versus Lee-Wick ghosts: physical Pauli-Villars fields, finite QED and quantum gravity

We reconsider the Lee-Wick (LW) models and compare their properties to the properties of the models that contain purely virtual particles. We argue against the ... (read more)
22A1 Damiano Anselmi
Dressed propagators, fakeon self-energy and peak uncertainty

We study the resummation of self-energy diagrams into dressed propagators in the case of purely virtual particles and compare the results with those obtained for ... (read more)
21A5 Damiano Anselmi
Diagrammar of physical and fake particles and spectral optical theorem

We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman $i\epsilon $ prescription) and purely virtual particles (defined by ... (read more)
21A4 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva and Martti Raidal
A fake doublet solution to the muon anomalous magnetic moment

Extensions to the Standard Model that use strictly off-shell degrees of freedom – the fakeons – allow for new measurable interactions at energy scales usually ... (read more)
21A3 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva, Martti Raidal
Phenomenology of a Fake Inert Doublet Model

We introduce a new way of modeling the physics beyond the Standard Model by considering fake, strictly off-shell degrees of freedom: the fakeons. To demonstrate ... (read more)
21A2 Damiano Anselmi
Perturbation spectra and renormalization-group techniques in double-field inflation and quantum gravity cosmology

We study primordial cosmology with two scalar fields that participate in inflation at the same time, by coupling quantum gravity (i.e., the theory $R+R^2+C^2$ with ... (read more)
21A1 Damiano Anselmi, Filippo Fruzza and Marco Piva
Renormalization-group techniques for single-field inflation in primordial cosmology and quantum gravity

We study inflation as a “cosmic” renormalization-group flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $\alpha ... (read more)

Field redefinitions

06T1 Theorem
Terms quadratically proportional to the field equations and field redefinitions

May 20, 2006

Consider an action $S$ depending on fields $\phi_{i}$, where the index $i$ labels both the field type, the component and the spacetime point. Add a term quadratically proportional to the field equations $S_{i}\equiv \delta S/\delta \phi _{i}$ and define the modified action
\begin{equation}
\phantom{(1)}\qquad\qquad\qquad S^{\prime }(\phi _{i})=S(\phi _{i})+S_{i}F_{ij}S_{j}, \qquad\qquad\qquad (1)
\end{equation}
where $F_{ij}$ is symmetric and can contain derivatives acting to its left and to its right. Summation over repeated indices (including the integrationover spacetime points) is understood. Then there exists a field redefinition
\begin{equation}
\phantom{(1)}\qquad\qquad\qquad\phi _{i}^{\prime }=\phi _{i}+\Delta _{ij}S_{j}, \qquad\qquad\qquad (2)
\end{equation}
with $\Delta _{ij}$ symmetric, such that, perturbatively in $F$ and to all orders in powers of $F$,
\begin{equation}
\phantom{(1)}\qquad\qquad\qquad S^{\prime }(\phi _{i})=S(\phi _{i}^{\prime }). \qquad\qquad\qquad (3)
\end{equation}

Read the proof →

Posted in Theorems, Field redefinitions | Tags: Action, Field equations, Field redefinitions

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:

US IT DE FR ES UK JP CA

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

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