Course
19S1 D. Anselmi
Theories of gravitation
Program
Recent Papers
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24A1 Damiano AnselmiCosmological 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)
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23A3 Damiano AnselmiGauge 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)
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23A2 Damiano AnselmiPropagators 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)
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23A1 Damiano AnselmiQuantum 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)
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22A5 Damiano AnselmiA 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)
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22A4 Damiano AnselmiPurely 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)
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22A3 Damiano AnselmiPurely 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)
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22A2 Damiano AnselmiPurely 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)
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22A1 Damiano AnselmiDressed 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)
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21A5 Damiano AnselmiDiagrammar 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)
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21A4 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva and Martti RaidalA 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)
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21A3 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva, Martti RaidalPhenomenology 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)
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21A2 Damiano AnselmiPerturbation 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)
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21A1 Damiano Anselmi, Filippo Fruzza and Marco PivaRenormalization-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)
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20A5 Damiano AnselmiHigh-order corrections to inflationary perturbation spectra in quantum gravity
We compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means the ... (read more)
Gauge anomalies
15A2 Damiano AnselmiAdler-Bardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories
We prove the Adler-Bardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, local Lorentz symmetry and Abelian and non-Abelian Yang-Mills symmetries, and that the local functionals of vanishing ghost numbers satisfy a variant of the Kluberg-Stern–Zuber conjecture. We show that if the gauge anomalies are trivial at one loop, for every truncation of the theory there exists a subtraction scheme where they manifestly vanish to all orders, within the truncation. Outside the truncation the cancellation of gauge anomalies can be enforced by fine-tuning local counterterms. The framework of the proof is worked out by combining a recently formulated chiral dimensional regularization with a gauge invariant higher-derivative regularization. If the higher-derivative regularizing terms are placed well beyond the truncation, and the energy scale $\Lambda $ associated with them is kept fixed, the theory is super-renormalizable and has the property that, once the gauge anomalies are canceled at one loop, they manifestly vanish from two loops onwards by simple power counting. When the $\Lambda $ divergences are subtracted away and $\Lambda $ is sent to infinity, the anomaly cancellation survives in a manifest form within the truncation and in a nonmanifest form outside. The standard model coupled to quantum gravity satisfies all the assumptions, so it is free of gauge anomalies to all orders.
Phys. Rev. D 91 (2015) 105016 | DOI: 10.1103/PhysRevD.91.105016
15A1 Damiano AnselmiWard identities and gauge independence in general chiral gauge theories
Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible for interesting effects. We prove that gauge invariance always implies gauge independence, which in turn ensures perturbative unitarity. Precisely, we consider potentially anomalous theories that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem. We show that when we make a canonical transformation on the tree-level action, it is always possible to re-renormalize the divergences and re-fine-tune the finite local counterterms, so that the renormalized $\Gamma $ functional of the transformed theory is also free of gauge anomalies, and is related to the renormalized $\Gamma $ functional of the starting theory by a canonical transformation. An unexpected consequence of our results is that the beta functions of the couplings may depend on the gauge-fixing parameters, although the physical quantities remain gauge independent. We discuss nontrivial checks of high-order calculations based on gauge independence and determine how powerful they are.
Phys. Rev. D 92 (2015) 025027 | DOI: 10.1103/PhysRevD.92.025027
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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
Sections
- Cosmology (14)
- Phenomenology beyond SM (7)
- Quantum gravity (59)
- Standard model (11)
- Adler-Bardeen theorem (5)
- Background field method (3)
- Unitarity of quantum field theory (25)
- Purely virtual particles (44)
- Renormalization of general gauge theories (16)
- Field-covariant quantum field theory (4)
- Lorentz violating quantum field theory (11)
- Renormalization group (14)
- Infinite reduction of couplings (5)
- Regularization (5)
- Conformal field theory (20)
- Topological field theory (5)
- Instantons (4)
- Field redefinitions (4)
- Dimensional regularization (5)
- Philosophy of science (8)
- Biophysics (3)
- Videos (20)
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