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)
Background field method
Using the background field method and the Batalin-Vilkovisky formalism, we prove a key theorem on the cohomology of perturbatively local functionals of arbitrary ghost numbers, in renormalizable and nonrenormalizable quantum field theories whose gauge symmetries are general covariance, local Lorentz symmetry, non-Abelian Yang-Mills symmetries and Abelian gauge symmetries. Interpolating between the background field approach and the usual, nonbackground approach by means of a canonical transformation, we take advantage of the properties of both approaches and prove that a closed functional is the sum of an exact functional plus a functional that depends only on the physical fields and possibly the ghosts. The assumptions of the theorem are the mathematical versions of general properties that characterize the counterterms and the local contributions to the potential anomalies. This makes the outcome a theorem on the cohomology of renormalization, rather than the whole local cohomology. The result supersedes numerous involved arguments that are available in the literature.
Phys. Rev. D 93 (2016) 065034 | DOI: 10.1103/PhysRevD.93.065034
14B1 Damiano AnselmiRenormalization
Course on renormalization, taught in 2015.
Last update: September 15th 20123, 242 pages
Buy hard copy of 2023 Edition (final one) on
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Contents:
Preface
1. Functional integral
- 1.1 Path integral
- Schroedinger equation
- Free particle
- 1.2 Free field theory
- 1.3 Perturbative expansion
- Feynman rules
- 1.4 Generating functionals, Schwinger-Dyson equations
- 1.5 Advanced generating functionals
- 1.6 Massive vector fields
- 1.7 Fermions
2. Renormalization
- 2.1 Dimensional regularization
- 2.1.1 Limits and other operations in $D$ dimensions
- 2.1.2 Functional integration measure
- 2.1.3 Dimensional regularization for vectors and fermions
- 2.2 Divergences and counterterms
- 2.3 Renormalization to all orders
- 2.4 Locality of counterterms
- 2.5 Power counting
- 2.6 Renormalizable theories
- 2.7 Composite fields
- 2.8 Maximum poles of diagrams
- 2.9 Subtraction prescription
- 2.10 Regularization prescription
- 2.11 Comments about the dimensional regularization
- 2.12 About the series resummation
3. Renormalization group
- 3.1 The Callan-Symanzik equation
- 3.2 Finiteness of the beta function and the anomalous dimensions
- 3.3 Fixed points of the RG flow
- 3.4 Scheme (in)dependence
- 3.5 A deeper look into the renormalization group
4. Gauge symmetry
- 4.1 Abelian gauge symmetry
- 4.2 Gauge fixing
- 4.3 Non-Abelian global symmetry
- 4.4 Non-Abelian gauge symmetry
5. Canonical gauge formalism
- 5.1 General idea behind the canonical gauge formalism
- 5.2 Systematics of the canonical gauge formalism
- 5.3 Canonical transformations
- 5.4 Gauge fixing
- 5.5 Generating functionals
- 5.6 Ward identities
6. Quantum electrodynamics
- 6.1 Ward identities
- 6.2 Renormalizability of QED to all orders
7 Non-Abelian gauge field theories
- 7.1 Renormalizability of non-Abelian gauge theories to all orders
- Raw subtraction
A. Notation and useful formulas
The PDF of the 2015 edition is available here below.
13A3 D. Anselmi Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalization
We investigate the background field method with the Batalin-Vilkovisky formalism, to generalize known results, study parametric completeness and achieve a better understanding of several properties. In particular, we study renormalization and gauge dependence to all orders. Switching between the background field approach and the usual approach by means of canonical transformations, we prove parametric completeness without making use of cohomological theorems, namely show that if the starting classical action is sufficiently general all divergences can be subtracted by means of parameter redefinitions and canonical transformations. Our approach applies to renormalizable and non-renormalizable theories that are manifestly free of gauge anomalies and satisfy the following assumptions: the gauge algebra is irreducible and closes off shell, the gauge transformations are linear functions of the fields, and closure is field-independent. Yang-Mills theories and quantum gravity in arbitrary dimensions are included, as well as effective and higher-derivative versions of them, but several other theories, such as supergravity, are left out.
Phys. Rev. D 89 (2014) 045004 | DOI: 10.1103/PhysRevD.89.045004
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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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