Course
19S1 D. Anselmi
Theories of gravitation
Program
Recent Papers

22A5 Damiano Anselmi
A new quantization principle from a minimally non timeordered productWe formulate a new quantization principle for perturbative quantum field theory, based on a minimally non timeordered 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 gravityQuantum field theory is extended to include purely virtual “cloud sectors”, which allow us to define pointdependent observables, including a gauge invariant metric and gauge ... (read more)

22A3 Damiano Anselmi
Purely virtual extension of quantum field theory for gauge invariant fields: YangMills theoryWe extend quantum field theory by including purely virtual “cloud” sectors, which allow us to define physical offshell correlation functions of gauge invariant quark and ... (read more)

22A2 Damiano Anselmi
Purely virtual particles versus LeeWick ghosts: physical PauliVillars fields, finite QED and quantum gravityWe reconsider the LeeWick (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 selfenergy and peak uncertaintyWe study the resummation of selfenergy 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 theoremWe 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 momentExtensions to the Standard Model that use strictly offshell 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 ModelWe introduce a new way of modeling the physics beyond the Standard Model by considering fake, strictly offshell degrees of freedom: the fakeons. To demonstrate ... (read more)

21A2 Damiano Anselmi
Perturbation spectra and renormalizationgroup techniques in doublefield inflation and quantum gravity cosmologyWe 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
Renormalizationgroup techniques for singlefield inflation in primordial cosmology and quantum gravityWe study inflation as a “cosmic” renormalizationgroup flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $\alpha ... (read more)

20A5 Damiano Anselmi
Highorder corrections to inflationary perturbation spectra in quantum gravityWe compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the nexttonexttoleading log order in quantum gravity with purely virtual particles (which means the ... (read more)

20A4 Damiano Anselmi
Cosmic inflation as a renormalizationgroup flow: the running of power spectra in quantum gravityWe study the running of power spectra in inflationary cosmology as a renormalizationgroup flow from the de Sitter fixed point. The beta function is provided ... (read more)

20A3 Damiano Anselmi
Quantum field theories of arbitraryspin massive multiplets and Palatini quantum gravityWe formulate quantum field theories of massive fields of arbitrary spins. The presence of both physical and fake particles, organized into multiplets, makes it possible ... (read more)

20A2 Damiano Anselmi, Eugenio Bianchi and Marco Piva
Predictions of quantum gravity in inflationary cosmology: effects of the Weylsquared termWe derive the predictions of quantum gravity with fakeons on the amplitudes and spectral indices of the scalar and tensor fluctuations in inflationary cosmology. The ... (read more)

20A1 Damiano Anselmi
The quest for purely virtual quanta: fakeons versus FeynmanWheeler particlesThe search for purely virtual quanta has attracted interest in the past. We consider various proposals and compare them to the concept of fake particle, ... (read more)
Functional integral
We develop a general fieldcovariant approach to quantum gauge theories. Extending the usual set of integrated fields and external sources to “proper” fields and sources, which include partners of the composite fields, we define the master functional $\Omega$, which collects oneparticle irreducible diagrams and upgrades the usual $\Gamma$functional in several respects. The functional $\Omega$ is determined from its classical limit applying the usual diagrammatic rules to the proper fields. Moreover, it behaves as a scalar under the most general perturbative field redefinitions, which can be expressed as linear transformations of the proper fields. We extend the BatalinVilkovisky formalism and the master equation. The master functional satisfies the extended master equation and behaves as a scalar under canonical transformations. The most general perturbative field redefinitions and changes of gaugefixing can be encoded in proper canonical transformations, which are linear and do not mix integrated fields and external sources. Therefore, they can be applied as true changes of variables in the functional integral, instead of mere replacements of integrands. This property overcomes a major difficulty of the functional $\Gamma$. Finally, the new approach allows us to prove the renormalizability of gauge theories in a general fieldcovariant setting. We generalize known cohomological theorems to the master functional and show that when there are no gauge anomalies all divergences can be subtracted by means of parameter redefinitions and proper canonical transformations.
Eur. Phys. J. C 73 (2013) 2363  DOI: 10.1140/epjc/s1005201323634
We study a new generating functional of oneparticle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The functional $\Gamma$ does not transform as a scalar under the transformation law inherited from its very definition, although it does transform as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W = ln Z with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to the socalled proper fields, which allows us to work without passing through Z, W or $\Gamma$. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields.
Eur. Phys. J. C 73 (2013) 2385  DOI: 10.1140/epjc/s100520132385y
Consider a functional integral
\[
\mathcal{I}=\int [\mathrm{d}\varphi ]\hspace{0.02in}\exp \left( S(\varphi)+\int J\left( \varphi bU\right) \right) ,
\]
where $U(\varphi ,bJ)$ is a local function of $\varphi$ and $J$, and $b$ is a constant. Then there exists a perturbatively local change of variables
\[
\varphi =\varphi (\varphi ^{\prime },b,bJ)=\varphi ^{\prime }+\mathcal{O}(b),
\]
expressed as a series expansion in $b$, such that
\[
\mathcal{I}=\int [\mathrm{d}\varphi ^{\prime }]\hspace{0.02in}\exp \left(
S^{\prime }(\varphi ^{\prime },b)+\int J\varphi ^{\prime }\right) ,
\]
where $S^{\prime }(\varphi ^{\prime },b)=S(\varphi (\varphi^{\prime },b,0))$.
In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and parameters. Because of this, we cannot write simple identities relating bare and renormalized generating functionals, or generating functionals before and after nonlinear changes of field variables. In this paper we investigate this issue and work out a general fieldcovariant approach to quantum field theory, which allows us to treat all perturbative changes of field variables, including the relation between bare and renormalized fields, as true changes of variables in the functional integral, under which the functionals Z and W = ln Z behave as scalars. We investigate the relation between composite fields and changes of field variables, and show that, if J are the sources coupled to the elementary fields, all changes of field variables can be expressed as Jdependent redefinitions of the sources L coupled to the composite fields. We also work out the relation between the renormalization of variablechanges and the renormalization of composite fields. Using our transformation rules it is possible to derive the renormalization of a theory in a new variable frame from the renormalization in the old variable frame, without having to calculate it anew. We define several approaches, useful for different purposes, in particular a linear approach where all variable changes are described as linear source redefinitions. We include a number of explicit examples.
Eur. Phys. J. C 73 (2013) 2338  DOI: 10.1140/epjc/s1005201323385
07A1 Damiano Anselmi and Anna Benini
Improved SchwingerDeWitt techniques for higherderivative perturbations of operator determinants
We consider higherderivative perturbations of quantum gravity and quantum field theories in curved space and investigate tools to calculate counterterms and shortdistance expansions of Feynman diagrams. In the case of single higherderivative insertions we derive a closed formula that relates the perturbed oneloop counterterms to the unperturbed SchwingerDeWitt coefficients. In the more general case, we classify the contributions to the shortdistance expansion and outline a number of simplification methods. Certain difficulties of the common differential technique in the presence of higherderivative perturbations are avoided by a systematic use of the CampbellBakerHausdorff formula, which in some cases reduces the computational effort considerably.
J. High Energy Phys. 10 (2007) 099  DOI: 10.1088/11266708/2007/10/099
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Book
14B1 D. Anselmi
Renormalization
Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)
Last update: May 9th 2015, 230 pages
Avaibable on Amazon:
Contents:
Preface
1. Functional integral
2. Renormalization
3. Renormalization group
4. Gauge symmetry
5. Canonical formalism
6. Quantum electrodynamics
7. NonAbelian gauge field theories
Notation and useful formulas
References
Sections
 Cosmology (13)
 Phenomenology beyond SM (5)
 Quantum gravity (55)
 Standard model (10)
 AdlerBardeen theorem (5)
 Background field method (3)
 Unitarity of quantum field theory (25)
 Fakeons (42)
 Renormalization of general gauge theories (16)
 Fieldcovariant 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 (7)
 Biophysics (3)
 Videos (20)
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