Course
19S1 D. Anselmi
Theories of gravitation
Program
Recent Papers
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
-
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)
Field-covariance
13A1 D. Anselmi Renormalization of gauge theories without cohomology
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.
Eur. Phys. J. C 73 (2013) 2508 | DOI: 10.1140/epjc/s10052-013-2508-5
We develop a general field-covariant 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 one-particle 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 Batalin-Vilkovisky 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 gauge-fixing 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 field-covariant 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/s10052-013-2363-4
We study a new generating functional of one-particle 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 so-called 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/s10052-013-2385-y
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 field-covariant 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 J-dependent redefinitions of the sources L coupled to the composite fields. We also work out the relation between the renormalization of variable-changes 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/s10052-013-2338-5
Search this site
YouTube Channel
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)
Most used tags
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
Search documents
Archive
- May 2024
- June 2023
- April 2023
- October 2022
- July 2022
- April 2022
- March 2022
- February 2022
- January 2022
- September 2021
- May 2021
- March 2021
- December 2020
- November 2020
- October 2020
- July 2020
- June 2020
- May 2020
- January 2020
- December 2019
- November 2019
- October 2019
- September 2019
- June 2019
- May 2019
- April 2019
- March 2019
- January 2019
- November 2018
- October 2018
- September 2018
- June 2018
- March 2018
- January 2018
- April 2017
- March 2017
- January 2017
- December 2016
- June 2016
- November 2015
- January 2015
- August 2014
- May 2014
- February 2014
- November 2013
- May 2013
- March 2013
- January 2013
- September 2012
- May 2012
- January 2011
- February 2010
- December 2009
- April 2009
- August 2008
- July 2007
- April 2007
- November 2006
- May 2006
- September 2005
- March 2005
- February 2005
- April 2004
- September 2003
- December 2002
- October 2002
- May 2002
- October 2001
- July 2001
- January 2001
- May 2000
- December 1999
- November 1999
- August 1999
- June 1999
- May 1999
- March 1999
- November 1998
- September 1998
- August 1998
- February 1997
- July 1996
- July 1995
- April 1995
- November 1994
- July 1994
- September 1993
- July 1993