Recent theorems
- 13T1 Theorem Replacing fields with the solutions of their field equations preserves the master equation
- 12T1 Theorem Procedure to convert the functional integral to the conventional form
- 06T1 Theorem Terms quadratically proportional to the field equations and field redefinitions
- 05T1 Theorem Maximum poles of Feynman diagrams
Recent Papers
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18A2 Damiano Anselmi and Marco Piva The ultraviolet behavior of quantum gravity
A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the ... (read more)
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18A1 Damiano Anselmi Fakeons and Lee-Wick models
The “fakeon” is a fake degree of freedom, i.e. a degree of freedom that does not belong to the physical spectrum, but propagates inside the ... (read more)
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17A3 Damiano Anselmi On the quantum field theory of the gravitational interactions
We study the main options for a unitary and renormalizable, local quantum field theory of the gravitational interactions. The first model is a Lee-Wick superrenormalizable ... (read more)
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17A2 Damiano Anselmi and Marco Piva Perturbative unitarity of Lee-Wick quantum field theory
We study the perturbative unitarity of the Lee-Wick models, formulated as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions ... (read more)
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17A1 Damiano Anselmi and Marco Piva A new formulation of Lee-Wick quantum field theory
The Lee-Wick models are higher-derivative theories that are claimed to be unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a new ... (read more)
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16A3 Damiano Anselmi Algebraic cutting equations
We prove a set of polynomial identities for complex numbers associated with Feynman diagrams. The equations are at the core of perturbative unitarity in quantum ... (read more)
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16A2 Ugo G. Aglietti and Damiano Anselmi Inconsistency of Minkowski higher-derivative theories
We show that Minkowski higher-derivative quantum field theories are generically inconsistent, because they generate nonlocal, non-Hermitian ultraviolet divergences, which cannot be removed by means of ... (read more)
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16A1 Damiano Anselmi Aspects of perturbative unitarity
We reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the ... (read more)
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15A4 Damiano Anselmi Background field method and the cohomology of renormalization
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, ... (read more)
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15A3 Damiano Anselmi Some reference formulas for the generating functions of canonical transformations
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating ... (read more)
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15A2 Damiano Anselmi Adler-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, ... (read more)
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15A1 Damiano Anselmi Ward 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 ... (read more)
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14A2 D. Anselmi Weighted power counting and chiral dimensional regularization
We define a modified dimensional-regularization technique that overcomes several difficulties of the ordinary technique, and is specially designed to work efficiently in chiral and parity ... (read more)
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14A1 D. Anselmi Adler-Bardeen theorem and manifest anomaly cancellation to all orders in gauge theories
We reconsider the Adler-Bardeen theorem for the cancellation of gauge anomalies to all orders, when they vanish at one loop. Using the Batalin-Vilkovisky formalism and ... (read more)
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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. ... (read more)
Ward identities
15A2 Damiano Anselmi Adler-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 Anselmi Ward 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
Last update: May 9th 2015, 230 pages
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
Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)
Sections
- Unitarity of quantum field theory (7)
- Fakeons (2)
- Renormalization of general gauge theories (14)
- Field-covariant quantum field theory (4)
- Adler-Bardeen theorem (5)
- Quantum gravity (16)
- Lorentz violating quantum field theory (8)
- Background field method (3)
- Infinite reduction of couplings (4)
- Renormalization group (14)
- Regularization (5)
- Conformal field theory (20)
- Topological field theory (5)
- Instantons (4)
- Field redefinitions (4)
- Dimensional regularization (5)
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