Dr. Marco Benini

ehemaliger Mitarbeiter

Kontakt

...
  • Classical and quantum field theory on curved spacetimes
  • Algebraic quantum field theory
  • Gauge theories and their topological features
  • Humboldt-Stipendium

2018 | The stack of Yang-Mills fields on Lorentzian manifolds | Marco Benini, Alexander Schenkel, Urs Schreiber Zeitschrift: Comm. Math. Phys. Verlag: Springer Seiten: 765-820 Band: 359, no. 2 Link zur Publikation, Link zum Preprint

The stack of Yang-Mills fields on Lorentzian manifolds

Autoren: Marco Benini, Alexander Schenkel, Urs Schreiber (2018)

We provide an abstract definition and an explicit construction of the stack of non-Abelian Yang-Mills fields on globally hyperbolic Lorentzian manifolds. We also formulate a stacky version of the Yang-Mills Cauchy problem and show that its well-posedness is equivalent to a whole family of parametrized PDE problems. Our work is based on the homotopy theoretical approach to stacks proposed in [S. Hollander, Israel J. Math. 163, 93-124 (2008)], which we shall extend by further constructions that are relevant for our purposes. In particular, we will clarify the concretification of mapping stacks to classifying stacks such as BGcon.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
765-820
Band:
359, no. 2

2017 | Quantum field theories on categories fibered in groupoids | Marco Benini, Alexander Schenkel Zeitschrift: Comm. Math. Phys. Verlag: Springer Seiten: 19-64 Band: 356, no. 1 Link zur Publikation, Link zum Preprint

Quantum field theories on categories fibered in groupoids

Autoren: Marco Benini, Alexander Schenkel (2017)

We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first examples of homotopical quantum field theories resembling some aspects of gauge theories.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
19-64
Band:
356, no. 1

2017 | Hadamard states for quantum Abelian duality | Marco Benini, Matteo Capoferri, Claudio Dappiaggi Zeitschrift: Ann. Henri Poincaré Verlag: Springer Seiten: 3325-3370 Band: 18, no. 10 Link zur Publikation, Link zum Preprint

Hadamard states for quantum Abelian duality

Autoren: Marco Benini, Matteo Capoferri, Claudio Dappiaggi (2017)

Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C*-algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states to such algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three C*-algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors we obtain a state for the full theory, providing ultimately a unitary implementation of Abelian duality.

Zeitschrift:
Ann. Henri Poincaré
Verlag:
Springer
Seiten:
3325-3370
Band:
18, no. 10

2017 | Poisson algebras for non-linear field theories in the Cahiers topos | Marco Benini, Alexander Schenkel Zeitschrift: Ann. Henri Poincare Verlag: Springer Seiten: 1435-1464 Band: 18, no. 4 Link zur Publikation, Link zum Preprint

Poisson algebras for non-linear field theories in the Cahiers topos

Autoren: Marco Benini, Alexander Schenkel (2017)

We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a presymplectic current. We formulate the Hamiltonian vector field equation in this setting and show that it selects a family of observables which forms a Poisson algebra. Our approach provides a clean splitting between geometric and algebraic aspects of the construction of a Poisson algebra, which are sufficient to guarantee existence, and analytical aspects that are crucial to analyze its properties.

Zeitschrift:
Ann. Henri Poincare
Verlag:
Springer
Seiten:
1435-1464
Band:
18, no. 4

2017 | Abelian duality on globally hyperbolic spacetimes | Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo Zeitschrift: Comm. Math. Phys. Verlag: Springer Seiten: 361-392 Band: 349, no. 1 Link zur Publikation, Link zum Preprint

Abelian duality on globally hyperbolic spacetimes

Autoren: Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo (2017)

We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of C*-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
361-392
Band:
349, no. 1

2016 | Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies | Marco Benini Zeitschrift: J. Math. Phys. Verlag: American Institute of Physics Seiten: 053502 Band: 57 Link zur Publikation, Link zum Preprint

Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies

Autoren: Marco Benini (2016)

Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincaré duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincaré duality for the new cohomology groups.

Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
Seiten:
053502
Band:
57

2015 | Models of free quantum field theories on curved backgrounds | Marco Benini, Claudio Dappiaggi Verlag: Springer Buchtitel: R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds.): Advances in Algebraic Quantum Field Theory Seiten: 75-124 Link zur Publikation, Link zum Preprint

Models of free quantum field theories on curved backgrounds

Autoren: Marco Benini, Claudio Dappiaggi (2015)

Free quantum field theories on curved backgrounds are discussed via three explicit examples: the real scalar field, the Dirac field and the Proca field. The first step consists of outlining the main properties of globally hyperbolic spacetimes, that is the class of manifolds on which the classical dynamics of all physically relevant free fields can be written in terms of a Cauchy problem. The set of all smooth solutions of the latter encompasses the dynamically allowed configurations which are used to identify via a suitable pairing a collection of classical observables. As a last step we use such collection to construct a *-algebra which encodes the information on the dynamics and on the canonical commutation or anti-commutation relations depending whether the underlying field is a Fermion or a Boson.

Verlag:
Springer
Buchtitel:
R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds.): Advances in Algebraic Quantum Field Theory
Seiten:
75-124

2015 | Cheeger-Simons differential characters with compact support and Pontryagin duality | Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo Link zum Preprint

Cheeger-Simons differential characters with compact support and Pontryagin duality

Autoren: Christian Becker, Marco Benini, Alexander Schenkel, Richard J. Szabo (2015)

By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology and differential forms with compact support, in full analogy to ordinary differential cohomology. By extending some results for relative differential cohomology we prove an excision theorem for differential cohomology. We further establish Pontryagin duality for differential cohomology: On any oriented manifold, ordinary differential cohomology is isomorphic to the smooth Pontryagin dual of compactly supported differential cohomology. For manifolds of finite-type, a similar result is obtained interchanging ordinary with compactly supported differential cohomology.

2015 | Relative Cauchy evolution for the vector potential on globally hyperbolic spacetimes | Marco Benini Zeitschrift: Mathematics and Mechanics of Complex Systems Verlag: Mathematical Science Publishers Seiten: 177-210 Band: 3, no. 2 Link zur Publikation

Relative Cauchy evolution for the vector potential on globally hyperbolic spacetimes

Autoren: Marco Benini (2015)

The dynamics of the electromagnetic vector potential is analyzed in full detail in view of the principle of general local covariance of Brunetti, Fredenhagen and Verch. Exploiting this result, the relative Cauchy evolution for the vector potential is introduced and its relation with the energy-momentum tensor is established, extending the well known results for Klein–Gordon and Dirac fields.

Zeitschrift:
Mathematics and Mechanics of Complex Systems
Verlag:
Mathematical Science Publishers
Seiten:
177-210
Band:
3, no. 2

2015 | Homotopy colimits and global observables in Abelian gauge theory | Marco Benini, Alexander Schenkel, Richard J. Szabo Zeitschrift: Lett. Math. Phys. Verlag: Springer Seiten: 1193-1222 Band: 105, no. 9 Link zur Publikation, Link zum Preprint

Homotopy colimits and global observables in Abelian gauge theory

Autoren: Marco Benini, Alexander Schenkel, Richard J. Szabo (2015)

We study chain complexes of field configurations and observables for Abelian gauge theory on contractible manifolds, and show that they can be extended to non-contractible manifolds by using techniques from homotopy theory. The extension prescription yields functors from a category of manifolds to suitable categories of chain complexes. The extended functors properly describe the global field and observable content of Abelian gauge theory, while the original gauge field configurations and observables on contractible manifolds are recovered up to a natural weak equivalence.

Zeitschrift:
Lett. Math. Phys.
Verlag:
Springer
Seiten:
1193-1222
Band:
105, no. 9

2014 | Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states | Marco Benini, Claudio Dappiaggi, Simone Murro Zeitschrift: J. Math. Phys. Verlag: American Institute of Physics Seiten: Art. ID: 082301 Link zur Publikation, Link zum Preprint

Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states

Autoren: Marco Benini, Claudio Dappiaggi, Simone Murro (2014)

We discuss the quantization of linearized gravity on globally hyperbolic, asymptotically flat, vacuum spacetimes and the construction of distinguished states which are both of Hadamard form and invariant under the action of all bulk isometries. The procedure, we follow, consists of looking for a realization of the observables of the theory as a sub-algebra of an auxiliary, non-dynamical algebra constructed on future null infinity ℑ+. The applicability of this scheme is tantamount to proving that a solution of the equations of motion for linearized gravity can be extended smoothly to ℑ+. This has been claimed to be possible provided that a suitable gauge fixing condition, first written by Geroch and Xanthopoulos, is imposed. We review its definition critically showing that there exists a previously unnoticed obstruction in its implementation leading us to introducing the concept of radiative observables. These constitute an algebra for which a Hadamard state induced from null infinity and invariant under the action of all spacetime isometries exists and it is explicitly constructed.

Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
Seiten:
Art. ID: 082301

2014 | Locality in Abelian gauge theories over globally hyperbolic spacetimes | Marco Benini Zeitschrift: PhD thesis Verlag: University of Pavia Link zum Preprint

Locality in Abelian gauge theories over globally hyperbolic spacetimes

Autoren: Marco Benini (2014)

The thesis investigates the locality axiom of general local covariance for Abelian gauge theories. Two models, Maxwell k-forms (higher analogues of the electromagnetic vector potential) and the U(1) Yang-Mills model are analyzed over globally hyperbolic spacetimes. Our attention is mainly focused on the locality axiom of general local covariance, which states that a causal embedding between spacetimes should induce an inclusion at the level of observables. Both at the classical and at the quantum level, it turns out that the models we consider violate locality depending on certain global features of the background spacetime. For Maxwell k-forms, we prove that there is no coherent way to recover the locality axiom. For the U(1) Yang-Mills model we adopt two different approaches: in the first one locality can be recovered coherently, but the class of observables we consider fails in detecting those field configurations which correspond to the Aharonov-Bohm effect; conversely, in our second approach observables are defined in the spirit of Wilson loops (hence capturing also Aharonov-Bohm configurations), but a no-go theorem shows that locality cannot be recovered in a coherent way.

Zeitschrift:
PhD thesis
Verlag:
University of Pavia

2014 | A C*-algebra for quantized Abelian principal U(1)-connections on globally hyperbolic Lorentzian manifolds | Marco Benini, Claudio Dappiaggi, Thomas-Paul Hack, Alexander Schenkel Zeitschrift: Commun. Math. Phys. Verlag: Springer Seiten: 477-504 Band: 332, no. 1 Link zur Publikation, Link zum Preprint

A C*-algebra for quantized Abelian principal U(1)-connections on globally hyperbolic Lorentzian manifolds

Autoren: Marco Benini, Claudio Dappiaggi, Thomas-Paul Hack, Alexander Schenkel (2014)

The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes of connections. The C*-algebra we construct generalizes the usual CCR-algebras since, contrary to the standard field-theoretic models, it is based on a presymplectic Abelian group instead of a symplectic vector space. We prove a no-go theorem according to which neither this functor, nor any of its quotients, satisfies the strict axioms of general local covariance. As a byproduct, we prove that a morphism violates the locality axiom if and only if a certain induced morphism of cohomology groups is non-injective. We then show that fixing any principal U(1)-bundle, there exists a suitable category of sub-bundles for which a quotient of our functor yields a quantum field theory in the sense of Haag and Kastler. We shall provide a physical interpretation of this feature and we obtain some new insights concerning electric charges in locally covariant quantum field theory.

Zeitschrift:
Commun. Math. Phys.
Verlag:
Springer
Seiten:
477-504
Band:
332, no. 1

2014 | Quantized Abelian principal connections on Lorentzian manifolds | Marco Benini, Claudio Dappiaggi, Alexander Schenkel Zeitschrift: Commun. Math. Phys. Verlag: Springer Seiten: 123-152 Band: 330, no. 1 Link zur Publikation, Link zum Preprint

Quantized Abelian principal connections on Lorentzian manifolds

Autoren: Marco Benini, Claudio Dappiaggi, Alexander Schenkel (2014)

We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group, namely the group of vertical principal bundle automorphisms. Properties of our functor are investigated in detail and, similar to earlier works, it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated. Furthermore, we prove that, for Abelian structure groups containing a nontrivial compact factor, the gauge invariant Borchers-Uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections. We introduce a topological generalization of the concept of locally covariant quantum fields. As examples, we construct for the category of principal U(1)-bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the Chern class and the electric charge. In this case we also prove that the electric charges can be consistently set to zero, which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory.

Zeitschrift:
Commun. Math. Phys.
Verlag:
Springer
Seiten:
123-152
Band:
330, no. 1

2013 | Quantum field theories on affine bundles | Marco Benini, Claudio Dappiaggi, Alexander Schenkel Zeitschrift: Ann. Henri Poincaré Verlag: Springer Seiten: 171-211 Band: 15, no. 1 Link zur Publikation, Link zum Preprint

Quantum field theories on affine bundles

Autoren: Marco Benini, Claudio Dappiaggi, Alexander Schenkel (2013)

We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory, which allows us to prove that these models satisfy the principle of general local covariance. Our analysis is a preparatory step towards a full-fledged quantization scheme for the Maxwell field, which emphasises the affine bundle structure of the bundle of principal U(1)-connections. As a by-product, our construction provides a new class of exactly tractable locally covariant quantum field theories, which are a mild generalization of the linear ones. We also show the existence of a functorial assignment of linear quantum field theories to affine ones. The identification of suitable algebra homomorphisms enables us to induce whole families of physical states (satisfying the microlocal spectrum condition) for affine quantum field theories by pulling back quasi-free Hadamard states of the underlying linear theories.

Zeitschrift:
Ann. Henri Poincaré
Verlag:
Springer
Seiten:
171-211
Band:
15, no. 1

2013 | Quantum field theory on curved backgrounds - A primer | Marco Benini, Claudio Dappiaggi, Thomas-Paul Hack Zeitschrift: Int. J. Mod. Phys. A Verlag: World Scientific Seiten: Art. ID: 1330023 Link zur Publikation, Link zum Preprint

Quantum field theory on curved backgrounds - A primer

Autoren: Marco Benini, Claudio Dappiaggi, Thomas-Paul Hack (2013)

Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a suitable algebra of observables is assigned to a physical system, which is meant to encode all algebraic relations among observables, such as commutation relations, while, in the second step, one must select an algebraic state in order to recover the standard Hilbert space interpretation of a quantum system. As quantum field theories possess infinitely many degrees of freedom, many unitarily inequivalent Hilbert space representations exist and the power of such approach is the ability to treat them all in a coherent manner. We will discuss in detail the algebraic approach for free fields in order to give to the reader all necessary information to deal with the recent literature, which focuses on the applications to specific problems, mostly in cosmology.

Zeitschrift:
Int. J. Mod. Phys. A
Verlag:
World Scientific
Seiten:
Art. ID: 1330023

2011 | Relative Cauchy evolution for spin 1 fields | Marco Benini Zeitschrift: MSc thesis Verlag: University of Pavia Link zum Preprint

Relative Cauchy evolution for spin 1 fields

Autoren: Marco Benini (2011)

In this thesis the generally covariant locality principle for bosonic free fields has been thoroughly analyzed devoting particular attention to the case of spin 1 fields on curved spacetimes (Proca and Maxwell fields). This has been obtained in two steps: In the first place the preliminary study of the corresponding field equations led to the construction of a symplectic space of solutions describing the classical theories of the considered fields. Secondly the locally covariant quantum theory of the field under consideration has been obtained through the assignment of the Weyl algebra associated to the symplectic space describing the classical theory. The last part of the thesis has been devoted to the proof of the relative Cauchy evolution for both the Proca field and the Maxwell field.

Zeitschrift:
MSc thesis
Verlag:
University of Pavia