1,720,977 research outputs found
Non-trivial Bundles and Algebraic Classical Field Theory
No full textInspired by the recent algebraic approach to classical field theory, we propose a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of observables over such sections, i.e., appropriate smooth functions on them. The kinematics will be further specified by means of the Peierls brackets, which in turn are defined via the causal propagators of linearized field equations. We shall compare the formalism we use with the more traditional ones
Algebraic Approach to Bose–Einstein Condensation in Relativistic Quantum Field Theory: Spontaneous Symmetry Breaking and the Goldstone Theorem
No full textWe construct states describing Bose–Einstein condensates at finite temperature for a relativistic massive complex scalar field with ||4-interaction. We start with the linearized theory over a classical condensate and construct interacting fields by perturbation theory. Using the concept of thermal masses, equilibrium states at finite temperature can be constructed by the methods developed in Fredenhagen and Lindner (Commun Math Phys 332:895, 2014) and Drago et al. (Ann Henri Poincaré 18:807, 2017). Here, the principle of perturbative agreement plays a crucial role. The apparent conflict with Goldstone’s theorem is resolved by the fact that the linearized theory breaks the U(1) symmetry; hence, the theorem applies only to the full series but not to the truncations at finite order which therefore can be free of infrared divergences
-algebraic approach to interacting quantum field theory: Inclusion of Fermi fields
Full text linkWe extend the -algebraic approach to interacting quantum field theory,
proposed recently by Detlev Buchholz and one of us (KF) to Fermi fields. The
crucial feature of our approach is the use of auxiliary Grassmann variables in
a functorial way.Comment: 25 page
Advances in algebraic quantum field theory
No full textThis text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory
Unitary, Anomalous Master Ward Identity and its Connections to the Wess–Zumino Condition, BV Formalism and L_infinity-algebras
Full text linkThe C*-algebraic construction of QFT by Buchholz and one of us relies on the causal structure of space-time and a classical Lagrangian. In one of our previous papers, we have introduced additional structure into this construction, namely an action of symmetries, which is related to fixing renormalization conditions. This action characterizes anomalies and satisfies a cocycle condition which is summarized in the unitary anomalous Master Ward identity. Here (using perturbation theory) we show how this cocycle condition is related to the Wess–Zumino consistency relation and the consistency relation for the anomaly in the BV formalism, where the latter follows from the generalized Jacobi identity for the associated L_infinity-algebra. In addition, we give a proof that perturbative agreement (i.e., independence of a perturbative QFT on the splitting of the Lagrangian into free and interacting parts) can be achieved by finite renormalizations
The Unitary Master Ward Identity: Time Slice Axiom, Noether’s Theorem and Anomalies
Full text linkAbstractThe C*-algebraic formulation of generic interacting quantum field theories, recently presented by Detlev Buchholz and one of the authors (KF), is enriched by a unitary version of the Master Ward Identity, which was postulated some time ago by Franz Marc Boas, Ferdinand Brennecke and two of us (MD,KF). It is shown that the corresponding axiom implies the validity of the time slice axiom. Moreover, it opens the way for a new approach to Noether’s Theorem where it yields directly the unitaries implementing the symmetries. It also unravels interesting aspects of the role of anomalies in quantum field theory.</jats:p
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Quantum Spacetime and Algebraic Quantum Field Theory
No full textWe review the investigations on the quantum structure of spactime, to be found at the Planck scale if one takes into account the operational limitations to localization of events which result from the concurrence of Quantum Mechanics and General Relativity. We also discuss the different approaches to (perturbative) Quantum Field Theory on Quantum Spacetime, and some of the possible cosmological consequences
Quantum Spacetime and Algebraic Quantum Field Theory
No full textWe review the investigations on the quantum structure of spactime, to be found at the Planck scale if one takes into account the operational limitations to localization of events which result from the concurrence of Quantum Mechanics and General Relativity. We also discuss the different approaches to (perturbative) Quantum Field Theory on Quantum Spacetime, and some of the possible cosmological consequences
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