Quantized abelian principal connections on Lorentzian manifolds

DOI10.1007/s00220-014-1917-0zbMath1295.83033arXiv1303.2515OpenAlexW3105291853MaRDI QIDQ2509621

Alexander Schenkel, Claudio Dappiaggi, Marco Benini

Publication date: 29 July 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.2515

zbMATH Keywords

Chern classLorentzian manifoldscovariant functorBorchers-Uhlmann algebra\(\ast\)-algebrashyperbolic spacetimeabelian principal bundlelocally covariant quantum fieldtopological generalization

Mathematics Subject Classification ID

Topological characterizations of particular spaces (54F65) Quantum field theory on curved space or space-time backgrounds (81T20) Applications of differential geometry to physics (53Z05) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Methods of quantum field theory in general relativity and gravitational theory (83C47) Eta-invariants, Chern-Simons invariants (58J28)

Related Items (25)

Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states ⋮ The Casimir effect from the point of view of algebraic quantum field theory ⋮ Hadamard states for quantum abelian duality ⋮ Quantum field theories on categories fibered in groupoids ⋮ Higher Structures in Algebraic Quantum Field Theory ⋮ Locally covariant quantum field theory and the problem of formulating the same physics in all space–times ⋮ Quantum fields and local measurements ⋮ Differential cohomology and locally covariant quantum field theory ⋮ On the Cauchy problem for the Faraday tensor on globally hyperbolic manifolds with timelike boundary ⋮ Quantum field theory on affine bundles ⋮ A \(C^*\)-algebra for quantized principal \(U(1)\)-connections on globally hyperbolic Lorentzian manifolds ⋮ Homotopy colimits and global observables in abelian gauge theory ⋮ Gupta-Bleuler quantization of the Maxwell field in globally hyperbolic space-times ⋮ Locally covariant quantum field theory with external sources ⋮ Abelian duality on globally hyperbolic spacetimes ⋮ The Calabi complex and Killing sheaf cohomology ⋮ Quantum fields in curved spacetime, semiclassical gravity, quantum gravity phenomenology, and analogue models: parallel session D4 ⋮ Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss' law ⋮ Quantum field theory on curved spacetimes: Axiomatic framework and examples ⋮ Cohomology with causally restricted supports ⋮ Models of Free Quantum Field Theories on Curved Backgrounds ⋮ Dynamical locality of the free Maxwell field ⋮ Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies ⋮ On Maxwell's equations on globally hyperbolic spacetimes with timelike boundary ⋮ Linear Yang-Mills theory as a homotopy AQFT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topological quantum field theories
• Perturbative algebraic quantum field theory and the renormalization groups
• Quantization of Maxwell's equations on curved backgrounds and general local covariance
• Wave equations on Lorentzian manifolds and quantization.
• The generalized Peierls bracket
• The generally covariant locality principle -- a new paradigm for local quantum field theory
• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Dynamical locality and covariance: what makes a physical theory the same in all spacetimes?
• Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss' law
• Linear bosonic and fermionic quantum gauge theories on curved spacetimes
• Quantum field theory on affine bundles
• Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
• ENDOMORPHISMS AND AUTOMORPHISMS OF LOCALLY COVARIANT QUANTUM FIELD THEORIES
• QUANTUM FIELD THEORY ON CURVED BACKGROUNDS — A PRIMER
• Classical and Quantum Fields on Lorentzian Manifolds
• Lectures on Algebraic Geometry I
• Complex Analytic Connections in Fibre Bundles
• Quantization of the Maxwell field in curved spacetimes of arbitrary dimension
• Eichfeldtheorie
• RENORMALIZED QUANTUM YANG–MILLS FIELDS IN CURVED SPACETIME
• QUANTIZED ELECTROMAGNETIC FIELD ON A MANIFOLD
• HADAMARD STATES FOR THE VECTOR POTENTIAL ON ASYMPTOTICALLY FLAT SPACETIMES
• QUANTIZATION OF LINEARIZED GRAVITY IN COSMOLOGICAL VACUUM SPACETIMES
• THE RENORMALIZED LOCALLY COVARIANT DIRAC FIELD
• The commutation laws of relativistic field theory
• A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework.

This page was built for publication: Quantized abelian principal connections on Lorentzian manifolds