THE LOCALLY COVARIANT DIRAC FIELD

DOI10.1142/S0129055X10003990zbMath1216.81113arXiv0911.1304MaRDI QIDQ3573128

Ko Sanders

Publication date: 30 June 2010

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

Full work available at URL: https://arxiv.org/abs/0911.1304

zbMATH Keywords

spin structuresDirac equationscategory theorycohomologiesQFT on curved spaces

Mathematics Subject Classification ID

Quantum field theory on curved space or space-time backgrounds (81T20) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (32)

FERMIONIC FIELDS IN THE FUNCTIONAL APPROACH TO CLASSICAL FIELD THEORY ⋮ REMARKS ON THE REEH–SCHLIEDER PROPERTY FOR HIGHER SPIN FREE FIELDS ON CURVED SPACETIMES ⋮ Locally covariant charged fields and background independence ⋮ The current density in quantum electrodynamics in external potentials ⋮ Hadamard property of the \textit{in} and \textit{out} states for Dirac fields on asymptotically static spacetimes ⋮ A no-go theorem for the consistent quantization of spin-\(3/2\) fields on general curved spacetimes ⋮ Quantum field theories on categories fibered in groupoids ⋮ An analogue of the Coleman-Mandula theorem for quantum field theory in curved spacetimes ⋮ A new class of fermionic projectors: Møller operators and mass oscillation properties ⋮ Dynamical locality and covariance: what makes a physical theory the same in all spacetimes? ⋮ Locally covariant chiral fermions and anomalies ⋮ Deformations of quantum field theories on spacetimes with Killing vector fields ⋮ The first law of black hole mechanics for fields with internal gauge freedom ⋮ Batalin-Vilkovisky formalism in the functional approach to classical field theory ⋮ Functional properties of Hörmander's space of distributions having a specified wavefront set ⋮ Aharonov-Bohm superselection sectors ⋮ Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes ⋮ THE RENORMALIZED LOCALLY COVARIANT DIRAC FIELD ⋮ Quantization of Maxwell's equations on curved backgrounds and general local covariance ⋮ Quantum field theory in static external potentials and Hadamard states ⋮ The microlocal spectrum condition, initial value formulations, and background independence ⋮ Trace anomaly for chiral fermions via Hadamard subtraction ⋮ Models of Free Quantum Field Theories on Curved Backgrounds ⋮ Algebraic Quantum Field Theory in Curved Spacetimes ⋮ On the Spin-Statistics Connection in Curved Spacetimes ⋮ Local incompatibility of the microlocal spectrum condition with the KMS property along spacelike directions in quantum field theory on curved spacetime ⋮ A SIMPLER SOLUTION OF THE NON-UNIQUENESS PROBLEM OF THE COVARIANT DIRAC THEORY ⋮ ENDOMORPHISMS AND AUTOMORPHISMS OF LOCALLY COVARIANT QUANTUM FIELD THEORIES ⋮ QUANTUM FIELD THEORY ON CURVED BACKGROUNDS — A PRIMER ⋮ Deformations of quantum field theories on de Sitter spacetime ⋮ Cauchy problem and Green's functions for first order differential operators and algebraic quantization ⋮ Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime
• Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime
• On the propagation of polarization sets for systems of real principal type
• A quantum weak energy inequality for Dirac fields in curved spacetime
• Fundamental geometric structures for the Dirac equation in general relativity
• The generally covariant locality principle -- a new paradigm for local quantum field theory
• Currents and the energy-momentum tensor in classical field theory: A fresh look at an old problem.
• Micro-local approach to the Hadamard condition in quantum field theory on curved space-time
• The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
• The operator product expansion for perturbative quantum field theory in curved spacetime
• Quantum energy inequalities and local covariance. II: Categorical formulation
• Classifying spaces and spectral sequences
• Fourier integral operators. II
• Properties of the Dirac Matrices
• THE EXTENDED ALGEBRA OF OBSERVABLES FOR DIRAC FIELDS AND THE TRACE ANOMALY OF THEIR STRESS-ENERGY TENSOR
• An explicit quantum weak energy inequality for Dirac fields in curved spacetimes
• MICROLOCAL SPECTRUM CONDITION AND HADAMARD FORM FOR VECTOR-VALUED QUANTUM FIELDS IN CURVED SPACETIME
• Microlocal analysis of quantum fields on curved space–times: Analytic wave front sets and Reeh–Schlieder theorems
• Spinor Structure of Space-Times in General Relativity. I
• Spinor Structure of Space-Times in General Relativity. II
• On the diagonalization of a bilinear Hamiltonian by a Bogoliubov transformation
• General Relativity
• Clifford modules and generalized Dirac operators
• The Hadamard condition for Dirac fields and adiabatic states on Robertson-Walker spacetimes
• A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework.

This page was built for publication: THE LOCALLY COVARIANT DIRAC FIELD