The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor

Abstract

We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We shall explicitly calculate its trace anomaly in particular.

arXiv comment65 pages

References in corpus (30)

• The generally covariant locality principle -- A new paradigm for local quantum physics
• Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
• The motion of point particles in curved spacetime
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
• Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
• The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
• Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
• Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
• Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions
• On the Renormalization Group in Curved Spacetime
• Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime
• Adiabatic vacuum states on general spacetime manifolds: Definition, construction, and physical properties
• Currents and the Energy-Momentum Tensor in Classical Field Theory: A fresh look at an Old Problem
• Comments on the Stress-Energy Tensor Operator in Curved Spacetime
• Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems
• The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson-Walker Spacetimes
• A Quantum Weak Energy Inequality for Dirac fields in curved spacetime
• Stable cosmological models driven by a free quantum scalar field
• A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework
• States of Low Energy on Robertson-Walker Spacetimes
• The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes
• The State Space of Perturbative Quantum Field Theory in Curved Spacetimes
• Nuclearity, Local Quasiequivalence and Split Property for Dirac Quantum Fields in Curved Spacetime
• Proof of the symmetry of the off-diagonal Hadamard/Seeley-deWitt's coefficients in $C^{\infty }$ Lorentzian manifolds by a local Wick rotation
• Aspects of locally covariant quantum field theory
• Proof of the symmetry of the off-diagonal heat-kernel and Hadamard's expansion coefficients in general $C^{\infty }$ Riemannian manifolds
• An explicit quantum weak energy inequality for Dirac fields in curved spacetimes
• Singularity structure of the two point function of the free Dirac field on a globally hyperbolic spacetime
• Perturbative Algebraic Quantum Field Theory and the Renormalization Groups

Cited by in corpus (44)

• Quantum fields in curved spacetime
• Quantum Field Theory on Curved Backgrounds -- A Primer
• A smooth introduction to the wavefront set
• Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?
• The locally covariant Dirac field
• Classical and Quantum Fields on Lorentzian Manifolds
• Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes
• Fermionic fields in the functional approach to classical field theory
• Linear bosonic and fermionic quantum gauge theories on curved spacetimes
• The Fermionic Projector in a Time-Dependent External Potential: Mass Oscillation Property and Hadamard States
• Endomorphisms and automorphisms of locally covariant quantum field theories
• Homotopical Quantum Field Theory
• The renormalized locally covariant Dirac field
• On the Backreaction of Scalar and Spinor Quantum Fields in Curved Spacetimes - From the Basic Foundations to Cosmological Applications
• Renormalised fermion vacuum expectation values on anti-de Sitter space-time
• Deformations of quantum field theories on spacetimes with Killing vector fields
• Trace anomaly for chiral fermions via Hadamard subtraction
• Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
• The Fermionic Signature Operator and Quantum States in Rindler Space-Time
• Locally covariant chiral fermions and anomalies
• A rigorous geometric derivation of the chiral anomaly in curved backgrounds
• Hadamard renormalization for a charged scalar field
• Analysis of scalar and fermion quantum field theory on anti-de Sitter space-time
• Quantization of the massive gravitino on FRW spacetimes
• The Regularized Hadamard Expansion
• $C^{\ast }$-algebraic approach to interacting quantum field theory: Inclusion of Fermi fields
• Quantum field theories on categories fibered in groupoids
• The Lambda CDM-model in quantum field theory on curved spacetime and Dark Radiation
• A simpler solution of the non-uniqueness problem of the covariant Dirac theory
• Pure quasifree states of the Dirac field from the fermionic projector
• Equivalence of the adiabatic expansion and Hadamard renormalization for a charged scalar field
• A new class of Fermionic Projectors: Møller operators and mass oscillation properties
• A No-Go Theorem for the Consistent Quantization of Spin 3/2 Fields on General Curved Spacetimes
• Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges
• Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
• Gravitational chiral anomaly for spin 3/2 field interacting with spin 1/2 field
• The Semiclassical Einstein Equation on Cosmological Spacetimes
• The quantization of Proca fields on globally hyperbolic spacetimes: Hadamard states and Møller operators
• The Fermionic Signature Operator and Hadamard States in the Presence of a Plane Electromagnetic Wave
• Aharonov-Bohm superselection sectors
• Quantum field theory on curved spacetime and the standard cosmological model
• Locality in Abelian gauge theories over globally hyperbolic spacetimes
• Fermions on adS
• Explicit construction of Hadamard states for Quantum Field Theory in curved spacetimes