Pure quasifree states of the Dirac field from the fermionic projector

Abstract

We consider the quantised free Dirac field on oriented and globally hyperbolic ultrastatic slab spacetimes with compact spatial section and demonstrate how a gauge invariant, pure and quasifree state on the C*-completion of the self-dual CAR-algebra can be extracted from the fermionic projector construction of Finster and Reintjes. This state is analogous to the "SJ-state" of the free scalar field recently discussed in the literature. We prove that this state generically fails to be Hadamard. However, we also show how a modified version of the construction, inspired by work of Brum and Fredenhagen, yields states which are Hadamard. We also relate the Hadamard condition to the finiteness of fluctuations of Wick polynomials.

v2 26pp. New results added concerning fluctuations of Wick polynomials

References in corpus (4)

• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"
• The Necessity of the Hadamard Condition
• On a Recent Construction of "Vacuum-like" Quantum Field States in Curved Spacetime
• "Vacuum-like" Hadamard states for quantum fields on curved spacetimes

Cited by in corpus (8)

• The Fermionic Projector in a Time-Dependent External Potential: Mass Oscillation Property and Hadamard States
• Locally covariant quantum field theory and the problem of formulating the same physics in all spacetimes
• Algebraic Classical and Quantum Field Theory on Causal Sets
• The art of the state
• Snowmass White Paper: The Quest to Define QFT
• A new class of Fermionic Projectors: Møller operators and mass oscillation properties
• The Fermionic Signature Operator in the Exterior Schwarzschild Geometry
• Aharonov-Bohm superselection sectors