English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Quantum fields are well known to violate the weak energy condition of generalrelativity: the renormalised energy density at any given point is unboundedfrom below as a function of the quantum state. By contrast, for the scalar andelectromagnetic fields it has been shown that weighted averages of the energydensity along timelike curves satisfy `quantum weak energy inequalities'(QWEIs) which constitute lower bounds on these quantities. Previously, DiracQWEIs have been obtained only for massless fields in two-dimensionalspacetimes. In this paper we establish QWEIs for the Dirac and Majorana fieldsof mass $m\ge 0$ on general four-dimensional globally hyperbolic spacetimes,averaging along arbitrary smooth timelike curves with respect to any of a largeclass of smooth compactly supported positive weights. Our proof makes essentialuse of the microlocal characterisation of the class of Hadamard states, forwhich the energy density may be defined by point-splitting.Comment: 31 pages, LaTeX2

A Quantum Weak Energy Inequality¶for Dirac Fields in Curved Spacetime