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Practical Derivations of Fermion and Gauge Boson Reduction Formulae in Curved Spacetimes

Jesse Huhtala, Iiro Vilja

Abstract

LSZ-type reduction formulae are derived for gauge fields and fermions in curved spacetime. The formulae are derived using a conserved current method applicable also to flat spacetimes. The method generalizes to more general quantum field theories. The formulae are then applied to a few problems to illustrate their use.

Practical Derivations of Fermion and Gauge Boson Reduction Formulae in Curved Spacetimes

Abstract

LSZ-type reduction formulae are derived for gauge fields and fermions in curved spacetime. The formulae are derived using a conserved current method applicable also to flat spacetimes. The method generalizes to more general quantum field theories. The formulae are then applied to a few problems to illustrate their use.
Paper Structure (15 sections, 61 equations, 1 table)

This paper contains 15 sections, 61 equations, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Fermions
  4. Gauge fields
  5. Reduction formulae in curved spacetime
  6. General reduction
  7. The fermion formula
  8. Derivation by EOM manipulation
  9. Using a conserved current
  10. The gauge field formula
  11. Using the formulae
  12. The general setup
  13. In-in calculation: Decay of a scalar field
  14. In-out calculations: using Bogoljubov coefficients
  15. Discussion