Classical Simulations of Quantum Field Theory in Curved Spacetime I: Fermionic Hawking-Hartle Vacua from a Staggered Lattice Scheme
| Autor: | Guifre Vidal, Adam G. M. Lewis |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Physics and Astronomy (miscellaneous) High Energy Physics::Lattice FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) 01 natural sciences General Relativity and Quantum Cosmology Renormalization High Energy Physics - Lattice De Sitter universe 0103 physical sciences Minkowski space Schwarzschild metric Quantum field theory 010306 general physics Mathematical physics Physics Quantum Physics Quantum field theory in curved spacetime Spacetime 010308 nuclear & particles physics High Energy Physics - Lattice (hep-lat) lcsh:QC1-999 Atomic and Molecular Physics and Optics Unruh effect High Energy Physics - Theory (hep-th) Quantum Physics (quant-ph) lcsh:Physics |
| Zdroj: | Quantum, Vol 4, p 351 (2020) |
| ISSN: | 2521-327X |
| Popis: | We numerically compute renormalized expectation values of quadratic operators in a quantum field theory (QFT) of free Dirac fermions in curved two-dimensional (Lorentzian) spacetime. First, we use a staggered-fermion discretization to generate a sequence of lattice theories yielding the desired QFT in the continuum limit. Numerically-computed lattice correlators are then used to approximate, through extrapolation, those in the continuum. Finally, we use so-called point-splitting regularization and Hadamard renormalization to remove divergences, and thus obtain finite, renormalized expectation values of quadratic operators in the continuum. As illustrative applications, we show how to recover the Unruh effect in flat spacetime and how to compute renormalized expectation values in the Hawking-Hartle vacuum of a Schwarzschild black hole and in the Bunch-Davies vacuum of an expanding universe described by de Sitter spacetime. Although here we address a non-interacting QFT using free fermion techniques, the framework described in this paper lays the groundwork for a series of subsequent studies involving simulation of interacting QFTs in curved spacetime by tensor network techniques. Comment: 29 pages, 9 figures |
| Databáze: | OpenAIRE |
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