Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913244914909184 |
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| author | Benini, Marco Musante, Giorgio Schenkel, Alexander |
| author_facet | Benini, Marco Musante, Giorgio Schenkel, Alexander |
| contents | We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of $m$-dimensional globally hyperbolic Lorentzian manifolds. Our comparison is realized as an explicit isomorphism of time-orderable prefactorization algebras. The key ingredients of our approach are the retarded and advanced Green's homotopies associated with free BV theories, which generalize retarded and advanced Green's operators to cochain complexes of linear differential operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_02546 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory Benini, Marco Musante, Giorgio Schenkel, Alexander Mathematical Physics High Energy Physics - Theory Quantum Algebra 81T70, 81T20, 58J45 We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of $m$-dimensional globally hyperbolic Lorentzian manifolds. Our comparison is realized as an explicit isomorphism of time-orderable prefactorization algebras. The key ingredients of our approach are the retarded and advanced Green's homotopies associated with free BV theories, which generalize retarded and advanced Green's operators to cochain complexes of linear differential operators. |
| title | Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Algebra 81T70, 81T20, 58J45 |
| url | https://arxiv.org/abs/2212.02546 |