From Green Function to Quantum Field
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866912985677561856 |
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| author | Sorkin, Rafael D. |
| author_facet | Sorkin, Rafael D. |
| contents | A pedagogical introduction to the theory of a gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function $W(x,y)=\langleϕ(x)ϕ(y)\rangle$ regarded abstractly as a two-index tensor on the vector space of (spacetime) field configurations, and secondly how one can arrive at $W(x,y)$ starting from nothing but the retarded Green function $G(x,y)$. Conceiving the theory in this manner seems well suited to curved spacetimes and to causal sets. It makes it possible to provide a general spacetime region with a distinguished "vacuum" or "ground state", and to recognize some interesting formal relationships, including a general condition on $W(x,y)$ expressing zero-entropy or "purity". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_00610 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | From Green Function to Quantum Field Sorkin, Rafael D. General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Quantum Physics A pedagogical introduction to the theory of a gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function $W(x,y)=\langleϕ(x)ϕ(y)\rangle$ regarded abstractly as a two-index tensor on the vector space of (spacetime) field configurations, and secondly how one can arrive at $W(x,y)$ starting from nothing but the retarded Green function $G(x,y)$. Conceiving the theory in this manner seems well suited to curved spacetimes and to causal sets. It makes it possible to provide a general spacetime region with a distinguished "vacuum" or "ground state", and to recognize some interesting formal relationships, including a general condition on $W(x,y)$ expressing zero-entropy or "purity". |
| title | From Green Function to Quantum Field |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/1703.00610 |