dorsal/arxiv
View SchemaQuantum Field Symbolic Analog Computation: Relativity Model
| Authors | A. C. Manoharan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0002017 |
| URL | https://arxiv.org/abs/quant-ph/0002017 |
Abstract
It is natural to consider a quantum system in the continuum limit of space-time configuration. Incorporating also, Einstein's special relativity, leads to the quantum theory of fields. Non-relativistic quantum mechanics and classical mechanics are special cases. By studying vacuum expectation values (Wightman functions W(n; z) where z denotes the set of n complex variables) of products of quantum field operators in a separable Hilbert space, one is led to computation of holomorphy domains for these functions over the space of several complex variables, C^n. Quantum fields were reconstructed from these functions by Wightman. Computer automation has been accomplished as deterministic exact analog computation (computation over "cells" in the continuum of C^n) for obtaining primitive extended tube domains of holomorphy. This is done in a one dimensional space plus one dimensional time model. By considering boundary related semi-algebraic sets, some analytic extensions of these domains are obtained by non-deterministic methods. The novel methods of computation raise interesting issues of computability and complexity. Moreover, the computation is independent of any particular form of Lagrangian or dynamics, and is uniform in n, qualifying for a universal quantum machine over C^infinity.
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"abstract": "It is natural to consider a quantum system in the continuum limit of\nspace-time configuration. Incorporating also, Einstein\u0027s special relativity,\nleads to the quantum theory of fields. Non-relativistic quantum mechanics and\nclassical mechanics are special cases. By studying vacuum expectation values\n(Wightman functions W(n; z) where z denotes the set of n complex variables) of\nproducts of quantum field operators in a separable Hilbert space, one is led to\ncomputation of holomorphy domains for these functions over the space of several\ncomplex variables, C^n. Quantum fields were reconstructed from these functions\nby Wightman. Computer automation has been accomplished as deterministic exact\nanalog computation (computation over \"cells\" in the continuum of C^n) for\nobtaining primitive extended tube domains of holomorphy. This is done in a one\ndimensional space plus one dimensional time model. By considering boundary\nrelated semi-algebraic sets, some analytic extensions of these domains are\nobtained by non-deterministic methods. The novel methods of computation raise\ninteresting issues of computability and complexity. Moreover, the computation\nis independent of any particular form of Lagrangian or dynamics, and is uniform\nin n, qualifying for a universal quantum machine over C^infinity.",
"arxiv_id": "quant-ph/0002017",
"authors": [
"A. C. Manoharan"
],
"categories": [
"quant-ph"
],
"title": "Quantum Field Symbolic Analog Computation: Relativity Model",
"url": "https://arxiv.org/abs/quant-ph/0002017"
},
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