2012/12/31 by Varadarajan Parthasarathy, Parthasarathy, Varadarajan
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #astro-ph.CO
paper · pdf · doi:10.48550/arxiv.1212.6960
46 pages, 2 Tables, M.Sc Thesis
arxiv created 2012/12/31 · openalex publication_date 2012/12/31 · arxiv updated 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a correlation function (or n-point function), can the corresponding nature of space-time be determined ? To answer this question it is required to derive the Ward Identity (WI), analyse the symmetries and arrive at the law of conservation. Modus operandi involves Lie differentiating two-point function considering the symmetry to be non-anomalous. The WI so obtained is shown to form a Lie algebra which determines the nature of space-time. Solving the identity results in a law of conservation, which physically explains the reason for WI to form an algebra and contains in it an equation of motion for four-point function. As a special case, a relation between mass and potential involving the spatial derivatives of four- and five- point function is obtained. Finally, the conservation equation is exploited to get the probability amplitude for the two-point function which shows how correlation functions provide an opportunity to probe the fundamental laws of physics.