An Analysis On Ward Identity For Multi-Field Inflation
  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.
