Monday, November 23 2020
16:30 - 17:00

IMSc Webinar

Institute Seminar days : A covariant approach to lattice

Partha Mukhopadhyay

Two crucial aspects of modern physical theories are symmetries and
having infinite number of degrees of freedom. While the first one helps us
to understand the theories at deeper levels, the latter gives rise to
difficulties such as divergences. An important approach to deal with this is
to define the theories on a lattice instead of space-time continuum.
However, in traditional lattice theories certain important symmetries are
lost and are recovered only in the continuum limit. We explore a new
covariant (i.e. visibly symmetric) approach where all such symmetries can be
preserved. As a result, there arises a possibility of much simpler
description of lattice theories. The construction relies on the existence of
a logarithmic discrete derivative that satisfies Leibniz rule. The resultant
discrete calculus behaves exactly in the same way as the ordinary calculus
to which it merges in the continuum limit.

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