Title: Group Invariant Polynomial- paving the path to operator construction.
Abstract : Lagrangian is considered to be one of the primary objects to model physical phenomena. The knowledge of quantum fields that represent the particles and their transformation property under the assigned symmetry of the theory/system is needed to construct the unique Lagrangian. The Lagrangian can be thought of as a polynomial of those quantum fields and the mass dimension of the operators play a crucial role to determine the order of that polynomial. Though we restrict ourselves mostly up to order 4 (renormalizable terms), we can add higher-order terms in the polynomial. Adding higher order, i.e., higher mass dimensional operators in the Lagrangian is what we note as grabbing the footprints of unknown UV theory though these effective operators. The present era of particle physics encourages us to look beyond renormalizable terms, and thus the Effective Field Theory has drawn our attention in the past few years. For any given theory, constructing effective operators is a tedious task -- our estimation should not be less or more. The operator set must be independent and complete such that they can form a basis at each order. To make life easy, we have come up with an algorithm and developed a Mathematica code "GrIP" which allows one to compute operator basis at any given mass dimension. There are many additional advantages of this code. I will unveil them during my talk. I will start with the mathematical framework of our work based on which we have developed the algorithm. Then I will demonstrate the
working principle of "GrIP". I will also float some possible directions to continue the discussion.