Aspects of Regularization and Renormalization in Physical Theories

Pal, Mainak (2014) Aspects of Regularization and Renormalization in Physical Theories. Masters thesis, Indian Institute ofScience Education and Research Kolkata.

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Abstract

Concept of regularizability and renormalizability of a theory is of utmost importance in physics. Question of renormalizability arises when a physical theory appears to predict in�nite values of physically measurable quantities. These in�nite values usually occur due to in�nite degrees of freedom (DOF) in quantum �eld theory (QFT), divergence of perturbation series, sometimes due to singular nature of the scattering potential and etc. Di�erent techniques of extracting �nite values for the seemingly divergent quantities are termed regularizing methods and the entire process of calculation of �nite values of physically measurable quantities through various regularizing methods is called renormalization. First part of this work is a study of di�erent techniques of regularization and renormalization by their application on a quantum mechanical (QM) problem of scattering of a particle o� a attractive Dirac-delta potential where in�nities occur due to singular nature of the potential. While formulating a theory for a physical system, if issues of renormalizability pop up, there's a method of repeated transformations (termed as `renormalization group transformations') of the Hamiltonian to sum over interactions at various length scales to carry out the renormalization. Second part of the work is a study of the formulation of the renormalization group theory and its application on di�erent systems in statistical mechanics addressing critical phenomena.

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