RENORMALIZATION GROUP Meaning and
Definition
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The renormalization group is a mathematical tool and concept used in theoretical physics, particularly in quantum field theory and statistical mechanics. It refers to a method of studying and describing the behavior of physical systems at different length scales and energy levels.
In simple terms, the renormalization group is a way to understand how the properties of a system change as we zoom in or out and examine it at different scales. The behavior of a physical system often depends on the interactions between its constituent parts, which can vary depending on the energy at which the system operates. This means that the properties and behavior of a system can be different when observed at different energies or length scales.
The renormalization group provides a systematic way of accounting for these energy-dependent changes. By considering how the system evolves under changes in energy scales, one can identify the dominant interactions and understand how they affect the overall behavior of the system. This leads to the identification of universal properties and the emergence of certain phenomena that remain invariant under these energy transformations.
In essence, the renormalization group allows physicists to study systems at their natural energy scales and identify the underlying physics that governs their behavior. It has been successfully applied to various fields of physics, such as the study of phase transitions, critical phenomena, and the behavior of fundamental particles in quantum field theory.
Etymology of RENORMALIZATION GROUP
The term "renormalization group" was coined in the field of theoretical physics, specifically in the branch of quantum field theory and statistical mechanics. It was first introduced by Kenneth Wilson in the 1970s.
The etymology of the term can be understood by breaking it down into two components: "renormalization" and "group".
1. Renormalization: The term "renormalization" refers to a procedure used in quantum field theory and statistical mechanics to tackle the divergence problem that arises in certain calculational techniques. In these theories, calculations often lead to infinite or poorly defined quantities. Renormalization is a method that allows physicists to assign meaningful values to these results by subtracting or modifying infinities in a systematic way.
2. Group: In mathematics, a "group" refers to a set equipped with a binary operation that satisfies certain properties, such as closure, associativity, identity element, and inverse element.
