Book on gauge transformations/symmetry & geometrical phases?

• Quantum
• Joker93
In summary, studying gauge transformations and symmetry is crucial in understanding the fundamental principles of physics and their role in theories such as quantum mechanics and electromagnetism. A gauge transformation is a mathematical operation that changes the description of a physical system while preserving its physical properties, and it is closely related to symmetry. Geometrical phases, which are phase shifts that occur during cyclic processes, are important in modern physics due to their applications in quantum mechanics, condensed matter physics, and understanding phenomena such as the Aharonov-Bohm effect and topological phases of matter.
Joker93
Hello!
I will be attending a course on condensed matter physics with emphasis on geometrical phases and I was wondering if the are any good books on gauge transformations, gauge symmetry and geometrical phases that you know of.

There are several recommendations threads for condensed matter. Do a forum search :)

1. What is the purpose of studying gauge transformations and symmetry in a book?

Studying gauge transformations and symmetry is important in understanding the underlying principles of physics and how they govern the behavior of particles and fields. These concepts are essential in the development of theories such as quantum mechanics and electromagnetism.

2. What is a gauge transformation?

A gauge transformation is a mathematical operation that changes the description of a physical system without altering its physical properties. In other words, it is a change of coordinates that preserves the physical content of a theory.

3. How do gauge transformations relate to symmetry?

Gauge transformations are closely related to symmetry because they are a way of expressing the symmetries of a physical system. In fact, many symmetries, such as rotational symmetry and gauge symmetry, can be described using gauge transformations.

4. What is a geometrical phase?

A geometrical phase is a phase shift that occurs when a system is taken through a cyclic process in its parameter space. It is a manifestation of the geometric properties of the system and is independent of the dynamics of the process.

5. Why are geometrical phases important in modern physics?

Geometrical phases have many applications in modern physics, including the study of quantum mechanics, condensed matter physics, and quantum information. They also play a crucial role in understanding physical phenomena such as the Aharonov-Bohm effect and topological phases of matter.

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