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DuckAmuck
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- TL;DR Summary
- How are these two related?
If you have a U(1) generator, can it just be normalized to SU(1)?
The "S" stands for determinant = 1 or trace = 0 for the Lie algebras. Elements of ##U(1)## are all ##|z|=1##, so they have already determinat =1.DuckAmuck said:Summary:: How are these two related?
If you have a U(1) generator, can it just be normalized to SU(1)?
so could one say SU(1) = U(1)? If not, why not.fresh_42 said:The "S" stands for determinant = 1 or trace = 0 for the Lie algebras. Elements of ##U(1)## are all ##|z|=1##, so they have already determinat =1.
U(1) is a mathematical notation used to represent the unitary group of degree 1, which is a special group of matrices with complex entries that have a determinant of 1. It is commonly used in the field of quantum mechanics to describe symmetries and transformations.
SU(1) is a mathematical notation used to represent the special unitary group of degree 1, which is a subgroup of the unitary group U(1). It consists of matrices with complex entries that have a determinant of 1 and a trace of 0. It is commonly used in the field of quantum mechanics to describe symmetries and transformations.
No, U(1) and SU(1) are not the same thing. While they both represent special groups of matrices with complex entries, SU(1) is a subgroup of U(1) and has additional restrictions on the determinant and trace of its matrices.
U(1) and SU(1) have significant applications in the field of quantum mechanics, where they are used to describe symmetries and transformations of particles and their interactions. They also have connections to other areas of physics, such as electromagnetism and the Standard Model of particle physics.
Yes, U(1) and SU(1) have applications in other fields such as computer science, where they are used in quantum computing and error correction codes. They also have connections to geometry and topology, making them useful in areas such as string theory and differential equations.