Chiral symmetries associated with angular momentum

In quantum mechanics courses, symmetries of a physical system are usually introduced as operators which commute with the Hamiltonian. In this paper we will consider chiral symmetries which anticommute with the Hamiltonian. Typically, introductory courses at the (under)graduate level do not discuss t...

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Bibliographic Details
Published inEuropean journal of physics Vol. 35; no. 2; pp. 25007 - 11
Main Authors Bhattacharya, M, Kleinert, M
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.03.2014
Subjects
Angular momentum
chiral symmetries
Dirac equation
Encounters
Operators
Quantum mechanics
rotation
Students
Superconductivity
Symmetry
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Summary:In quantum mechanics courses, symmetries of a physical system are usually introduced as operators which commute with the Hamiltonian. In this paper we will consider chiral symmetries which anticommute with the Hamiltonian. Typically, introductory courses at the (under)graduate level do not discuss these simple, useful and beautiful symmetries at all. The first time a student encounters them is when the Dirac equation is discussed in a course on relativistic quantum mechanics, or when particle-hole symmetry is studied in the context of superconductivity. In this paper, we will show how chiral symmetries can be simply elucidated using the theory of angular momentum, which is taught in virtually all introductory quantum mechanics courses.
Bibliography:EJP-100005
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0143-0807
1361-6404
DOI:10.1088/0143-0807/35/2/025007