User:ShaoTang: Difference between revisions
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with <math>\epsilon</math> a real infintesimal.For this to be unitary and linear,t must be Hermitian and linear, so it is a candidate for an observable.Indeed, most(and perhaps all) of the oberservables of physics, such as angular momentum or momentum, arise in this way from symmetry transformations. | with <math>\epsilon</math> a real infintesimal.For this to be unitary and linear,t must be Hermitian and linear, so it is a candidate for an observable.Indeed, most(and perhaps all) of the oberservables of physics, such as angular momentum or momentum, arise in this way from symmetry transformations. | ||
The set of symmetry transformations has certain properties that define it as a ''group''.(From The Quantum Theory Of Fields Volume I,Steven Weinberg) | |||
2,Symmetry breaking: | 2,Symmetry breaking: | ||
Revision as of 20:12, 30 October 2011
Collective modes and Broken Symmetry
1,What is symmetry in physics? A symmetry transformation is a change in our point of view that does not change the result of possible experiments.In particular, a symmetry transformation that is infinitesimally close to being trivial can be represented by a linear unitary operator that is infinitesimally close to be trivial can be represented by a linear unitary operator that is infinitesimally close to the identity:
with a real infintesimal.For this to be unitary and linear,t must be Hermitian and linear, so it is a candidate for an observable.Indeed, most(and perhaps all) of the oberservables of physics, such as angular momentum or momentum, arise in this way from symmetry transformations.
The set of symmetry transformations has certain properties that define it as a group.(From The Quantum Theory Of Fields Volume I,Steven Weinberg)
2,Symmetry breaking:
Explicit symmetry breaking
Spontanous symmetry breaking
3,Why broken symmetry in low tempreture?