User:ShaoTang: Difference between revisions
No edit summary |
mNo edit summary |
||
| Line 4: | Line 4: | ||
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: | 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: | ||
<math>U=1+i\epsilon t</math> | <math>U=1+i\epsilon t</math> | ||
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. | |||
2,Symmetry breaking: | 2,Symmetry breaking: | ||
Revision as of 18:42, 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.
2,Symmetry breaking: Explicit symmetry breaking Spontanous symmetry breaking
3,Why broken symmetry in low tempreture?