1 Symmetry in Physics Kihyeon Cho March 23, 2010 High Energy Physics

2 Line Symmetry Shape has line symmetry when one half of it is the mirror image of the other half. Symmetry exists all around us and many people see it as being a thing of beauty.

3 Is a butterfly symmetrical?

4 Line Symmetry exists in nature but you may not have noticed.

5 At the beach there are a variety of shells with line symmetry.

6 Under the sea there are also many symmetrical objects such as these crabs and this starfish.

7 Animals that have Line Symmetry Here are a few more great examples of mirror image in the animal kingdom.

8 THESE MASKS HAVE SYMMETRY These masks have a line of symmetry from the forehead to the chin. The human face also has a line of symmetry in the same place.

9 Human Symmetry The 'Proportions of Man' is a famous work of art by Leonardo da Vinci that shows the symmetry of the human form.

10 REFLECTION IN WATER If an object is reflected in water it is considered to have line symmetry along the waterline.

11 The Taj Mahal Symmetry exists in architecture all around the world. The best known example of this is the Taj Mahal.

12 This photograph shows 2 lines of symmetry. One vertical, the other along the waterline. (Notice how the prayer towers, called minarets, are reflected in the water and side to side).

13 2D Shapes and Symmetry After investigating the following shapes by cutting and folding, we found:

14 an equilateral triangle has 3 internal angles and 3 lines of symmetry.

15 a square has 4 internal angles and 4 lines of symmetry.

16 a regular pentagon has 5 internal angles and 5 lines of symmetry.

17 a regular hexagon has 6 internal angles and 6 lines of symmetry.

18 a regular octagon has 8 internal angles and 8 lines of symmetry.

19

카이럴 대칭성 20 질량이 없는 광자만 카이럴 대칭성을 가진다. => “ 카이럴 대칭성 ” 파괴는 질량을 가진다. Nanbu 노벨상 2008 카이럴 대칭성 => 입자의 진행 방향에 대하여 스핀이 오른쪽 회전 (+1) 스핀이 왼쪽 회전 (-1)

21 Conserved Quantities and Symmetries Every conservation law corresponds to an invariance of the Hamiltonian (or Lagrangian) of the system under some transformation. We call these invariances symmetries. There are 2 types of transformations: continuous and discontinuous Continuous  give additive conservation laws x  x+dx or   +d  examples of conserved quantities: electric charge momentum baryon # Discontinuous  give multiplicative conservation laws parity transformation: x, y, z  (-x), (-y), (-z) charge conjugation (particle  antiparticle): e -  e + examples of conserved quantities: parity (in strong and EM) charge conjugation (in strong and EM) parity and charge conjugation (strong, EM, almost always in weak)

22 quark  anti quark  quark  anti quark ……  decay Time We are all the children of Broken symmetry Just tiny deviation from perfect symmetry seems to have been enough

23 Why matter dominant world? 사하로프의 3 조건 Baryon number violation CP violation Start from thermal equilibrium

사하로프의 3 조건 24

25 C, P, T violation? Since early universe… “Alice effect” Intuitively… Boltzmann and S=kln  C is violated P is violated T is violated

‘CP’ 란 무엇인가 ? 26

27 Three Important Discrete Symmetries Parity, P –Parity reflects a system through the origin. Converts right-handed coordinate systems to left-handed ones. –Vectors change sign but axial vectors remain unchanged x   xL  L Charge Conjugation, C –Charge conjugation turns a particle into its anti-particle e   e  K   K   Time Reversal, T –Changes the direction of motion of particles in time t  t CPT theorem –One of the most important and generally valid theorems in quantum field theory. –All interactions are invariant under combined C, P and T transformations. –Implies particle and anti-particle have equal masses and lifetimes  

28 Parity Quantum Number

29 Charge-conjugation Quantum Number

30 Charge conjugate and Parity CP is the product of two symmetries: C for charge conjugation, which transforms a particle into its antiparticle, and P for parity, which creates the mirror image of a physical system.symmetriescharge conjugationantiparticleparity C

31 C P CP

32 C and P violation! Experiments show that only circled ones exist in Nature C and P are both maximally violated! But, CP and T seems to be conserved, or is it? CP We can test this in 1 st generation meson system: Pions

33 Mirror symmetry  Parity P All events should occur in exactly the same way whether they are seen directly or in mirror. There should not be any difference between left and right and nobody should be able to decide whether they are in their own world or in a looking glass world Charge symmetry  Charge C Particles should behave exactly like their alter egos, antiparticles, which have exactly the same properties but the opposite charge Time symmetry  Time T Physical events at the micro level should be equally independent whether they occur forwards or backwards in time. There are 3 different principles of symmetry in the basic theory for elementary particles Three principles of symmetry Violation in

34 Mirror symmetry  Parity P All events should occur in exactly the same way whether they are seen directly or in mirror. There should not be any difference between left and right and nobody should be able to decide whether they are in their own world or in a looking glass world Charge symmetry  Charge C Particles should behave exactly like their alter egos, antiparticles, which have exactly the same properties but the opposite charge Time symmetry  Time T Physical events at the micro level should be equally independent whether they occur forwards or backwards in time. There are 3 different principles of symmetry in the basic theory for elementary particles Three principles of symmetry Violation in Violation in

35 CP and T violation! For 37 years, CP violation involve Kaons only! Is CP violation a general property of the SM or is it simply an accident to the Kaons only? CP violation T violation K 0   +   - We can test this in 2 nd generation meson system: Kaons Need 3 rd generation system: B-mesons and B-factories

36 노벨 물리학상 2008 Citation: 5483

Why CP violation? 37

38 References I.S.Cho’s talk (2008) Class P by Richard Kass (2003) B.G Cheon’s Summer School (2002) S.H Yang’s Colloquium (2001) Class by Jungil Lee (2004) PDG home page ( Newton (2009.1)