PHYS 3446 – Lecture #20Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Monday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu1PHYS 3446 – Lecture #20Monday, Nov. 20, 2006Dr. Jae Yu1. Parity•Properties of Parity•Determination of Parity•Conservation and violation of parity 2. Time Reversal and Charge Conjugation 3. The Standard Model Quarks and LeptonsGauge BosonsSymmetry Breaking and the Higgs particleMonday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu2•2nd term exam–In class, this Wednesday, Nov. 22–Covers: Ch 4 – CH11•Workshop on Saturday, Dec. 2–10am – 5pm–CPB 303 and other HEP areas•Write up due: Before class Wednesday, Dec. 6AnnouncementsMonday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu3•Due date: Prior to class on Wednesday, Dec. 6•Requirements–Need to put the name(s) of the person(s) who wrote the given sections–Professionally prepared in MS words•No spelling or grammar mistakes•The style of the write up should be unified so that it looks like written by one person–All contents on the template and more should be contained in the write up–Pictures, diagrams and photos should be added w/ appropriate figure captions numbered in order of appearance. The captions should go at the bottom of the figure.–References must be indicated throughout the text in order of appearance. They must be properly matched in the list of bibliography at the end of the document.–Tables must be added and numbered in order of appearance. The caption should go on top of the table.•Key evaluation points –Quality of the document – 30%–Content and organization of the document – 20 %–Satisfaction of the above requirements – 25%–Thoughtfulness, usefulness and relevance of contents of the document – 25%•E.g. The contact information of vendors must be usable for the construction Write Up Requirements and EvaluationMonday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu4•Requirements–Professionally prepared using power points•Need your presentations 30 min prior to the class–Each presentation must be 10min (presentation) + 2min (question and answer)–Must have the following components:•General Introduction•Motivation•Design considerations and requirements•Design features•Test of design and its functionality•Conclusions and future improvements•Key evaluation points – 25% each–Quality of the slides –Content and organization of the slides–Knowledge on presentation material – answers to questions–Manner of presentationPresentation RequirementsMonday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu5•Monday, Dec. 4:1. Shane2. Daniel3. Heather4. Justin5. Cassie6. Layne•Wednesday, Dec. 6:1. Pierce2. Jessica3. James4. Matt5. LaurenPresentation ScheduleMonday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu6•To keep local gauge invariance, new particles had to be introduced in gauge theories–U(1) gauge introduced a new field (particle) that mediates the electromagnetic force: Photon–SU(2) gauge introduces three new fields that mediate weak force•Charged current mediator: W+ and W- •Neutral current: Z0–SU(3) gauge introduces 8 mediators (gluons) for the strong force•Unification of electromagnetic and weak force SU(2)xU(1) gauge introduces a total of four mediators–Neutral current: Photon, Z0–Charged current: W+ and W- Gauge Fields and MediatorsMonday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu7•The space inversion transformation (mirror image) Switch right- handed coordinate system to left-handed•How is this different than normal spatial rotation?–Rotation is continuous in a given coordinate system•Quantum numbers related to rotational transformation are continuous –Space inversion cannot be obtained through any set of rotational transformation•Quantum numbers related to space inversion is discrete•Parity is an example of the discrete transformationParityctxyz� �� �� �� �� �� �Parityuuuuuurctxyz� �� �-� �� �-� �-� �Monday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu8•Position and momentum vectors change sign under space inversion•Where as their magnitudes do not change signs•Vectors (particles w/ JP=1-) change signs under space-inversion while the scalars (particles w/ JP=0+) do not.Properties of Parityrrr r r= �r rp mr=r r& Puuurr-r Puuurmr p- =-r r&p p p= �r r Puuur( ) ( )r r r r r- �- = � =r r r r Puuur( ) ( )p p p p p- �- = � =r r r rMonday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu9•Some vectors, however, behave like a scalar–Angular momentum–These are called pseudo-vectors or axial vectors (particles w/ JP=1+)•Likewise some scalars behave like vectors–These are called pseudo-scalars (particles w/ JP=0-)•Two successive application of parity operations must turn the coordinates back to original– –The possible values (eigen values) of parity, P, are +1 (even) or -1 (odd).•Parity is a multiplicative quantum number Properties of ParityL r p= �rr r( )a b c״rr r Puuur( ) ( )r p- �- =r rr p L� =rr r Puuur( )( )( )( )a b c- �- �- =rr r( )a b c״ -rr r2P y =( )P P y =( )P y- =yMonday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu10•Two parity quantum numbers–Intrinsic parity: Bosons have the same intrinsic parities as their anti-particles while fermions have opposite parity than its anti-particle (odd) Why?–Parity under spatial transformation that follows the rule: P=(-1)l•l is the orbital angular momentum quantum number•Are electromagnetic and gravitational forces invariant under parity operation or space inversion?–Newton’s equation of motion for a point-like particle–For electromagnetic and gravitational forces we can write the forces , and thus are invariant under parity.Parity22d rm Fdt=rr22 2ˆd r Cm F rdt r= =rrMonday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu11•How do we find out the intrinsic parity of particles?–Use observation of decays and production processes–Absolute determination of parity is not possible, just like electrical charge or other quantum numbers.–Thus the accepted convention is to assign +1 intrinsic parity to proton, neutron and the hyperon.•The parities of other particles are determined relative to these assignments through the analysis of parity conserving interactions involving these particles.• hyperon is always produced
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