RG and me

1. RG and me Love at first bite NSF DMR 0103639 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAA

2. The RG: What ? a a’, b  b’ etc is renormalization Ignoring y is the tree level

3. Who are x and y? • x is long wavelength, y is short wavelength • x is low energy modes, y is high energy modes • x and y stand for many variables, so y is y1,y2 etc. and we can eliminate y over and over and watch the flow

4. The RG: Why? • If we make a’=a by rescaling x, then • if b’>b it is relevant • If b’<b it is irrelevant • If b’=b it is marginal • Useful for Hamiltonian perturbations

5. = + The RG: How to at one loop. One loop Tree

6. Nonrelativistic fermions Where is the low energy physics ? What is the role of interactions?

7. Strategy • 0. Focus on annulus near K_F • 1. Write an action for H_0 • 2. Find and RG to make it fixed point. • 3.Add all possible interactions and see how they flow under RG.

8. The shell game

9. Gaussian Fixed Point If we lower cutoff by s, So goes into itself under the transformation

10. Fate of interactions • Add Only quartic interaction survives tree-level RG Also u cannot depend on k or !

11. The survivors at tree level 1 3 3 1 2 4 2 4 1=3 and 2=4 1+2=0 and 3+4=0 ForwardScattering BCS Channel

12. One loop • F remains marginal • V flows as follows:

13. How to solve fixed point theoryA small parameter 1/N i j i j i k j = + k j i i j i j One loop i j i j i j + + i j i j j i

14. Large N for Fermi liquid • N= K_F/L Just sum bubbles i i j j

15. New directions for Fermions(with Senthil) d=2 d=3

16. Other applications • Matter at finite density (Alford, Rajagopal, Wilczek, Hsu) • Nuclear physics (Schwenk, Brown, Kuo) • Quantum dots with random matrices Murthy, Mathur and Myself

17. One loop F is marginal i k j Q k i j One loop i j k+Q j i k P-k + + j i k j i

18. Flow of V • V flows as follows -k k -k k