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Published byPhilomena Mason Modified over 9 years ago
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RG and me Love at first bite TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA A AA A A A AA A NSF DMR 0103639
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The RG: What ? a a’, b b’ etc is renormalization Ignoring y is the tree level
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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 y 1,y 2 etc. and we can eliminate y over and over and watch the flow
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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
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The RG: How to at one loop. =+ Tree One loop
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Nonrelativistic fermions Where is the low energy physics ? What is the role of interactions?
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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.
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The shell game
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Gaussian Fixed Point If we lower cutoff by s, S o goes into itself under the transformation
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Fate of interactions Add Only quartic interaction survives tree-level RG Also u cannot depend on k or !
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The survivors at tree level 1 2 3 4 1=3 and 2=4 1 2 3 4 1+2=0 and 3+4=0 Forward Scattering BCS Channel
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One loop F remains marginal V flows as follows:
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How to solve fixed point theory A small parameter 1/N =+ One loop + + i i i i i i i i i i j j j j j j k k i j j j j j i j
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Large N for Fermi liquid N= K_F/ Just sum bubbles i j i j
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New directions for Fermions (with Senthil) d=2 d=3
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Other applications Matter at finite density (Alford, Rajagopal, Wilczek, Hsu) Nuclear physics (Schwenk, Brown, Kuo) Quantum dots with random matrices Murthy, Mathur and Myself
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One loop F is marginal One loop + + i i i i i i j j k k j j j j kP-k k k+Q Q
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V flows as follows Flow of V k-k k
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