Hamiltonian Flow in Coulomb Gauge YangMills theory H
Hamiltonian Flow in Coulomb Gauge Yang-Mills theory H. Reinhardt Tübingen Collaborators: M. Leder, J. Pawlowski, A. Weber 1
Hamiltonian approach to YMT n canonical quantization 2
Hamiltonian approach to YMT n canonical quantization n Coulomb gauge 3
Hamiltonian approach to YMT n n canonical quantization n Coulomb gauge variational solution n ansatz for vacuum wave functional n DSE to calculate n minimization of 4
Hamiltonian approach to YMT n n n canonical quantization n Coulomb gauge variational solution n ansatz for vacuum wave functional n DSE to calculate n minimization of FRG flow equations 5
Variational approach n trial ansatz n : C. Feuchter & H. R. PRD 70(2004) gluon propagator variational kernel determined from 7
Numerical results gluon energy D. Epple, H. Reinhardt, W. Schleifenbaum, PRD 75 (2007) 8
Static gluon propagator in D=3+1 G. Burgio, M. Quandt , H. R. , PRL 102(2009) 9
ghost formfactor gost propagator ghost form factor D. Epple, H. Reinhardt, W. Schleifenbaum, PRD 75 (2007) Input: 12
ghost formfactor: lattice see talk by G. Burgio 13
The color dielectric function of the QCD vacuum ghost propagator n dielectric „constant“ n H. Reinhardt, PRL 101 (2008) 15
The color dielectric function of the QCD vacuum ghost propagator n dielectric „constant“ n H. Reinhardt, PRL 101 (2008) n horizon condition: n n : QCD vacuum-perfect color dia-electricum n 16
The color dielectric function of the QCD vacuum ghost propagator n dielectric „constant“ n H. Reinhardt, PRL 101 (2008) n horizon condition: n n : QCD vacuum-perfect color dia-electricum n n QED: screening 17
n Can we avoid the input of the horizon condition ? n n Yes we can : RG-flow equation: n indirect test of our ansatz for the wave functional M. Leder, J. Pawlowski, H. R, A. Weber 20
Renormalization group flow equation 21
Renormalization group Wetterich flow equation 22
Effective action: 1 PI-vertices 23
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RG-flow equation Wetterich 1993 25
RG-flow equation propagator flow 26
Hamiltonian flow 27
Hamiltonian flow in Coulomb gauge YMT 28
RG- flow equation 29
Hamiltonian FRG flow equation no ansatz for n indirect specification of n truncation of flow equation n form of the propagators&vertices assumed n intial condition to propagators&vertices in the UV n 30
Truncation of FRG flow equation n gluon propagator n ghost-gluon-vertex n n no tadpoles ghost dominance n no gluon loops 31
RG- flow equation ghost dominance 32
Integrating the RG-flow equation 33
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ghost form factor d(p) 35
gluon energy 36
FRG & DSE n Replacement in loop integrals of FRG: n FRG flow eq. approach DSE-variational 37
RG-Flow vs DSE: ghost form factor 38
RG-Flow vs DSE: gluon energy 39
IR- exponents n satisfy sum rule n smaller than for DSE 41
Summary & Conclusion n Hamiltonian FRG-flow equation of YMT in Coulomb gauge : Input: n ghost dominance n scaling of ghost in the IR output : n horizon condition n YM vacuum=perfect dual superconductor IR-exponents n satisfy sum rule n smaller than in variational approach outlook: n Coulomb form factor n inclusion of quarks n n 42
Thanks for your attention 44
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non-perturbative approaches to continuum Yang-Mills theory DSE n FRG flow equations n Variational Hamiltonian approch n 46
Variational approach n trial ansatz n : C. Feuchter & H. R. PRD 70(2004) gluon propagator variational kernel determined from 48
- Slides: 39