Constraining spectral functions at finite temperature and chemical potential with exact sum rules in asymptotically free theories
- Center for Theoretical Physics, Laboratory for Nuclear Science Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
Within the framework of the operator product expansion and the renormalization group equation, we show that the temperature and chemical potential dependence of the zeroth moment of a spectral function (SF) is completely determined by the one-loop structure in an asymptotically free theory, and in particular in QCD. Logarithmic corrections are found to play an essential role in the derivation. This exact result constrains the shape of SF`s, and implies striking effects near phase transitions. Phenomenological parametrizations of the SF, often used in applications such as the analysis of lattice QCD data or QCD sum rule calculations at finite temperature and baryon density, must satisfy these constraints. We also explicitly illustrate in detail the exact sum rule in the Gross-Neveu model.
- Research Organization:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- DOE Contract Number:
- AC02-76ER03069; FG06-88ER40427
- OSTI ID:
- 69564
- Journal Information:
- Physical Review, D, Vol. 52, Issue 2; Other Information: PBD: 15 Jul 1995
- Country of Publication:
- United States
- Language:
- English
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