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Mesons at finite baryon density in ( 2 + 1 )
| Content Provider | Semantic Scholar |
|---|---|
| Author | Costas, Gil G. |
| Copyright Year | 2003 |
| Abstract | We discuss the critical properies of the three-dimensional Gross-Neveu model at nonzero temperature and nonzero chemical potential. We also present numerical and analytical results for the in-medium interaction due to scalar meson exchange. Further, we discuss in-medium modifications of mesonic dispersion relations and wavefunctions. §1. Introduction Chiral phase transitions and the spectrum of excitations in strongly interacting matter at finite baryon chemical potential remain interesting challenges. Strongly interacting systems are intrinsically non-perturbative and therefore most of our knowledge about the relevant phenomena comes from lattice simulations. Unfortunately, the complex nature of the determinant of the QCD Dirac operator at finite chemical potential makes it impossible to use standard simulation techniques to study Fermi surface phenomena in Euclidean simulations. In order to understand what ingredients might play a decisive role in more complex systems such as gauge theories, we have studied the simplest non-trivial model simulable with µ = 0 using standard algorithms, namely the three-dimensional Gross-Neveu model (GNM 3). Its Lagrangian in Euclidean metric is written in terms of 4N f-component spinors ψ, ¯ ψ as L = ¯ ψ(∂ / + m)ψ − g 2 2N f (¯ ψψ) 2. In the chiral limit m = 0 the model has a global Z 2 symmetry ψ → γ 5 ψ, ¯ ψ → − ¯ ψγ 5. At tree level, the fields σ and π have no dynamics; they are trully auxiliary fields. However, they acquire dynamical content by dint of quantum effects arising from integrating out the fermions. The model is renormalizable in the 1/N f expansion unlike in the loop expansion. 1) Apart from the obvious numerical advantages of working with a relatively simple model there are several other motivations for studying this model. At T = µ = 0 for sufficiently strong coupling g 2 , the chiral symmetry is spontaneously broken by a condensate ¯ ψψ = 0 leading to a dynamically generated fermion mass gap given by M f = g 2 ¯ ψψ ≫ m in the large-N f approximation. The spectrum of excitations contains both baryons and mesons, i.e. the elementary fermions f and the composite f ¯ f states. The critical coupling g 2 c at which the gap M f /Λ U V → 0, defines an ultraviolet stable fixed point of the renormalisation group at which an interacting continuum limit may be taken. This picture has been verified both … |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-lat/0308021v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Algorithm Approximation Arabic numeral 0 Boson sampling Complex systems Coupling (computer programming) Diagram Dirac operator Euclidean distance Femtometer Fixed point (mathematics) Fixed-Point Number Interaction Lattice gauge theory Mesons Motivation Numerical analysis Perturbation theory (quantum mechanics) Phase Transition Propagator Quantum Hall effect Simulation Singlet state Spinor Time complexity Triune continuum paradigm biological signaling confirmation - ResponseLevel exponential |
| Content Type | Text |
| Resource Type | Article |
