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Effective Action of Non-Local Nambu-Jona-Lasinio Model in a Constant Magnetic Field

Tabatabaee Mehr, Mohammad Ali | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45681 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Sadooghi, Neda
  7. Abstract:
  8. In the framework of the Standard Model of Particle Physics, Quantum Chromodynamics (QCD) is known to be the only theory which describes the strong nuclear force. Because of the property of asymptotic freedom, perturbative methods fail to describe QCD at low energies. Here, mesons and baryons build the main degrees of freedom of QCD. To describe the dynamics of mesons at low energies, nonperturbative methods are used. The Nambu–Jona-Lasinio (NJL) model is one of the most important effective models, which is used to study the nonperturbative phenomena of QCD at low energies. The Lagrangian density of this model includes a local four-fermion term,which descibes the interaction between the quarks. In this thesis, we consider an extension of the local NJL model, the so called non-local NJL model, that includes a certain distribution function in the bosonic current, that describes the nonlocal nature of the interaction between a quark and an antiquark. The aim is to determine the bosonic effective action of this model in a constant magnetic field. To this purpose, we use two different methods and will show that the effective action of the magnetized nonlocal NJL model is the same as the effective action of the magnetized local NJL model, provided that we replace the constituent quark mass m + σ with m + p 1+(eBd2)2 .Here, m is the current quark mass, σ is the chiral condensate, eB, describes the strength of the magnetic field and d characterizes the width of the Gaussian distribution function, which plays the role of nonlocality in the four-Fermi interaction of the nonlocal NJL model
  9. Keywords:
  10. Ritus Method ; Quantum Chromo Dynamics ; Effective Action ; Constant Magnetic Field ; Schwinger Proper-Time Method ; Nonlocal Nambu-Jona-Lasinio

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