Proper-Time Formalism in a Constant Magnetic Field at Finite Temperature and Chemical Potential

Abstract

We investigate scalar and spinor field theories in a constant magnetic field at finite temperature and chemical potential. In an external constant magnetic field the exact solution of the two-point Green functions are obtained by using the Fock-Schwinger proper-time formalism. We extend it to the thermal field theory and find the expressions of the Green functions exactly for the temperature, the chemical potential and the magnetic field. For practical calculations the contour of the proper-time integral is carefully selected. The physical contour is discussed in a constant magnetic field at finite temperature and chemical potential. As an example, behavior of the vacuum self-energy is numerically evaluated for the free scalar and spinor fields.

arXiv comment17 pages, 4 figures. Compared previous result, comments, figure, reference added and typos corrected

References in corpus (4)

• Magnetic Fields in the Early Universe
• Four-fermion Interaction Model in a Constant Magnetic Field at Finite Temperature and Chemical Potential
• Dynamical symmetry breaking in the external gravitational and constant magnetic fields
• Axion Decay in a Constant Electromagnetic Background Field and at Finite Temperature using World-line Methods

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