Analytical approach to chiral symmetry breaking in Minkowsky space

Abstract

The mass gap equation for spontaneous chiral symmetry breaking is studied directly in Minkowsky space. In hadronic physics, spontaneous chiral symmetry breaking is crucial to generate a constituent mass for the quarks, and to produce the Partially Conserved Axial Current theorems, including a small mass for the pion. Here a class of finite kernels is used, expanded in Yukawa interactions. The Schwinger-Dyson equation is solved with an analytical approach. This improves the state of the art of solving the mass gap equation, which is usually solved with the equal-time approximation or with the Euclidean approximation. The mapping from the Euclidean space to the Minkowsky space is also illustrated.

7 pages, 3 figures

References in corpus (4)

• Analytic proof that the Quark Model complies with the PCAC theorems
• Chiral symmetry breaking solutions for QCD in the truncated Coulomb gauge
• Quark Schwinger-Dyson Evaluation of the l1, l2 Coefficients in the Chiral Lagrangian
• Vacuum replicas in two-dimensional QCD

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• Dynamical electroweak symmetry breaking due to strong Yukawa interactions
• Schwinger-Dyson Equation in Minkowski Space beyond the IE Approximation
• Quark Schwinger-Dyson equation in temporal Euclidean space
• Quark mass function in Minkowski space
• Some Analytical Aspects in Field Theories with Dynamical Mass Generation
• Quark mass function at finite temperature in real-time formalism