In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry m...

The global chiral symmetry of a SU(2) gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff Λ and the boundary conditions for the relevant couplings. The physical theory is obtained at Λ = 0. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the...

The importance of the spectral density of the Dirac operator in studying spontaneous chiral symmetry breaking and anomalous U(1)A symmetry breaking are reviewed. It is shown that both types of symmetry breaking can be traced to effects of modes near zero virtuality. Above Tc, where chiral symmetry is restored, it is shown on general grounds that (in the mq → 0 limit), the density of states vani...

I discuss the quark parton structure of octet baryons and the fragmentation of quarks into baryons in a spectator diquark model. The hyperfine interaction, responsible for the ∆-N and Σ-Λ mass splittings, leads not only to sizable SU(3) and SU(6) symmetry breaking in the quark distributions among the octet baryons but also to significant polarized non-strange quark distributions for the Λ. The ...

Retaining only the ‘timelike’ component A0 of the vector potential a skelet model with explicit global center symmetry is constructed for SU(2) Yang-Mills theory. It is shown that the A0 gluon vacuum is equivalent with the 4-dimensional Coulomb-gas. In 1–loop approximation, the effective theory of the skelet model exhibits non-local self-interaction. A coupling constant λ is found that governs ...

We show that the Standard Model Lagrangian, including small neutrino masses, has an anomaly-free discrete Z6 symmetry. This symmetry can emerge naturally from (I3 R + Li + Lj − 2Lk) gauge symmetry (Li is the ith lepton number) and ensure the stability of the nucleon even when the threshold of new physics Λ is low. All ∆B = 1 and ∆B = 2 (B is the baryon number) effective operators are forbidden ...

This paper presents symmetry classes of the Hartree-Fock (HF) solutions of spin and orbital ordered states in a t2g Hubbard model on a two-dimensional square lattice. Using a group theoretical bifurcation theory of the Hartree-Fock equation, we obtained many types of broken symmetry solutions which bifurcate from the normal state through one step transition in cases of commensurate ordering vec...