According to the Nielsen-Ninomiya No-Go theorem, the doubling of fermions on the lattice cannot be suppressed in a chiral theory. Whereas Wilson and staggered fermions suppress doublers with explicit breaking of chiral symmetry, the random lattice does so by spontaneous chiral symmetry breaking even in the free theory. I present results for meson masses, the chiral condensate and fermionic eige...

It is found that in the SM the Ward-Takahashi(WT) identities of the axial-vector currents and the charged vector currents of fermions are invalid after spontaneous symmetry breaking. The spin-0 components of Z and W fields are revealed from the invalidity of these WT identities. The masses of these spin-0 components are at 10 14 GeV. They are ghosts. Therefore, unitarity of the SM after spontan...

According to the Nielsen-Ninomiya No-Go theorem, the doubling of fermions on the lattice cannot be suppressed in a chiral theory. Whereas Wilson and staggered fermions suppress doublers with explicit breaking of chiral symmetry, the random lattice does so by spontaneous chiral symmetry breaking even in the free theory. I present results for meson masses, the chiral condensate and fermionic eige...

We study spontaneous symmetry breaking in (φ)1+1 using the light-front formulation of the field theory. Since the physical vacuum is always the same as the perturbative vacuum in light-front field theory the fields must develop a vacuum expectation value through the zero-mode components of the field. We solve the nonlinear operator equation for the zero-mode in the one-mode approximation. We fi...

Asymmetric autocatalysis and inhibition have been proposed as key processes in the spontaneous emergence of chiral symmetry breaking in a prebiotic world. An elementary lattice model is formulated to simulate the kinetics of chiral symmetry breaking via autocatalysis and inhibition in a mixture of prochiral reactants, chiral products, and inert solvent. Starting from a chirally unbiased initial...

Spontaneous breaking of parity or time reversal invariance offers a solution to the strong CP problem, the stability of which under quantum gravitational effects provides an upper limit on the scale of symmetry breaking. Even more important, these Planck scale effects may provide a simple and natural way out of the resulting domain wall problem. ∗Invited talk at the 4th Hellenic School on Eleme...

Spontaneous symmetry breaking phenomena in the transverse field mixed $p$-spin glass model finite dimensions are studied with Nishimori's gauge theory. Useful identities theory enable us to study $\mathbb Z_2$-symmetry breaking. It is proven that ferromagnetic long-range order and spontaneous magnetization at an arbitrary temperature bounded by those on Nishimori line corresponding classical mo...

We investigate the influence of spontaneous symmetry breaking on the decoherence of a many-particle quantum system. This decoherence process is analyzed in an exactly solvable model system that is known to be representative of symmetry broken macroscopic systems in equilibrium. It is shown that spontaneous symmetry breaking imposes a fundamental limit to the time that a system can stay quantum ...

We describe one of the remarkable problems of theoretical physics persevering up to the beginning of the millennium. All gauge theories with spontaneous gauge symmetry breaking from the standard model of particle physics with the electroweak symmetry breaking at the Fermi scale, 246 GeV, up to strings, supergravity, and the M(embrane)-theory superunification with symmetry breaking starting near...

We show that in SU(3)C ⊗ SU(3)L ⊗ U(1)N (3-3-1) models embedded with a singlet scalar playing the role of the axion, after imposing scale invariance, dynamical symmetry breaking of Peccei-Quinn symmetry occurs through the one-loop effective potential for the singlet field. We, then, analyze the structure of spontaneous symmetry breaking by studying the new scalar potential for the model, and ve...