Modern Physics Letters A

The dynamical fermion mass generation on the 3-brane in the 5D spacetime is discussed in a model with bulk fermions in interaction with fermions on the branes assuming the presence of a constant Abelian gauge field A₅ in the bulk. We calculate the effective potential as a function of the fermion masses and the gauge field A₅. The masses can be found from the stationarity condition for the effective potential (the gap equation). We formulate the equation for the mass spectrum of the 4D-fermions. The phases with finite and vanishing fermion masses are studied and the dependence of the masses on the radius of the fifth dimension is analyzed. The influence of the A₅-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable. The critical values of the A₅ field, the coupling constant and the radius are examined.

We argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy–momentum space. We discuss the freezing of vacuum energy in such a dynamical energy–momentum space and present a phenomenologically viable seesaw formula for the cosmological constant in this context.

In this paper, we show the equivalence between a classical static scalar field theory and the (closed) de Sitter cosmological model whose potential represents shape invariance property. Based on this equivalence, we calculate the one-loop quantum cosmological correction to the ground state energy of the kink-like solution in the (closed) de Sitter cosmological model in which the fluctuation potential V′′ has a shape invariance property. It is shown that this type of correction, which yields a renormalized mass in the case of scalar field theory, may be interpreted as a renormalized gravitational constant in the case of (closed) de Sitter cosmological model.

Having its origin in a successful mapping technique, the Fock–Tani formalism, the corrected model retains the basic aspects of the predictions with the inclusion of bound-state corrections. Evaluation of the decay amplitudes has been performed for open-flavor strong decays in the light meson sector. The bound-state corrections introduce a fine-tuning for the former model, in particular, the adjustment of the D/S ratios in b₁→ωπ, a₁→ρπ and h₁→ρπ decays.

We study an effective gauge theory whose gauge group is a semidirect product G = G_c ⋊ Γ with G_c and Γ being a connected Lie group and a finite group, respectively. The semidirect product is defined through a projective homomorphism (i.e. homomorphism up to the center of G_c) from Γ into G_c. To be specific, we take SU(3)_L as G_c and ℤ₃ × ℤ₃ as Γ. We notice that the irreducible representations of the gauge group G necessarily contain three G_c-multiplets in spite of the Abelian nature of Γ = ℤ₃ × ℤ₃. This triplication phenomenon is due to the semidirect product structure of G. We suggest that the appearance of three families is attributable to this triplication. We give a toy model on the lepton mixing and show that under a particular vacuum alignment the tri-bimaximal mixing matrix is reproduced.

We study the modification of Newton's second law, upto first order in the deformation parameter a, in the κ-spacetime. We derive the deformed Hamiltonian, expressed in terms of the commutative phase space variables, describing the particle moving in a central potential in the κ-spacetime. Using this, we find the modified equations of motion and show that there is an additional force along the radial direction. Using Pioneer anomaly data, we set a bound for a. We also analyze the violation of equivalence principle predicted by the modified Newton's equation, valid up to first order in a and use this also to set an upper bound on a.