The weak-field expansion of the charged fermion propagator under a uniform magnetic field is studied. Starting from Schwinger's proper-time representation, we express the charged fermion propagator as an infinite series corresponding to different Landau levels. This infinite series is then reorganized according to the powers of the external field strength B. For illustration, we apply this expansion to γ → νν and ν → νγ decays, which involve charged fermions in the internal loop. The leading and subleading magnetic-field effects to the above processes are computed.

In this paper we construct a covariant light-front model of heavy mesons within the framework of heavy quark effective theory (HQET). The covariant model consists of the light-front heavy meson bound states constructed in the heavy quark limit with heavy quark symmetry and heavy quark effective theory as its basis. Within this model, the Isgur-Wise function and decay constants in the infinite quark mass limit can be evaluated in a very simple and the most general way. The results are ensured to be consistent with heavy quark symmetry. From the heavy-quark-limit bound states, we can further develop a systematic approach to calculate 1/m Q corrections from the 1/m Q expansion of QCD. This covariant model can serve as a quasi-first-principles description of heavy meson dynamics, namely, a phenomenological covariant bound state in the heavy quark limit which is consistent with heavy quark symmetry, plus a reliable first-principles computation of the 1/m Q corrections in HQET in terms of the 1/m Q expansion of the fundamental QCD theory.

A consistent treatment of B → πlν decay is given on the light-front. The B to π transition form factors are calculated in the entire physical range of momentum transfer for the first time. The valence-quark contribution is obtained using relativistic light-front wave functions. Higher quark-antiquark Fock-state of the B-meson bound state is represented effectively by the |B * π configuration, and its effect is calculated in the chiral perturbation theory.Wave function renormalization is taken into account consistently. The |B * π contribution dominates near the zero-recoil point (q 2 ≃ 25 GeV 2 ), and decreases rapidly as the recoil momentum increases. We find that the calculated form factor f + (q 2 ) follows approximately a dipole q 2 -dependence in the entire range of momentum transfer.

We study the neutrino-photon processes such as γγ → νν, νγ → νγ, and νν → γγ in a background magnetic field smaller than the critical magnetic field B c ≡ m 2 e /e. Using Schwinger's formalism, we extract leading magneticfield contributions to the above processes. Our result is valid throughout the kinematic regime where both neutrino and photon energies are significantly smaller than m W . We briefly discuss the astrophysical implications of our result.