A quantum mechanical wave of a finite size moves like a classical particle and shows a unique decay probability. Because the wave function evolves according to the Schrödinger equation, it preserves the total energy but not the kinetic energy in the intermediate-time region of a decay process where those of the parent and daughters overlap. The decay rate computed with Fermi's golden rule requires corrections that vary with the distance between the initial and final states, and the energy distribution of the daughter is distorted from that of plane waves. The corrections have universal properties in relativistically invariant systems and reveal macroscopic quantum phenomena for light particles. The implications for precision experiments in beta decays and various radiative transitions are presented.Typeset by REVT E X

The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane Typeset by REVT E X 1

Anomalous transitions involving photons derived by many-body interaction of the form, ∂ µ G µ , in the standard model are studied. This does not affect the equation of motion in the bulk, but makes wave functions modified, and causes the unusual transition characterized by the time-independent probability. In the transition probability at a time-interval T expressed generally in the form P = T Γ 0 + P (d) , now with P (d) = 0. The diffractive term P (d) has the origin in the overlap of waves of the initial and final states, and reveals the characteristics of waves. In particular, the processes of the neutrino-photon interaction ordinarily forbidden by Landau-Yang's theorem (Γ 0 = 0) manifests itself through the boundary interaction. The new term leads to physical processes over a wide energy range to have finite probabilities. New methods of detecting neutrinos using laser are proposed that are based on this difractive term, which enhance the detectability of neutrinos by many orders of magnitude.

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It is pointed out that an agreement of the one particle energy spectrum of the cosmic background radiation (CMBR) with Plank distribution of 2.725 [K] does not give a strong constraint on the coherence length of CMBR if the mean free path of CMBR is very long. The coherence length in this situation is estimated as a few times of kBT . Due to this finite coherence length, the attenuation length of ultra-high energy cosmic rays (UHECR) is reduced in the ∆ resonance region,i.e., around 10 20 [eV]. The small attenuation length makes the suppression of the flux of cosmic rays in this energy region less prominent than the naive estimation.