Yutaka Tobita

Matter-enhanced transition probabilities in quantum field theory

Abstract The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincare 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 waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S -matrix, S [ T ] , that satisfies the boundary condition at T. Using S [ T ] , the finite-size corrections of the form of 1 / T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths.

On Coherence Lengths of Wave Packets

The coherence lengths of one-particle states described using quantum wave functions are studied. We show that one particle states in various situations are not described using simple plane waves but using wave packets that are superpositions of plane waves. A wave packet is an approximate eigenstate of the free Hamiltonian and has a finite spatial size that we call the coherence length. The coherence lengths in the coordinate space and momentum space are studied in this paper. We investigate several mechanisms of forming wave packets, stabilities of wave packets, and transformations of wave packets. Subject Index: 060, 064

Neutrino Masses and Mixing

We report (1) the current status of neutrino parameters and (2) our recent work on implications of particles coherence, which are weakly related each others. In the first part, current status of the neutrino parameters obtained from oscillation experiments and their prospects are briefly reviewed. From various oscillation experiments, existence of three mass scales have been confirmed. One value of the difference of mass squared is around 10−3eV2 and another is around 10−5eV2. Although mixing angles are partly found, one important angle, θ13 is left unknown.In the second part, implications of coherence length of particles in the scattering of ultra‐high energy cosmic rays (UHCR) with cosmic background radiations (CBR) is discussed. Although coherence length is regarded usually irrelevant to observations, its role is important in several situations of recent experiments which include that of the ultra‐high energy charged particles. Here we discuss the scattering of UHCR with CBR.

Anomalous radiative transitions

Anomalous transitions involving photons derived by many-body interaction of the form, @µG 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 0 + P (d) , now with P (d) 6 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 ( 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.

Finite-Size Corrections to Fermi’s Golden Rule

The transition process in quantum mechanics has been studied with the probability ΓT proportional to the time interval T between the initial and final states, where Γ is the rate. Recently it was found that the constant term P(d) is added as P = ΓT +P(d). P(d) has been ignored for a macroscopic T, but that is not ignoable in various systems. We find P(d) in such processes that Γ ≈ 0 and show that it has wave-like properties and leads unusual quantum phenomena. P(d) is

Finite-size corrections to Fermi's golden rule

Decay rates and scattering cross sections in the situation where the wave functions overlap in wide area have been unclarified long time. We solve this problem with the scattering matricies that satisfy the boundary conditions of experiments of finite time interval T between the initial and final states, S[T]. S[T] is different from the standard S[∞] that satisfies them at T = ∞. The transition rates computed using Fermi’s golden rules need no corrections normaly. However they are subject to corrections of non-negligible magnitudes and necessary to compare the theory with experiments in the present case, particuraly for light particles. The wave functions that evolve according to Schrodinger equation conserve the total energy but not the kinetic energy at a finite t. Thus S[T] has variouis unusual properties which are caused by non-conservation of the kinetic-energy, different from those of S[∞]. The corrections can be computed rigorously and have universal properties in relativisticaly invariant systems. Derivations, origins, and unusual properties of the finite-size corrections of processes on neutrinos and gamma rays are presented. Especially applications to the determination of neutrino absolute mass and to phenomena of anomolous light emittion are presented. References: K.Ishikawa and Y. Tobita, “Finite-size corrections to Fermi’s golden rule,I”, arXiv:1303.468[hep-ph] K.Ishikawa and Y. Tobita,”Long range correlation of neutrino in hadron reactions I and II”arXiv:1206.2593[hep-ph],1209:5586[hep-ph], K.Ishikawa and Y. Tobita,”Quantum diffraction of neutrino “arXiv:1209.5585 (v2)[hep-ph] 1 APPC12 The 12th Asia Pacific Physics Conference