# Generalized S-Matrix in Mixed Representation

@article{Ishikawa2005GeneralizedSI, title={Generalized S-Matrix in Mixed Representation}, author={Kenzo Ishikawa and Takashi Shimomura}, journal={Progress of Theoretical Physics}, year={2005}, volume={114}, pages={1201-1234} }

We formulate a generalized scattering amplitude in which the momenta and positions of incoming particles and outgoing particles are specified. Ideal beams and ideal measuring instruments, for which the momenta and positions realize the minimum uncertainty, are studied using minimum wave packets, i.e., coherent states. In the present work, we elucidate the general features of the genelarized scattering amplitudes based on Φ 4 theory. We prove the completeness of many body states and determine…

## 11 Citations

New effect in wave-packet scatterings of quantum fields

- Education
- 2021

In a transition amplitude of wave-packets, e.g., that of the Φ → φφ decay process, there are in and out time boundaries for the initial Φ and ﬁnal φφ conﬁgurations, respectively, when the transition…

A complete set of Lorentz-invariant wave packets and modified uncertainty relation

- Physics
- 2021

We define a set of fully Lorentz-invariant wave packets and show that it spans the corresponding one-particle Hilbert subspace, and hence the whole Fock space as well, with a manifestly…

Finite-size corrections to Fermi's golden rule: I. Decay rates

- Physics
- 2013

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 Schr\"{o}dinger equation, it…

Anomalous radiative transitions

- Physics
- 2014

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…

Particle decay in Gaussian wave-packet formalism revisited

- PhysicsProgress of Theoretical and Experimental Physics
- 2018

We derive the Fermi's golden rule in the Gaussian wave-packet formalism of quantum field theory, proposed by Ishikawa, Shimomura, and Tobita, for the particle decay within a finite time interval. We…

Wave packets in QFT: Leading order width corrections to decay rates and clock behavior under Lorentz boosts

- PhysicsPhysical Review D
- 2021

Decay rates in quantum field theory (QFT) are typically calculated assuming the particles are represented by momentum eigenstates (i.e. plane waves). However, strictly speaking, localized free…

Scalar scattering amplitude in the Gaussian wave-packet formalism

- Physics
- 2020

We compute an $s$-channel $2\to2$ scalar scattering $\phi\phi\to\Phi\to\phi\phi$ in the Gaussian wave-packet formalism at the tree-level. We find that wave-packet effects, including shifts of the…

Novel approach to neutron electric dipole moment search using weak measurement

- PhysicsJournal of Physics B: Atomic, Molecular and Optical Physics
- 2021

We propose a novel approach in a search for the neutron electric dipole moment (EDM) by taking advantage of signal amplification in a weak measurement, known as weak value amplification. Considering…

2 2 0 Se p 20 05 Coherent lunar effect on solar neutrino : double slitt interference

- Physics

Coherent interaction of solar neutrino with the moon and its implication is investigated. We solve the Dirac equation with the moon potential and show that a phase shift of the neutrino wave function…