Apparent Superluminal Muon-neutrino Velocity as a Manifestation of Weak Value

The result of the OPERA experiment revealed that the velocity of muon-neutrinos was larger than the speed of light. We argue that this apparent superluminal velocity can be interpreted as a weak value, which is a new concept recently studied in the context of quantum physics. The OPERA experiment setup forms a scheme that manifests the neutrino velocity as a weak value. The velocity defined in the scheme of weak measurement can exceed the speed of light. The weak velocity is not a concept associated to a single phenomenon but it is a statistical concept defined by accumulating data at separated places and by comparing the data. Neither information nor physical influence is conveyed at the weak velocity. Thus the superluminal velocity in the sense of weak value does not contradict the causality law. We propose also a model for calculating the neutrino velocity with taking neutrino oscillation into account.Comment: 5 pages, no figur

Isoholonomic Problem and Holonomic Quantum Computation

Geometric phases accompanying adiabatic processes in quantum systems can be utilized as unitary gates for quantum computation. Optimization of control of the adiabatic process naturally leads to the isoholonomic problem. The isoholonomic problem in a homogeneous fiber bundle is formulated and solved completely.Comment: 7 pages, Proceedings of International Conference on Topology in Ordered Phases organized by Hokkaido University in March 200

Functional Integral in terms of the Field Strength: An Approach to Chiral Symmetry Breaking

The chiral symmetry breaking in the 4-dimensional QED with the chirally invariant four-fermion interaction is discussed by using a novel path integral expression in terms of the field-strength tensor. In the local potential approximation, we find that the chiral symmetry is spontaneously broken for any nonzero gauge and four-fermion couplings on the tree level of an auxiliary field $\sigma$. The present approach allows us to easily include higher orders of the gauge coupling so that the effective potential up to the sixth order is obtained.Comment: 18 pages, 2 figure

Complementarity and the nature of uncertainty relations in Einstein-Bohr recoiling slit experiment

A model of the Einstein-Bohr double-slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has the double slits in it, as well as the state of a particle incoming to the double slits, are described by quantum mechanics. Using this model, we analyzed complementarity between exhibiting the interference pattern and distinguishing the particle path. Comparing the Kennard-Robertson type and the Ozawa-type uncertainty relations, we conclude that the uncertainty relation involved in the double-slit experiment is not the Ozawa-type uncertainty relation but the Kennard-type uncertainty relation of the position and the momentum of the double-slit wall. A possible experiment to test the complementarity relation is suggested. It is also argued that various phenomena which occur at the interface of a quantum system and a classical system, including distinguishability, interference, decoherence, quantum eraser, and weak value, can be understood as aspects of entanglement.Comment: 13 pages, 2 figures. The title is changed. Some references are adde