Schwinger Formula Revisited

We apply the formal W.K.B. method in the complex plane to the quantum field theory to obtain the Schwinger formula for spin and spinless particles; i.e., we obtain the probability that the vacuum state remains unchanged in presence of a constant electric field. Finally, from Schwinger formula we calculate the probability that n pairs are produced.     

Pion-Muon Asymmetry Revisited

Long ago an unexpected and unexplainable phenomena was observed. The distribution of muons from positive pion decay at rest was anisotropic with an excess in the backward direction relative to the direction of the proton beam from which it was produced. Although this effect was observed by several different groups with pions produced by different means and detected by different methods, the result was not accepted by the physics community, because it is in direct conflict with a large set of other experiments indicating that the pion is a pseudoscalar particle. It is possible to satisfy both sets of experiments if helicity-zero vector particles exist and the pion is such a particle. Helicity-zero vector particles have direction but no net spin. For the neutral pion to be a vector particle requires an additional modification to conventional theory as discussed herein. An experiment is proposed which can prove that the asymmetry in the distribution of muons from pion decay is a genuine physical effect because the asymmetry can be modified in a controllable manner. A positive result will also prove that the pion is not a pseudoscalar particle.     

Dirac Reduction Revisited

Abstract

The procedure of Dirac reduction of Poisson operators on submanifolds is discussed within a particularly useful special realization of the general Marsden-Ratiu reduction procedure. The Dirac classification of constraints on ‘first-class’ constraints and ‘second-class’ constraints is reexamined.     

Popper's Experiment Revisited

Recently, there has been increasing theoretical and experimental interest in Popper's gedanken experiment. We calculate in this paper, using the path integral approach, the diffraction patterns predicted by quantum mechanics for this arrangement. The calculations confirm the narrowing of the width of the pattern in absence of the slit obtained experimentally by Kim and Shih (Y. Kim and Y. Shih, Found. Phys. 29, 1849 (1999)).     

Noncommutative Instantons Revisited

We find a new gauge in which U(1) noncommutative instantons are explicitly non-singular on noncommutative R ⁴. We also present a pedagogical introduction into noncommutative gauge theories.     

Fermionic Linear Optics Revisited

We provide an alternative view of the efficient classical simulatibility of fermionic linear optics in terms of Slater determinants. We investigate the generic effects of two-mode measurements on the Slater number of fermionic states. We argue that most such measurements are not capable (in conjunction with fermion linear optics) of an efficient exact implementation of universal quantum computation. Our arguments do not apply to the two-mode parity measurement, for which exact quantum computation becomes possible.     

The Equivalence Principle Revisited

The validity of the equivalence principle is examined. Since classical physics is not valid for point particles, and a mass density over a finite volume tends to collapse, stabilizing forces are necessary. These cause a deviation from geodesic motion. That deviation is discussed in the light of recent results which provide approximate expressions for the self-force of a finite size particle due to both its mass and its charge. The equivalence principle appears to be violated.     

Two-Dimensional Topological Strings Revisited

The topological string of the type A with a two-dimensional target space is studied, an explicit formula for the string partition function is found and the target space field theory reproducing this partition function is proposed. This field theory has an infinite set of additional deformations overlooked by the standard definition of the topological string. It can be in turn coupled to gravity, thereby realizing the “worldsheets for worldsheets” idea. We also exhibit the wave function nature of the string partition function and suggest a new relation to quantum integrable systems.     

Matrix Vieta Theorem Revisited

We give another proof of the noncommutative analog of the Vieta theorem. This proof gives a little bit stronger statement and leads to some generalizations.     

General Jacobi Identity Revisited

In a previous paper (Nishimura, 1997) we probedthe deeper structure of the Jacobi identity of vectorfields with respect to Lie brackets within the realm ofsynthetic differential geometry to find what might be called the general Jacobi identity ofmicrocubes. The main objective of this paper is topresent a less esoteric and more lucid proof ofit.     

Newton's First Law Revisited

The formulations of Newton's first law in Newton's Principia and in modern textbooks are examined critically. A special effort is made to differentiate clearly between definitions and nontrivial facts of nature, and this is done in as primitive terms as possible, with emphasis on the projective structure. A somewhat novel characterization of the term free particle is proprosed, and a new, coordinate-independent definition of the term straight line is provided. The analysis is performed in 4-dimensional spacetime, and separately for the idealized case of the absence of gravity and for the dynamics in the presence of gravity.     

The Pauli Principle Revisited

By the Pauli exclusion principle, no quantum state can be occupied by more than one electron. One can state this as a constraint on the one electron density matrix that bounds its eigenvalues by 1. Shortly after its discovery, the Pauli principle was replaced by anti-symmetry of the multi-electron wave function. In this paper we solve a longstanding problem about the impact of this replacement on the one electron density matrix, that goes far beyond the original Pauli principle. Our approach uses Berenstein and Sjamaar’s theorem on the restriction of an adjoint orbit onto a subgroup, and allows us to treat any type of permutational symmetry. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Three-Pulse ELDOR Theory Revisited

The current theory of three-pulse electron double resonance (PELDOR) has been generalized to the case, when paramagnetic particles (spin labels) in pairs or groups have the electron paramagnetic resonance (EPR) spectra, which overlap essentially or coincide. The PELDOR signal modulation induced by the dipole–dipole interaction between paramagnetic spin ½ particles in pairs embedded in disordered systems has been analyzed comprehensively. It has been shown that the PELDOR signal contains additional terms in contrast to the situation considered in the current theory, when the EPR spectra of the spin labels in the pairs do not overlap. In disordered systems, the pairs of spin labels have the characteristic dipolar interaction frequency. According to the current theory for pairs of spin labels, the PELDOR signal reveals the modulation with this characteristic frequency. The additional terms, which are obtained in this work, do not change the modulation frequency of the PELDOR signal for pairs of spin labels. However, these additional terms should be taken into account when analyzing the amplitude of the PELDOR signal and the amplitude of the modulation of the PELDOR signal. The consistent approach to treating the PELDOR data for the groups containing three or more spin labels has been outlined on the basis of the results for pairs of spin labels. It has been also analyzed how the spin flips and molecular motion or molecular isomerization can affect the manifestation of the interaction between the spin labels in PELDOR experiments. PELDOR experiments for the stable biradicals (biradicals I containing 1-oxyl-2,2,5,5-tetramethylpyrroline-3-yl spin labels and biradicals II containing 3-imidazoline spin labels) have been performed. The results have been interpreted within the theory developed in this work.     

The Equivalence Principle Revisited

A precise fomulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity but allowing for the presence of torsion. For the sake of brevity, a concise statement is proposed for the Principle: An ideal observer immersed in a gravitational field can choose a reference frame in which gravitation goes unnoticed. This statement is given a clear mathematical meaning through an accurate discussion of its terms. It holds for ideal observers (time-like smooth non-intersecting curves), but not for real, spatially extended observers. Analogous results hold for gauge fields. The difference between gravitation and the other fundamental interactions comes from their distinct roles in the equation of force.     

High-Dimensional Incipient Infinite Clusters Revisited

The incipient infinite cluster (IIC) measure is the percolation measure at criticality conditioned on the cluster of the origin to be infinite. Using the lace expansion, we construct the IIC measure for high-dimensional percolation models in three different ways, extending previous work by the second-named author and Járai. We show that each construction yields the same measure, indicating that the IIC is a robust object. Furthermore, our constructions apply to spread-out versions of both finite-range and long-range percolation models. We also get estimates on structural properties of the IIC, such as the volume of the intersection between the IIC and Euclidean balls.     

Superadditivity of Wigner-Yanase-Dyson Information Revisited

The Wigner-Yanase-Dyson information is an important variant of quantum Fisher information. Two fundamental requirements concerning this notion of information content originally postulated by Wigner and Yanase are convexity and superadditivity. The former was fully established by Lieb in 1973, and led to the first proof of the strong subadditivity of quantum entropy. The latter, although widely believed to be true, was quite recently disproved by Hansen. Nevertheless, superadditivity has also been established in two extreme cases, i.e., when the states are pure or classical. In this paper, we first review a scheme to classify bipartite states into a hierarchy of classical, semi-quantum, and quantum states, which are arranged in the order of increasing quantumness. We then prove the superadditivity of the Wigner-Yanase-Dyson information for all semi-quantum states. The convexity of the Wigner-Yanase-Dyson information plays a crucial role here.     

K-Essential Phantom Energy: Revisited

We generalize some of those results which are closely related to the canonical kinetic term in k-essence formalism by further tuning the parameter (β). The scale factor a(t) could be negative and decreasing within a specific range of β (≡−1/ω, ω : the equation-of-state parameter) during the initial evolutional period.     

General Jacobi Identity Revisited Again

Synthetic differential geometry occupies a unique position in topos-theoretic physics. Nevertheless it has appeared somewhat too conceptual to physicists in general, partly because it has appeared to lack computational aspects. Its computational facets are really concerned with computation of the quasi-colimit of a finite diagram of infinitesimal spaces, or equivalently, with computation of the limit of a finite diagram of Weil algebras. Indeed we have been forced to do a highly involved computation of the above kind by hand in our previous papers (Nishimura, H. in Int. J. Theor. Phys. 36:1099–1131, 1997 and Nishimura, H. in Int. J. Theor. Phys. 38:2163–2174, 1999). The principal objective in this paper is to show that Grö bner bases techniques provide us with means that relegate such computations to computers.     

A Theorem of Ludwig Revisited

Using a recent result of Busch and Gudder, we reconsider a theorem of Ludwig which allows one to identify a class of effect automorphisms as the symmetry transformations in quantum mechanics.