69,127 research outputs found

### Comment on Experiments Related to the Aharonov-Bohm Phase Shift

Recent experiments undertaken by Caprez, Barwick, and Batelaan should clarify
the connections between classical and quantum theories in connection with the
Aharonov-Bohm phase shift. It is pointed out that resistive aspects for the
solenoid current carriers play a role in the classical but not the quantum
analysis for the phase shift. The observed absence of a classical lag effect
for a macroscopic solenoid does not yet rule out the possibility of a lag
explanation of the observed phase shift for a microscopic solenoid.Comment: 9 page

### Highly connected manifolds with positive Ricci curvature

We prove the existence of Sasakian metrics with positive Ricci curvature on
certain highly connected odd dimensional manifolds. In particular, we show that
manifolds homeomorphic to the 2k-fold connected sum of S^{2n-1} x S^{2n} admit
Sasakian metrics with positive Ricci curvature for all k. Furthermore, a
formula for computing the diffeomorphism types is given and tables are
presented for dimensions 7 and 11.Comment: This is the version published by Geometry & Topology on 29 November
200

### On Sasaki-Einstein manifolds in dimension five

We prove the existence of Sasaki-Einstein metrics on certain simply connected
5-manifolds where until now existence was unknown. All of these manifolds have
non-trivial torsion classes. On several of these we show that there are a
countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde

### Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical
electromagnetic zero-point radiation has a scaling symmetry which is suitable
for understanding the equilibrium behavior of classical thermal radiation at a
spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical
electron theory, the masses of the particles are the only scale-giving
parameters associated with mechanics while the action-angle variables are scale
invariant. The theory thus separates the interaction of the action variables of
matter and radiation from the scale-giving parameters. Classical zero-point
radiation is invariant under scattering by the charged particles of
relativistic classical electron theory. The basic ideas of the matter
-radiation interaction are illustrated in a simple relativistic classical
electromagnetic example.Comment: 18 page

### The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics

The analysis of this article is entirely within classical physics. Any
attempt to describe nature within classical physics requires the presence of
Lorentz-invariant classical electromagnetic zero-point radiation so as to
account for the Casimir forces between parallel conducting plates at low
temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's
equations into solutions. In an inertial frame, conformal symmetry leaves
zero-point radiation invariant and does not connect it to non-zero-temperature;
time-dilating conformal transformations carry the Lorentz-invariant zero-point
radiation spectrum into zero-point radiation and carry the thermal radiation
spectrum at non-zero temperature into thermal radiation at a different
non-zero-temperature. However, in a non-inertial frame, a time-dilating
conformal transformation carries classical zero-point radiation into thermal
radiation at a finite non-zero-temperature. By taking the no-acceleration
limit, one can obtain the Planck radiation spectrum for blackbody radiation in
an inertial frame from the thermal radiation spectrum in an accelerating frame.
Here this connection between zero-point radiation and thermal radiation is
illustrated for a scalar radiation field in a Rindler frame undergoing
relativistic uniform proper acceleration through flat spacetime in two
spacetime dimensions. The analysis indicates that the Planck radiation spectrum
for thermal radiation follows from zero-point radiation and the structure of
relativistic spacetime in classical physics.Comment: 21 page

### Semisimple Lie groups satisfy property RD, a short proof

We give a short elementary proof of the fact that connected semisimple real
Lie groups satisfy property RD. The proof is based on a process of
linearization

### Ihara's lemma and level rising in higher dimension

A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the
classical Ihara's lemma which is used to rise the modularity property between
some congruent galoisian representations. In their work on Sato-Tate,
Clozel-Harris-Taylor proposed a generalization of the Ihara's lemma in higher
dimension for some similitude groups. The main aim of this paper is then to
prove some new instances of this generalized Ihara's lemma by considering some
particular non pseudo Eisenstein maximal ideals of unramified Hecke algebras.
As a consequence, we prove a level rising statement

- â€¦