126 research outputs found
Covariant harmonic oscillators: 1973 revisited
Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated
Do Small-mass Neutrinos participate in Gauge Transformations?
Neutrino oscillation experiments presently suggest that neutrinos have a
small but finite mass. If neutrinos are to have mass, there should be a Lorentz
frame in which they can be brought to rest. This paper discusses how Wigner's
little groups can be used to distinguish between massive and massless
particles. We derive a representation of the SL(2,c) group which separates out
the two sets of spinors contained therein. One set is gauge dependent. The
other set is gauge-invariant and represents polarized neutrinos. We show that a
similar calculation can be done for the Dirac equation. In the
large-momentum/zero-mass limit, the Dirac spinors can be separated into large
and small components. The large components are gauge invariant, while the small
components are not. These small components represent spin-
non-zero mass particles. If we renormalize the large components, these gauge
invariant spinors again represent the polarization of neutrinos. Massive
neutrinos cannot be invariant under gauge transformations.Comment: 15 page
Mirror symmetry on K3 surfaces via Fourier-Mukai transform
We use a relative Fourier-Mukai transform on elliptic K3 surfaces to
describe mirror symmetry. The action of this Fourier-Mukai transform on the
cohomology ring of reproduces relative T-duality and provides an
infinitesimal isometry of the moduli space of algebraic structures on
which, in view of the triviality of the quantum cohomology of K3 surfaces, can
be interpreted as mirror symmetry.Comment: 15 pages, AMS-LaTeX v1.2. Final version to appear in Commun. Math.
Phy
Is it possible to construct the Proton Structure Function by Lorentz-boosting the Static Quark-model Wave Function?
The energy-momentum relations for massive and massless particles are E =
p^2/2m and E = pc respectively. According to Einstein, these two different
expressions come from the same formula E = \sqrt{(cp)^2 + m^2 c^4}. Quarks and
partons are believed to be the same particles, but they have quite different
properties. Are they two different manifestations of the same covariant entity
as in the case of Einstein's energy-momentum relation? The answer to this
question is YES. It is possible to construct harmonic oscillator wave functions
which can be Lorentz-boosted. They describe quarks bound together inside
hadrons. When they are boosted to an infinite-momentum frame, these wave
functions exhibit all the peculiar properties of Feynman's parton picture. This
formalism leads to a parton distribution corresponding to the valence quarks,
with a good agreement with the experimentally observed distribution.Comment: LaTex 12 pages, 5 figures, presented at the 26th MRST Conference on
High-Eenergy Physics (Montreal, Canada, 2004), to be published in the
proceeding
Quantifying the Increase in Radiation Exposure Associated with SPECT/CT Compared to SPECT Alone for Routine Nuclear Medicine Examinations
Purpose. We quantify the additional radiation exposure in terms of effective dose incurred by patients in the CT portion of SPECT/CT examinations.
Methods. The effective dose from a variety of common nuclear medicine procedures is calculated and summarized. The extra exposure from the CT portion of the examination is summarized by examination and body part. Two hundred forty-eight scans from 221 patients are included in this study. The effective dose from the CT examination is also compared to average background radiation.
Results. We found that the extra effective dose is not sufficient to cause deterministic effects. However, the stochastic effects may be significant, especially in patients undergoing numerous follow-up studies. The cumulative effect might increase the radiation exposure compared to patient management with SPECT alone.
Conclusions. While the relative increase in radiation exposure associated with SPECT/CT is generally considered acceptable when compared with the benefits to the patient, physicians should make every effort to minimize this effect by using proper technical procedures and educating patients about the exposure they will receive
Standing waves in the Lorentz-covariant world
When Einstein formulated his special relativity, he developed his dynamics
for point particles. Of course, many valiant efforts have been made to extend
his relativity to rigid bodies, but this subject is forgotten in history. This
is largely because of the emergence of quantum mechanics with wave-particle
duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have
to deal with Lorentz transformations of waves. We now have some understanding
of plane waves or running waves in the covariant picture, but we do not yet
have a clear picture of standing waves. In this report, we show that there is
one set of standing waves which can be Lorentz-transformed while being
consistent with all physical principle of quantum mechanics and relativity. It
is possible to construct a representation of the Poincar\'e group using
harmonic oscillator wave functions satisfying space-time boundary conditions.
This set of wave functions is capable of explaining the quantum bound state for
both slow and fast hadrons. In particular it can explain the quark model for
hadrons at rest, and Feynman's parton model hadrons moving with a speed close
to that of light.Comment: LaTex 20 pages, presented at the 2004 meeting of the International
Association of Relativistic Dynamincs, to be published in the proceeding
Feynman's Decoherence
Gell-Mann's quarks are coherent particles confined within a hadron at rest,
but Feynman's partons are incoherent particles which constitute a hadron moving
with a velocity close to that of light. It is widely believed that the quark
model and the parton model are two different manifestations of the same
covariant entity. If this is the case, the question arises whether the Lorentz
boost destroys coherence. It is pointed out that this is not the case, and it
is possible to resolve this puzzle without inventing new physics. It is shown
that this decoherence is due to the measurement processes which are less than
complete.Comment: RevTex 15 pages including 6 figs, presented at the 9th Int'l
Conference on Quantum Optics (Raubichi, Belarus, May 2002), to be published
in the proceeding
Geometric Interpretation of the Mixed Invariants of the Riemann Spinor
Mixed invariants are used to classify the Riemann spinor in the case of
Einstein-Maxwell fields and perfect fluids. In the Einstein-Maxwell case these
mixed invariants provide information as to the relative orientation of the
gravitational and electromagnetic principal null directions. Consideration of
the perfect fluid case leads to some results about the behaviour of the
Bel-Robinson tensor regarded as a quartic form on unit timelike vectors.Comment: 31 pages, AMS-LaTe
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