364 research outputs found
Confined Quantum Time of Arrival for Vanishing Potential
We give full account of our recent report in [E.A. Galapon, R. Caballar, R.
Bahague {\it Phys. Rev. Let.} {\bf 93} 180406 (2004)] where it is shown that
formulating the free quantum time of arrival problem in a segment of the real
line suggests rephrasing the quantum time of arrival problem to finding a
complete set of states that evolve to unitarily arrive at a given point at a
definite time. For a spatially confined particle, here it is shown explicitly
that the problem admits a solution in the form of an eigenvalue problem of a
class of compact and self-adjoint time of arrival operators derived by a
quantization of the classical time of arrival. The eigenfunctions of these
operators are numerically demonstrated to unitarilly arrive at the origin at
their respective eigenvalues.Comment: accepted for publication in Phys. Rev.
Gravitational and electroweak unification by replacing diffeomorphisms with larger group
The covariance group for general relativity, the diffeomorphisms, is replaced
by a group of coordinate transformations which contains the diffeomorphisms as
a proper subgroup. The larger group is defined by the assumption that all
observers will agree whether any given quantity is conserved. Alternatively,
and equivalently, it is defined by the assumption that all observers will agree
that the general relativistic wave equation describes the propagation of light.
Thus, the group replacement is analogous to the replacement of the Lorentz
group by the diffeomorphisms that led Einstein from special relativity to
general relativity, and is also consistent with the assumption of constant
light velocity that led him to special relativity. The enlarged covariance
group leads to a non-commutative geometry based not on a manifold, but on a
nonlocal space in which paths, rather than points, are the most primitive
invariant entities. This yields a theory which unifies the gravitational and
electroweak interactions. The theory contains no adjustable parameters, such as
those that are chosen arbitrarily in the standard model.Comment: 28 pages
Confined Quantum Time of Arrivals
We show that formulating the quantum time of arrival problem in a segment of
the real line suggests rephrasing the quantum time of arrival problem to
finding states that evolve to unitarily collapse at a given point at a definite
time. For the spatially confined particle, we show that the problem admits a
solution in the form of an eigenvalue problem of a compact and self-adjoint
time of arrival operator derived by a quantization of the classical time of
arrival, which is canonically conjugate with the Hamiltonian in closed subspace
of the Hilbert space.Comment: Figures are now include
Nonperturbative Renormalization in Light-Cone Quantization
Two approaches to nonperturbative renormalization are discussed for theories
quantized on the light cone. One is tailored specifically to a calculation of
the dressed-electron state in quantum electrodynamics, where an invariant-mass
cutoff is used as a regulator and a Tamm-Dancoff truncation is made to include
no more than two photons. The other approach is based on Pauli-Villars
regulators and is applied to Yukawa theory and a related soluble model. In both
cases discretized light-cone quantization is used to obtain a finite matrix
problem that can be solved nonperturbatively.Comment: 10 pages, LaTeX/RevTex, no figures, to appear in the proceedings of
Orbis Scientiae 1997: Twenty-Five Coral Gables Conferences and their Impact
on High Energy Physics and Cosmology, B.N. Kursunoglu, e
On Quantum State Observability and Measurement
We consider the problem of determining the state of a quantum system given
one or more readings of the expectation value of an observable. The system is
assumed to be a finite dimensional quantum control system for which we can
influence the dynamics by generating all the unitary evolutions in a Lie group.
We investigate to what extent, by an appropriate sequence of evolutions and
measurements, we can obtain information on the initial state of the system. We
present a system theoretic viewpoint of this problem in that we study the {\it
observability} of the system. In this context, we characterize the equivalence
classes of indistinguishable states and propose algorithms for state
identification
Momentum of an electromagnetic wave in dielectric media
Almost a hundred years ago, two different expressions were proposed for the
energy--momentum tensor of an electromagnetic wave in a dielectric. Minkowski's
tensor predicted an increase in the linear momentum of the wave on entering a
dielectric medium, whereas Abraham's tensor predicted its decrease. Theoretical
arguments were advanced in favour of both sides, and experiments proved
incapable of distinguishing between the two. Yet more forms were proposed, each
with their advocates who considered the form that they were proposing to be the
one true tensor. This paper reviews the debate and its eventual conclusion:
that no electromagnetic wave energy--momentum tensor is complete on its own.
When the appropriate accompanying energy--momentum tensor for the material
medium is also considered, experimental predictions of all the various proposed
tensors will always be the same, and the preferred form is therefore
effectively a matter of personal choice.Comment: 23 pages, 3 figures, RevTeX 4. Removed erroneous factor of mu/mu_0
from Eq.(44
On the Weyl - Eddington - Einstein affine gravity in the context of modern cosmology
We propose new models of an `affine' theory of gravity in -dimensional
space-times with symmetric connections. They are based on ideas of Weyl,
Eddington and Einstein and, in particular, on Einstein's proposal to specify
the space - time geometry by use of the Hamilton principle. More specifically,
the connection coefficients are derived by varying a `geometric' Lagrangian
that is supposed to be an arbitrary function of the generalized (non-symmetric)
Ricci curvature tensor (and, possibly, of other fundamental tensors) expressed
in terms of the connection coefficients regarded as independent variables. In
addition to the standard Einstein gravity, such a theory predicts dark energy
(the cosmological constant, in the first approximation), a neutral massive (or,
tachyonic) vector field, and massive (or, tachyonic) scalar fields. These
fields couple only to gravity and may generate dark matter and/or inflation.
The masses (real or imaginary) have geometric origin and one cannot avoid their
appearance in any concrete model. Further details of the theory - such as the
nature of the vector and scalar fields that can describe massive particles,
tachyons, or even `phantoms' - depend on the concrete choice of the geometric
Lagrangian. In `natural' geometric theories, which are discussed here, dark
energy is also unavoidable. Main parameters - mass, cosmological constant,
possible dimensionless constants - cannot be predicted, but, in the framework
of modern `multiverse' ideology, this is rather a virtue than a drawback of the
theory. To better understand possible applications of the theory we discuss
some further extensions of the affine models and analyze in more detail
approximate (`physical') Lagrangians that can be applied to cosmology of the
early Universe.Comment: 15 pages; a few misprints corrected, one footnote removed and two
added, the formulae and results unchanged but the text somewhat edited, esp.
in Sections 4,5; the reference to the RFBR grant corrected
The Relativistic Electrodynamics Least Action Principles Revisited: New Charged Point Particle and Hadronic String Models Analysis
The classical relativistic least action principle is revisited from the
vacuum field theory approach. New physically motivated versions of relativistic
Lorentz type forces are derived, a new relativistic hadronic string model is
proposed and analyzed in detail.Comment: n/
Casimir Energy for a Spherical Cavity in a Dielectric: Applications to Sonoluminescence
In the final few years of his life, Julian Schwinger proposed that the
``dynamical Casimir effect'' might provide the driving force behind the
puzzling phenomenon of sonoluminescence. Motivated by that exciting suggestion,
we have computed the static Casimir energy of a spherical cavity in an
otherwise uniform material. As expected the result is divergent; yet a
plausible finite answer is extracted, in the leading uniform asymptotic
approximation. This result agrees with that found using zeta-function
regularization. Numerically, we find far too small an energy to account for the
large burst of photons seen in sonoluminescence. If the divergent result is
retained, it is of the wrong sign to drive the effect. Dispersion does not
resolve this contradiction. In the static approximation, the Fresnel drag term
is zero; on the mother hand, electrostriction could be comparable to the
Casimir term. It is argued that this adiabatic approximation to the dynamical
Casimir effect should be quite accurate.Comment: 23 pages, no figures, REVTe
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