926 research outputs found
Renormalization in general theories with inter-generation mixing
We derive general and explicit expressions for the unrenormalized and
renormalized dressed propagators of fermions in parity-nonconserving theories
with inter-generation mixing. The mass eigenvalues, the corresponding mass
counterterms, and the effect of inter-generation mixing on their determination
are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization
conditions and employing a number of very useful relations from Matrix Algebra,
we show explicitly that the renormalized dressed propagators satisfy important
physical properties.Comment: 14 pages; to appear in Phys. Rev.
TIME-OF-FLIGHT STUDIES OF ELECTRONS IN VACUUM
An electron gun, drift tube, and fast amplifier (described) were designed and tested as part of a time-offlight electron beam monochromator. Drift time distributions were obtained for electrons of mean energy from 3 to 15 ev, which required mean transit times from 800 to 350 nsec, respectively, with the latter minimum value corresponding to the effects of amplifier rise time and pulse width from the avalanche transistor pulser. The former value corresponds to an electron energy spread from the electron gun of about 0.6 ev. The reciprocal of the square of the transit time is a linear function of the electron gun accelerating potential with an intercept at -- 1.5 v attributed to contact potentials. Beam attenuation due to scattering off of residual gas in the vacuum system indicated that pressures below 10/sup -6/ mm Hg are required in order to avoid loss of electrons in drift distances of the order of one meter. (auth
Removing black-hole singularities with nonlinear electrodynamics
We propose a way to remove black hole singularities by using a particular
nonlinear electrodynamics Lagrangian that has been recently used in various
astrophysics and cosmological frameworks. In particular, we adapt the
cosmological analysis discussed in a previous work to the black hole physics.
Such analysis will be improved by applying the Oppenheimer-Volkoff equation to
the black hole case. At the end, fixed the radius of the star, the final
density depends only on the introduced quintessential density term
and on the mass.Comment: In this last updated version we correct two typos which were present
in Eqs. (21) and (22) in the version of this letter which has been published
in Mod. Phys. Lett. A 25, 2423-2429 (2010). In the present version, both of
Eqs. (21) and (22) are dimensionally and analytically correc
Shock waves and Birkhoff's theorem in Lovelock gravity
Spherically symmetric shock waves are shown to exist in Lovelock gravity.
They amount to a change of branch of the spherically symmetric solutions across
a null hypersurface. The implications of their existence for the status of
Birkhoff's theorem in the theory is discussed.Comment: 9 pages, no figures, clarifying changes made in the text of section
III and references adde
Linear stability analysis of resonant periodic motions in the restricted three-body problem
The equations of the restricted three-body problem describe the motion of a
massless particle under the influence of two primaries of masses and
, , that circle each other with period equal to
. When , the problem admits orbits for the massless particle that
are ellipses of eccentricity with the primary of mass 1 located at one of
the focii. If the period is a rational multiple of , denoted ,
some of these orbits perturb to periodic motions for . For typical
values of and , two resonant periodic motions are obtained for . We show that the characteristic multipliers of both these motions are given
by expressions of the form in the limit . The coefficient is analytic in at and
C(e,p,q)=O(e^{\abs{p-q}}). The coefficients in front of e^{\abs{p-q}},
obtained when is expanded in powers of for the two resonant
periodic motions, sum to zero. Typically, if one of the two resonant periodic
motions is of elliptic type the other is of hyperbolic type. We give similar
results for retrograde periodic motions and discuss periodic motions that
nearly collide with the primary of mass
Classification of symmetric periodic trajectories in ellipsoidal billiards
We classify nonsingular symmetric periodic trajectories (SPTs) of billiards
inside ellipsoids of R^{n+1} without any symmetry of revolution. SPTs are
defined as periodic trajectories passing through some symmetry set. We prove
that there are exactly 2^{2n}(2^{n+1}-1) classes of such trajectories. We have
implemented an algorithm to find minimal SPTs of each of the 12 classes in the
2D case (R^2) and each of the 112 classes in the 3D case (R^3). They have
periods 3, 4 or 6 in the 2D case; and 4, 5, 6, 8 or 10 in the 3D case. We
display a selection of 3D minimal SPTs. Some of them have properties that
cannot take place in the 2D case.Comment: 26 pages, 77 figures, 17 table
A Potential Foundation for Emergent Space-Time
We present a novel derivation of both the Minkowski metric and Lorentz
transformations from the consistent quantification of a causally ordered set of
events with respect to an embedded observer. Unlike past derivations, which
have relied on assumptions such as the existence of a 4-dimensional manifold,
symmetries of space-time, or the constant speed of light, we demonstrate that
these now familiar mathematics can be derived as the unique means to
consistently quantify a network of events. This suggests that space-time need
not be physical, but instead the mathematics of space and time emerges as the
unique way in which an observer can consistently quantify events and their
relationships to one another. The result is a potential foundation for emergent
space-time.Comment: The paper was originally titled "The Physics of Events: A Potential
Foundation for Emergent Space-Time". We changed the title (and abstract) to
be more direct when the paper was accepted for publication at the Journal of
Mathematical Physics. 24 pages, 15 figure
Eutactic quantum codes
We consider sets of quantum observables corresponding to eutactic stars.
Eutactic stars are systems of vectors which are the lower dimensional
``shadow'' image, the orthogonal view, of higher dimensional orthonormal bases.
Although these vector systems are not comeasurable, they represent redundant
coordinate bases with remarkable properties. One application is quantum secret
sharing.Comment: 6 page
Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems
We propose a matrix model for two- and many-valued logic using families of
observables in Hilbert space, the eigenvalues give the truth values of logical
propositions where the atomic input proposition cases are represented by the
respective eigenvectors. For binary logic using the truth values {0,1} logical
observables are pairwise commuting projectors. For the truth values {+1,-1} the
operator system is formally equivalent to that of a composite spin 1/2 system,
the logical observables being isometries belonging to the Pauli group. Also in
this approach fuzzy logic arises naturally when considering non-eigenvectors.
The fuzzy membership function is obtained by the quantum mean value of the
logical projector observable and turns out to be a probability measure in
agreement with recent quantum cognition models. The analogy of many-valued
logic with quantum angular momentum is then established. Logical observables
for three-value logic are formulated as functions of the Lz observable of the
orbital angular momentum l=1. The representative 3-valued 2-argument logical
observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table
Families of Graphs with W_r({G},q) Functions That Are Nonanalytic at 1/q=0
Denoting as the chromatic polynomial for coloring an -vertex
graph with colors, and considering the limiting function , a fundamental question in graph theory is the
following: is analytic or not at the origin
of the plane? (where the complex generalization of is assumed). This
question is also relevant in statistical mechanics because
, where is the ground state entropy of the
-state Potts antiferromagnet on the lattice graph , and the
analyticity of at is necessary for the large- series
expansions of . Although is analytic at for many
, there are some for which it is not; for these, has no
large- series expansion. It is important to understand the reason for this
nonanalyticity. Here we give a general condition that determines whether or not
a particular is analytic at and explains the
nonanalyticity where it occurs. We also construct infinite families of graphs
with functions that are non-analytic at and investigate the
properties of these functions. Our results are consistent with the conjecture
that a sufficient condition for to be analytic at is
that is a regular lattice graph . (This is known not to be a
necessary condition).Comment: 22 pages, Revtex, 4 encapsulated postscript figures, to appear in
Phys. Rev.
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