8,774 research outputs found
Statistics of weighted Poisson events and its applications
The statistics of the sum of random weights where the number of weights is
Poisson distributed has important applications in nuclear physics, particle
physics and astrophysics. Events are frequently weighted according to their
acceptance or relevance to a certain type of reaction. The sum is described by
the compound Poisson distribution (CPD) which is shortly reviewed. It is shown
that the CPD can be approximated by a scaled Poisson distribution (SPD). The
SPD is applied to parameter estimation in situations where the data are
distorted by resolution effects. It performs considerably better than the
normal approximation that is usually used. A special Poisson bootstrap
technique is presented which permits to derive confidence limits for
observations following the CPD.Comment: 14 pages, 2 figure
Weak Hopf Algebras II: Representation theory, dimensions and the Markov trace
If A is a weak C^*-Hopf algebra then the category of finite dimensional
unitary representations of A is a monoidal C^*-category with monoidal unit
being the GNS representation D_eps associated to the counit \eps. This category
has isomorphic left dual and right dual objects which leads, as usual, to the
notion of dimension function. However, if \eps is not pure the dimension
function is matrix valued with rows and columns labelled by the irreducibles
contained in D_eps. This happens precisely when the inclusions A^L < A and A^R
< A are not connected. Still there exists a trace on A which is the Markov
trace for both inclusions. We derive two numerical invariants for each C^*-WHA
of trivial hypercenter. These are the common indices I and \delta, of the Haar,
respectively Markov conditional expectations of either one of the inclusions
A^{L/R} \delta. In the
special case of weak Kac algebras we show that I=\delta is an integer.Comment: 45 pages, LaTeX, submitted to J. Algebr
Boundary reduction formula
An asymptotic theory is developed for general non-integrable boundary quantum
field theory in 1+1 dimensions based on the Langrangean description. Reflection
matrices are defined to connect asymptotic states and are shown to be related
to the Green functions via the boundary reduction formula derived. The
definition of the -matrix for integrable theories due to Ghoshal and
Zamolodchikov and the one used in the perturbative approaches are shown to be
related.Comment: 12 pages, Latex2e file with 5 eps figures, two Appendices about the
boundary Feynman rules and the structure of the two point functions are adde
Weak Hopf Algebras I: Integral Theory and C^*-structure
We give an introduction to the theory of weak Hopf algebras proposed recently
as a coassociative alternative of weak quasi-Hopf algebras. We follow an
axiomatic approach keeping as close as possible to the "classical" theory of
Hopf algebras. The emphasis is put on the new structure related to the presence
of canonical subalgebras A^L and A^R in any weak Hopf algebra A that play the
role of non-commutative numbers in many respects. A theory of integrals is
developed in which we show how the algebraic properties of A, such as the
Frobenius property, or semisimplicity, or innerness of the square of the
antipode, are related to the existence of non-degenerate, normalized, or Haar
integrals. In case of C^*-weak Hopf algebras we prove the existence of a unique
Haar measure h in A and of a canonical grouplike element g in A implementing
the square of the antipode and factorizing into left and right algebra
elements. Further discussion of the C^*-case will be presented in Part II.Comment: 40 pages, LaTeX, to appear in J. Algebr
Irreversible Quantum Mechanics in the Neutral K-System
The neutral Kaon system is used to test the quantum theory of resonance
scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with
complex Hamiltonian is obtained by truncating the complex basis vector
expansion of the exact theory in Rigged Hilbert space. This can be done for K_1
and K_2 as well as for K_S and K_L, depending upon whether one chooses the
(self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP.
As an unexpected curiosity one can show that the exact theory (without
truncation) predicts long-time 2 pion decays of the neutral Kaon system even if
the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include
Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group
The velocity basis of the Poincare group is used in the direct product space
of two irreducible unitary representations of the Poincare group. The velocity
basis with total angular momentum j will be used for the definition of
relativistic Gamow vectors.Comment: 14 pages; revte
The Higgs Boson Mass in Split Supersymmetry at Two-Loops
The mass of the Higgs boson in the Split Supersymmetric Standard Model is
calculated, including all one-loop threshold effects and the renormalization
group evolution of the Higgs quartic coupling through two-loops. The two-loop
corrections are very small (<<1 GeV), while the one-loop threshold corrections
generally push the Higgs mass down several GeV.Comment: 17 pages. 4 figures. Improved discussion and notation. Corrected
typos. Added references. Added plots. Main results unchange
The density matrix in the de Broglie-Bohm approach
If the density matrix is treated as an objective description of individual
systems, it may become possible to attribute the same objective significance to
statistical mechanical properties, such as entropy or temperature, as to
properties such as mass or energy. It is shown that the de Broglie-Bohm
interpretation of quantum theory can be consistently applied to density
matrices as a description of individual systems. The resultant trajectories are
examined for the case of the delayed choice interferometer, for which Bell
appears to suggest that such an interpretation is not possible. Bell's argument
is shown to be based upon a different understanding of the density matrix to
that proposed here.Comment: 15 pages, 4 figure
- …