24 research outputs found
Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice
We propose the fundamental and two dimensional representation of the Lorentz
groups on a (3+1)-dimensional hypercubic lattice, from which representations of
higher dimensions can be constructed. For the unitary representation of the
discrete translation group we use the kernel of the Fourier transform. From the
Dirac representation of the Lorentz group (including reflections) we derive in
a natural way the wave equation on the lattice for spin 1/2 particles. Finally
the induced representation of the discrete inhomogeneous Lorentz group is
constructed by standard methods and its connection with the continuous case is
discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission
How Stands Collapse II
I review ten problems associated with the dynamical wave function collapse
program, which were described in the first of these two papers. Five of these,
the \textit{interaction, preferred basis, trigger, symmetry} and
\textit{superluminal} problems, were discussed as resolved there. In this
volume in honor of Abner Shimony, I discuss the five remaining problems,
\textit{tails, conservation law, experimental, relativity, legitimization}.
Particular emphasis is given to the tails problem, first raised by Abner. The
discussion of legitimization contains a new argument, that the energy density
of the fluctuating field which causes collapse should exert a gravitational
force. This force can be repulsive, since this energy density can be negative.
Speculative illustrations of cosmological implications are offered.Comment: 37 page
One-Loop Maximal Helicity Violating Amplitudes in N=4 Super Yang-Mills Theories
One-loop maximal helicity violating (MHV) amplitudes in N=4 super Yang-Mills
(SYM) theories are analyzed, using the prescription of Cachazo, Svrcek, and
Witten (CSW). The relations between leading N_c amplitudes A_{n;1} and
sub-leading amplitudes A_{n;c} obtained by the CSW prescription are found to be
identical to those obtained from conventional field theory calculations.
Combining with existing results, this establishes the validity of the CSW
prescription to one-loop in the calculation of MHV amplitudes in N=4 SYM
theories of finite N_c.Comment: Minor changes and typos fixed. Published version in JHE
Quantum Mechanical Aspects of Cell Microtubules: Science Fiction or Realistic Possibility?
Recent experimental research with marine algae points towards quantum
entanglement at ambient temperature, with correlations between essential
biological units separated by distances as long as 20 Angstr\"oms. The
associated decoherence times, due to environmental influences, are found to be
of order 400 fs. This prompted some authors to connect such findings with the
possibility of some kind of quantum computation taking place in these
biological entities: within the decoherence time scales, the cell "quantum
calculates" the optimal "path" along which energy and signal would be
transported more efficiently. Prompted by these experimental results, in this
talk I remind the audience of a related topic proposed several years ago in
connection with the possible r\^ole of quantum mechanics and/or field theory on
dissipation-free energy transfer in microtubules (MT), which constitute
fundamental cell substructures. Quantum entanglement between tubulin dimers was
argued to be possible, provided there exists sufficient isolation from other
environmental cell effects. The model was based on certain ferroelectric
aspects of MT. In the talk I review the model and the associated experimental
tests so far and discuss future directions, especially in view of the algae
photo-experiments.Comment: 31 pages latex, 11 pdf figures, uses special macros, Invited Plenary
Talk at DICE2010, Castello Pasquini, Castiglioncello (Italy), September 13-18
201
Catching-up and falling behind knowledge spillover from American to German machine tool makers
In our days, German machine tool makers accuse their Chinese competitors of violating patent rights and illegally imitating German technology. A century ago, however, German machine tool makers used exactly the same methods to imitate American technology. To understand the dynamics of this catching-up process we use patent statistics to analyze firms? activities between 1877 and 1932. We show that German machine tool makers successfully deployed imitating and counterfeiting activities in the late 19th century and the 1920s to catchup to their American competitors. The German administration supported this strategy by stipulating a patent law that discriminated against foreign patent holders and probably also by delaying the granting of patents to foreign applicants. Parallel to the growing international competitiveness of German firms, however, the willingness to guarantee intellectual property rights of foreigners was also increasing because German firms had now to fear retaliatory measures in their own export markets when violating foreign property rights within Germany
Collapse models with non-white noises
We set up a general formalism for models of spontaneous wave function
collapse with dynamics represented by a stochastic differential equation driven
by general Gaussian noises, not necessarily white in time. In particular, we
show that the non-Schrodinger terms of the equation induce the collapse of the
wave function to one of the common eigenstates of the collapsing operators, and
that the collapse occurs with the correct quantum probabilities. We also
develop a perturbation expansion of the solution of the equation with respect
to the parameter which sets the strength of the collapse process; such an
approximation allows one to compute the leading order terms for the deviations
of the predictions of collapse models with respect to those of standard quantum
mechanics. This analysis shows that to leading order, the ``imaginary'' noise
trick can be used for non-white Gaussian noise.Comment: Latex, 20 pages;references added and minor revisions; published as J.
Phys. A: Math. Theor. {\bf 40} (2007) 15083-1509
Spectra of PP-Wave Limits of M-/Superstring Theory on AdS_p x S^q Spaces
In this paper we show how one can obtain very simply the spectra of the
PP-wave limits of M-theory over AdS_7(4) x S^4(7) spaces and IIB superstring
theory over AdS_5 x S^5 from the oscillator construction of the Kaluza-Klein
spectra of these theories over the corresponding spaces. The PP-wave symmetry
superalgebras are obtained by taking the number P of ``colors'' of oscillators
to be large (infinite). In this large P limit, the symmetry superalgebra
osp(8*|4) of AdS_7 x S^4 and the symmetry superalgebra osp(8|4,R) of AdS_4 x
S^7 lead to isomorphic PP-wave algebras, which is the semi-direct sum of
su(4|2) with H^(18,16), while the symmetry superalgebra su(2,2|4) of AdS_5 x
S^5 leads to the semi-direct sum of [psu(2|2) + psu(2|2) + u(1)] with H^(16,16)
as its PP-wave algebra [H^(m,n) denoting a super-Heisenberg algebra with m
bosonic and n fermionic generators]. The zero mode spectra of M-theory or IIB
superstring theory in the PP-wave limit corresponds simply to the unitary
positive energy representations of these algebras whose lowest weight vector is
the Fock vacuum of all the oscillators. General positive energy supermultiplets
including those corresponding to higher modes can similarly be constructed by
the oscillator method.Comment: Typos corrected; references added; minor modifications to improve
presentation; 37 pages, LaTeX fil
A Natural Supersymmetric Model with MeV Dark Matter
It has previously been proposed that annihilating dark matter particles with
MeV-scale masses could be responsible for the flux of 511 keV photons observed
from the region of the Galactic Bulge. The conventional wisdom, however, is
that it is very challenging to construct a viable particle physics model
containing MeV dark matter. In this letter, we challenge this conclusion by
describing a simple and natural supersymmetric model in which the lightest
supersymmetric particle naturally has a MeV-scale mass and the other
phenomenological properties required to generate the 511 keV emission. In
particular, the small ( ) effective couplings between dark
matter and the Standard Model fermions required in this scenario naturally lead
to radiative corrections that generate MeV-scale masses for both the dark
matter candidate and the mediator particle.Comment: 4 pages, 1 figure. v2: Small modification to discussion of spectru