45 research outputs found
Auxiliary Fields for Super Yang-Mills from Division Algebras
Division algebras are used to explain the existence and symmetries of various
sets of auxiliary fields for super Yang-Mills in dimensions .
(Contribution to G\"ursey Memorial Conference I: Strings and Symmetries)Comment: 7 pages, plain TeX, CERN-TH.7470/9
Octonionic representations of Clifford algebras and triality
The theory of representations of Clifford algebras is extended to employ the
division algebra of the octonions or Cayley numbers. In particular, questions
that arise from the non-associativity and non-commutativity of this division
algebra are answered. Octonionic representations for Clifford algebras lead to
a notion of octonionic spinors and are used to give octonionic representations
of the respective orthogonal groups. Finally, the triality automorphisms are
shown to exhibit a manifest \perm_3 \times SO(8) structure in this framework.Comment: 33 page
Octonion Quantum Chromodynamics
Starting with the usual definitions of octonions, an attempt has been made to
establish the relations between octonion basis elements and Gell-Mann \lambda
matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann
\lambda matrices of SU(3)symmetry and octonion basis elements. Consequently,
the quantum chromo dynamics (QCD) has been reformulated and it is shown that
the theory of strong interactions could be explained better in terms of
non-associative octonion algebra. Further, the octonion automorphism group
SU(3) has been suitably handled with split basis of octonion algebra showing
that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields
which are responsible for the existence of two gauge potentials respectively
associated with electric charge and magnetic monopole and supports well the
idea that the colored quarks are dyons
Complex actions in two-dimensional topology change
We investigate topology change in (1+1) dimensions by analyzing the
scalar-curvature action at the points of metric-degeneration
that (with minor exceptions) any nontrivial Lorentzian cobordism necessarily
possesses. In two dimensions any cobordism can be built up as a combination of
only two elementary types, the ``yarmulke'' and the ``trousers.'' For each of
these elementary cobordisms, we consider a family of Morse-theory inspired
Lorentzian metrics that vanish smoothly at a single point, resulting in a
conical-type singularity there. In the yarmulke case, the distinguished point
is analogous to a cosmological initial (or final) singularity, with the
spacetime as a whole being obtained from one causal region of Misner space by
adjoining a single point. In the trousers case, the distinguished point is a
``crotch singularity'' that signals a change in the spacetime topology (this
being also the fundamental vertex of string theory, if one makes that
interpretation). We regularize the metrics by adding a small imaginary part
whose sign is fixed to be positive by the condition that it lead to a
convergent scalar field path integral on the regularized spacetime. As the
regulator is removed, the scalar density approaches a
delta-function whose strength is complex: for the yarmulke family the strength
is , where is the rapidity parameter of the associated
Misner space; for the trousers family it is simply . This implies that
in the path integral over spacetime metrics for Einstein gravity in three or
more spacetime dimensions, topology change via a crotch singularity is
exponentially suppressed, whereas appearance or disappearance of a universe via
a yarmulke singularity is exponentially enhanced.Comment: 34 pages, REVTeX v3.0. (Presentational reorganization; core results
unchanged.
Quantum mechanics: Myths and facts
A common understanding of quantum mechanics (QM) among students and practical
users is often plagued by a number of "myths", that is, widely accepted claims
on which there is not really a general consensus among experts in foundations
of QM. These myths include wave-particle duality, time-energy uncertainty
relation, fundamental randomness, the absence of measurement-independent
reality, locality of QM, nonlocality of QM, the existence of well-defined
relativistic QM, the claims that quantum field theory (QFT) solves the problems
of relativistic QM or that QFT is a theory of particles, as well as myths on
black-hole entropy. The fact is that the existence of various theoretical and
interpretational ambiguities underlying these myths does not yet allow us to
accept them as proven facts. I review the main arguments and counterarguments
lying behind these myths and conclude that QM is still a
not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in
Found. Phy
Quantum field theory in static external potentials and Hadamard states
We prove that the ground state for the Dirac equation on Minkowski space in
static, smooth external potentials satisfies the Hadamard condition. We show
that it follows from a condition on the support of the Fourier transform of the
corresponding positive frequency solution. Using a Krein space formalism, we
establish an analogous result in the Klein-Gordon case for a wide class of
smooth potentials. Finally, we investigate overcritical potentials, i.e. which
admit no ground states. It turns out, that numerous Hadamard states can be
constructed by mimicking the construction of ground states, but this leads to a
naturally distinguished one only under more restrictive assumptions on the
potentials.Comment: 30 pages; v2 revised, accepted for publication in Annales Henri
Poincar
A three dimensional view of stereopsis in dentistry
Stereopsis and its role in dental practice has been a topic of debate in recent editions of this Journal. These discussions are particularly timely as they come at a point when virtual reality simulators are becoming increasingly popular in the education of tomorrow's dentists. The aim of this article is to discuss the lack of robust empirical evidence to ascertain the relationship (if any) between stereopsis and dentistry and to build a case for the need for further research to build a strong evidence base on the topic