6 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
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
Generalizations of normal ordering and applications to quantization in classical backgrounds
A nonlocal method of extracting the positive (or the negative) frequency part
of a field, based on knowledge of a 2-point function, leads to certain natural
generalizations of the normal ordering of quantum fields in classical
gravitational and electromagnetic backgrounds and illuminates the origin of the
recently discovered nonlocalities related to a local description of particles.
A local description of particle creation by gravitational backgrounds is given,
with emphasis on the case of black-hole evaporation. The formalism reveals a
previously hidden relation between various definitions of the particle current
and those of the energy-momentum tensor. The implications to particle creation
by classical backgrounds, as well as to the relation between vacuum energy,
dark matter, and cosmological constant, are discussed.Comment: 17 pages, revised, title shortened, to appear in Gen. Rel. Gra
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