25,661 research outputs found
Diffusive representations for fractional Laplacian: systems theory framework and numerical issues
Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not an easy task either. Thus, the framework of diffusive representations, as already developed for causal fractional integrals and derivatives,
is being applied to fractional Laplacian: it can be seen as an extension of the Wiener-Hopf factorization and splitting techniques to irrational transfer functions
The Pivotal Role of Causality in Local Quantum Physics
In this article an attempt is made to present very recent conceptual and
computational developments in QFT as new manifestations of old and well
establihed physical principles. The vehicle for converting the
quantum-algebraic aspects of local quantum physics into more classical
geometric structures is the modular theory of Tomita. As the above named
laureate to whom I have dedicated has shown together with his collaborator for
the first time in sufficient generality, its use in physics goes through
Einstein causality. This line of research recently gained momentum when it was
realized that it is not only of structural and conceptual innovative power (see
section 4), but also promises to be a new computational road into
nonperturbative QFT (section 5) which, picturesquely speaking, enters the
subject on the extreme opposite (noncommutative) side.Comment: This is a updated version which has been submitted to Journal of
Physics A, tcilatex 62 pages. Adress: Institut fuer Theoretische Physik
FU-Berlin, Arnimallee 14, 14195 Berlin presently CBPF, Rua Dr. Xavier Sigaud
150, 22290-180 Rio de Janeiro, Brazi
Wigner's infinite spin representations and inert matter
Positive energy ray representations of the Poincar\'e group are naturally
subdivided into three classes according to their mass and spin content: m>0,
m=0 finite helicity and m=0 infinite helicity. For a long time the localization
properties of the massless infinite spin class remained unknown before it
became clear that such matter does not permit compact spactime localization and
its generating covariant fields are localized on semi-infinite spacelike
strings. Using a new perturbation theory for higher spin fields we show that
infinite spin matter cannot interact with normal matter and we formulate
condition under which this also could happen for finite spin s>1 fields. This
raises the question of a possible connection between inert matter and dark
matter.Comment: 27 page
The role of positivity and causality in interactions involving higher spin
It is shown that the recently introduced positivity and causality preserving string-local quantum field theory (SLFT) resolves most No-Go situations in higher spin problems. This includes in particular the Velo–Zwanziger causality problem which turns out to be related in an interesting way to the solution of zero mass Weinberg–Witten issue. In contrast to the indefinite metric and ghosts of gauge theory, SLFT uses only positivity-respecting physical degrees of freedom. The result is a fully Lorentz-covariant and causal string field theory in which light- or space-like linear strings transform covariant under Lorentz transformation.
The cooperation of causality and quantum positivity in the presence of interacting
particles leads to remarkable conceptual changes. It turns out that the presence of H-selfinteractions in the Higgs model is not the result of SSB on a postulated Mexican hat potential, but solely the consequence of the implementation of positivity and causality. These principles (and not the imposed gauge symmetry) account also for the Lie-algebra structure of the leading contributions of selfinteracting vector mesons.
Second order consistency of selfinteracting vector mesons in SLFT requires the presence of H-particles; this, and not SSB, is the raison d'être for H.
The basic conceptual and calculational tool of SLFT is the S-matrix. Its string-independence is a powerful restriction which determines the form of interaction densities in terms of the model-defining particle content and plays a fundamental role in the construction of pl observables and sl interpolating fields
The Ongoing Impact of Modular Localization on Particle Theory
Modular localization is the concise conceptual formulation of causal
localization in the setting of local quantum physics. Unlike QM it does not
refer to individual operators but rather to ensembles of observables which
share the same localization region, as a result it explains the probabilistic
aspects of QFT in terms of the impure KMS nature arising from the local
restriction of the pure vacuum. Whereas it played no important role in the
perturbation theory of low spin particles, it becomes indispensible for
interactions which involve higher spin fields, where is leads to the
replacement of the operator (BRST) gauge theory setting in Krein space by a new
formulation in terms of stringlocal fields in Hilbert space. The main purpose
of this paper is to present new results which lead to a rethinking of important
issues of the Standard Model concerning massive gauge theories and the Higgs
mechanism. We place these new findings into the broader context of ongoing
conceptual changes within QFT which already led to new nonperturbative
constructions of models of integrable QFTs. It is also pointed out that modular
localization does not support ideas coming from string theory, as extra
dimensions and Kaluza-Klein dimensional reductions outside quasiclassical
approximations. Apart from hologarphic projections on null-surfaces, holograhic
relations between QFT in different spacetime dimensions violate the causal
completeness property, this includes in particular the Maldacena conjecture.
Last not least, modular localization sheds light onto unsolved problems from
QFT's distant past since it reveals that the Einstein-Jordan conundrum is
really an early harbinger of the Unruh effect.Comment: a small text overlap with unpublished arXiv:1201.632
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