12,299 research outputs found
Constant mean curvature foliations in cosmological spacetimes
Foliations by constant mean curvature hypersurfaces provide a possibility of
defining a preferred time coordinate in general relativity. In the following
various conjectures are made about the existence of foliations of this kind in
spacetimes satisfying the strong energy condition and possessing compact Cauchy
hypersurfaces. Recent progress on proving these conjectures under supplementary
assumptions is reviewed. The method of proof used is explained and the
prospects for generalizing it discussed. The relations of these questions to
cosmic censorship and the closed universe recollapse conjecture are pointed
out.Comment: 11 pages. Contribution to the Journees Relativiste
A Riccati type PDE for light-front higher helicity vertices
This paper is based on a curious observation about an equation related to the
tracelessness constraints of higher spin gauge fields. The equation also occurs
in the theory of continuous spin representations of the Poincar\'e group.
Expressed in an oscillator basis for the higher spin fields, the equation
becomes a non-linear partial differential operator of the Riccati type acting
on the vertex functions. The consequences of the equation for the cubic vertex
is investigated in the light-front formulation of higher spin theory. The
classical vertex is completely fixed but there is room for off-shell quantum
corrections.Comment: 27 pages. Updated to published versio
Axiomatic formulations of nonlocal and noncommutative field theories
We analyze functional analytic aspects of axiomatic formulations of nonlocal
and noncommutative quantum field theories. In particular, we completely clarify
the relation between the asymptotic commutativity condition, which ensures the
CPT symmetry and the standard spin-statistics relation for nonlocal fields, and
the regularity properties of the retarded Green's functions in momentum space
that are required for constructing a scattering theory and deriving reduction
formulas. This result is based on a relevant Paley-Wiener-Schwartz-type theorem
for analytic functionals. We also discuss the possibility of using analytic
test functions to extend the Wightman axioms to noncommutative field theory,
where the causal structure with the light cone is replaced by that with the
light wedge. We explain some essential peculiarities of deriving the CPT and
spin-statistics theorems in this enlarged framework.Comment: LaTeX, 13 pages, no figure
On the "principle of the quantumness", the quantumness of Relativity, and the computational grand-unification
After reviewing recently suggested operational "principles of the
quantumness", I address the problem on whether Quantum Theory (QT) and Special
Relativity (SR) are unrelated theories, or instead, if the one implies the
other. I show how SR can be indeed derived from causality of QT, within the
computational paradigm "the universe is a huge quantum computer", reformulating
QFT as a Quantum-Computational Field Theory (QCFT). In QCFT SR emerges from the
fabric of the computational network, which also naturally embeds gauge
invariance. In this scheme even the quantization rule and the Planck constant
can in principle be derived as emergent from the underlying causal tapestry of
space-time. In this way QT remains the only theory operating the huge computer
of the universe. Is QCFT only a speculative tautology (theory as simulation of
reality), or does it have a scientific value? The answer will come from Occam's
razor, depending on the mathematical simplicity of QCFT. Here I will just start
scratching the surface of QCFT, analyzing simple field theories, including
Dirac's. The number of problems and unmotivated recipes that plague QFT
strongly motivates us to undertake the QCFT project, since QCFT makes all such
problems manifest, and forces a re-foundation of QFT.Comment: To be published on AIP Proceedings of Vaxjo conference. The ideas on
Quantum-Circuit Field Theory are more recent. V4 Largely improved, with new
interesting results and concepts. Dirac equation solve
- âŠ