3,411 research outputs found
Improved Off-Shell Scattering Amplitudes in String Field Theory and New Computational Methods
We report on new results in Witten's cubic string field theory for the
off-shell factor in the 4-tachyon amplitude that was not fully obtained
explicitly before. This is achieved by completing the derivation of the
Veneziano formula in the Moyal star formulation of Witten's string field theory
(MSFT). We also demonstrate detailed agreement of MSFT with a number of
on-shell and off-shell computations in other approaches to Witten's string
field theory. We extend the techniques of computation in MSFT, and show that
the j=0 representation of SL(2,R) generated by the Virasoro operators
is a key structure in practical computations for generating
numbers. We provide more insight into the Moyal structure that simplifies
string field theory, and develop techniques that could be applied more
generally, including nonperturbative processes.Comment: 40 pages, 2 figures, LaTe
On eleven-dimensional Supergravity and Chern-Simons theory
We probe in some depth into the structure of eleven-dimensional,
osp(32|1)-based Chern-Simons supergravity, as put forward by Troncoso and
Zanelli (TZ) in 1997. We find that the TZ Lagrangian may be cast as a
polynomial in 1/l, where l is a length, and compute explicitly the first three
dominant terms. The term proportional to 1/l^9 turns out to be essentially the
Lagrangian of the standard 1978 supergravity theory of Cremmer, Julia and
Scherk, thus establishing a previously unknown relation between the two
theories. The computation is nontrivial because, when written in a sufficiently
explicit way, the TZ Lagrangian has roughly one thousand non-explicitly
Lorentz-covariant terms. Specially designed algebraic techniques are used to
accomplish the results.Comment: v1: 16 pages, no figures. v2: updated references and minor
corrections. v3: 10 pages, no figures. Paper fully rewritten; results and
conclusions unchanged. v4: 13 pages, no figures. Some minor changes and
improved bibliography. Version accepted for publication in NP
Dirac Equation in Scale Relativity
The theory of scale relativity provides a new insight into the origin of
fundamental laws in physics. Its application to microphysics allows to recover
quantum mechanics as mechanics on a non-differentiable (fractal) space-time.
The Schr\"odinger and Klein-Gordon equations have already been demonstrated as
geodesic equations in this framework. We propose here a new development of the
intrinsic properties of this theory to obtain, using the mathematical tool of
Hamilton's bi-quaternions, a derivation of the Dirac equation, which, in
standard physics, is merely postulated. The bi-quaternionic nature of the Dirac
spinor is obtained by adding to the differential (proper) time symmetry
breaking, which yields the complex form of the wave-function in the
Schr\"odinger and Klein-Gordon equations, the breaking of further symmetries,
namely, the differential coordinate symmetry () and the parity and time reversal symmetries.Comment: 33 pages, 4 figures, latex. Submitted to Phys. Rev.
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