88,058 research outputs found
Quantum Field Theory from First Principles
When quantum fields are studied on manifolds with boundary, the corresponding
one-loop quantum theory for bosonic gauge fields with linear covariant gauges
needs the assignment of suitable boundary conditions for elliptic differential
operators of Laplace type. There are however deep reasons to modify such a
scheme and allow for pseudo-differential boundary-value problems. When the
boundary operator is allowed to be pseudo-differential while remaining a
projector, the conditions on its kernel leading to strong ellipticity of the
boundary-value problem are studied in detail. This makes it possible to develop
a theory of one-loop quantum gravity from first principles only, i.e. the
physical principle of invariance under infinitesimal diffeomorphisms and the
mathematical requirement of a strongly elliptic theory. It therefore seems that
a non-local formulation of quantum field theory has some attractive features
which deserve further investigation.Comment: 16 pages, plain Tex, paper submitted for the Proceedings of the
Conference "Geometrical Aspects of Quantum Fields", Physics Department of
Londrina University, April 17-20, 200
Numerical study of the disordered Poland-Scheraga model of DNA denaturation
We numerically study the binary disordered Poland-Scheraga model of DNA
denaturation, in the regime where the pure model displays a first order
transition (loop exponent ). We use a Fixman-Freire scheme for the
entropy of loops and consider chain length up to , with
averages over samples. We present in parallel the results of various
observables for two boundary conditions, namely bound-bound (bb) and
bound-unbound (bu), because they present very different finite-size behaviors,
both in the pure case and in the disordered case. Our main conclusion is that
the transition remains first order in the disordered case: in the (bu) case,
the disorder averaged energy and contact densities present crossings for
different values of without rescaling. In addition, we obtain that these
disorder averaged observables do not satisfy finite size scaling, as a
consequence of strong sample to sample fluctuations of the pseudo-critical
temperature. For a given sample, we propose a procedure to identify its
pseudo-critical temperature, and show that this sample then obeys first order
transition finite size scaling behavior. Finally, we obtain that the disorder
averaged critical loop distribution is still governed by in
the regime , as in the pure case.Comment: 12 pages, 13 figures. Revised versio
Nonstandard Drinfeld-Sokolov reduction
Subject to some conditions, the input data for the Drinfeld-Sokolov
construction of KdV type hierarchies is a quadruplet (\A,\Lambda, d_1, d_0),
where the are -gradations of a loop algebra \A and \Lambda\in \A
is a semisimple element of nonzero -grade. A new sufficient condition on
the quadruplet under which the construction works is proposed and examples are
presented. The proposal relies on splitting the -grade zero part of \A
into a vector space direct sum of two subalgebras. This permits one to
interpret certain Gelfand-Dickey type systems associated with a nonstandard
splitting of the algebra of pseudo-differential operators in the
Drinfeld-Sokolov framework.Comment: 19 pages, LaTeX fil
Lagrange Stabilization of Pendulum-like Systems: A Pseudo H-infinity Control Approach
This paper studies the Lagrange stabilization of a class of nonlinear systems
whose linear part has a singular system matrix and which have multiple periodic
(in state) nonlinearities. Both state and output feedback Lagrange
stabilization problems are considered. The paper develops a pseudo H-infinity
control theory to solve these stabilization problems. In a similar fashion to
the Strict Bounded Real Lemma in classic H-infinity control theory, a Pseudo
Strict Bounded Real Lemma is established for systems with a single unstable
pole. Sufficient conditions for the synthesis of state feedback and output
feedback controllers are given to ensure that the closed-loop system is pseudo
strict bounded real. The pseudo H-infinity control approach is applied to solve
state feedback and output feedback Lagrange stabilization problems for
nonlinear systems with multiple nonlinearities. An example is given to
illustrate the proposed method
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