5,920 research outputs found
Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
We test the positivity property of the chiral perturbation theory (ChPT)
pion-pion scattering amplitudes within the Mandelstam triangle. In the one-loop
approximation, , the positivity constrains only the coefficients
and , namely one obtains that and the linear combination
are positive quantities. The two-loops approximation gives
inequalities involving all the six arbitrary parameters entering ChPT
amplitude, but the corrections to the one-loop approximation results are small.
ChPT amplitudes pass unexpectedly well all the positivity tests giving strong
support to the idea that ChPT is the good theory of the low energy pion-pion
scattering.Comment: 15 pages, Late
Poisson-Lie Structures and Quantisation with Constraints
We develop here a simple quantisation formalism that make use of Lie algebra
properties of the Poisson bracket. When the brackets and
, where is the Hamiltonian and are primary and
secondary constraints, can be expressed as functions of and
themselves, the Poisson bracket defines a Poisson-Lie structure. When this
algebra has a finite dimension a system of first order partial differential
equations is established whose solutions are the observables of the theory. The
method is illustrated with a few examples.Comment: 13 pages, Late
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