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Symmetries II: Discrete Symmetries

2011
This is probably the most technical chapter of this book. Discrete symmetries play a fundamental role in modern particle physics and cosmology. We have delayed their study until now to be able to develop all the tools required to explore some or their fascinating consequences.
Luis Álvarez-Gaumé   +1 more
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Continuous symmetries of discrete equations

Physics Letters A, 1991
Abstract Lie group techniques for solving differential equations are extended to differential-difference equations. As an application, it is shown that the two-dimensional Toda lattice has an infinite dimensional symmetry group with a Kac-Moody-Virasoro Lie algebra.
LEVI, Decio, WINTERNITZ P.
openaire   +2 more sources

ON TESTS OF SYMMETRY FOR DISCRETE POPULATIONS

Australian Journal of Statistics, 1974
SummaryIn this paper problems of tests of symmetry about the origin with discrete samples are considered. Recently Vorličková established the asymptotic normality of linear rank statistics and signed rank statistics in [5] and [6]. Here we propose statistics which are conditionally the sum of independent variables, including the locally most powerful ...
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Symmetries of the Discrete Nonlinear Schrödinger Equation

Theoretical and Mathematical Physics, 2001
The authors study the relation between the symmetries of the discrete nonlinear Schrödinger equation \[ \dot{Q}_{n}=\frac{i\gamma}{h^{2}}\left[\left(1-\varepsilon|Q_{n}|^{2 } \right)\left(Q_{n+1}+Q_{n-1}\right)-2Q_{n}\right] \tag{1} \] and the nonlinear Schrödinger equation \[ iu_{t}+\gamma u_{xx}-2\varepsilon\gamma|u|^{2}u=0.
Heredero RH, LEVI, Decio, Winternitz P.
openaire   +3 more sources

Representation of Discrete Symmetry Operators

Journal of Mathematical Physics, 1966
Representations of discrete symmetry operators (DSO's) connected with space (𝒫), time (T), and generalized charge (𝒞) are considered. It is shown that if one writes a DSO as exp (iπΩ) × a phase transformation, then (under certain conditions on Ωs) to each DSO there corresponds a set of Ωs which is closed with respect a Lie algebra, which is isomorphic ...
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Symmetries in Discrete-Time Mechanics

Annals of Physics, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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