Generalized coherent states for SU(n) systems

Generalized coherent states are developed for SU(n) systems for arbitrary $n$. This is done by first iteratively determining explicit representations for the SU(n) coherent states, and then determining parametric representations useful for applications. For SU(n), the set of coherent states is isomorphic to a coset space $SU(n)/SU(n-1)$, and thus shows the geometrical structure of the coset space. These results provide a convenient $(2n - 1)$--dimensional space for the description of arbitrary SU(n) systems. We further obtain the metric and measure on the coset space, and show some properties of the SU(n) coherent states.Comment: 11 page

Variational optimization of probability measure spaces resolves the chain store paradox

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game's expected payoff functionals. Optimizing such functionals requires generalized variational and functional optimization methods to locate novel equilibria. These variational methods can reconcile game theoretic prediction and observed human behaviours, as we illustrate by resolving the chain store paradox. Our generalized optimization analysis has significant implications for economics, artificial intelligence, complex system theory, neurobiology, and biological evolution and development.optimization; probability measure space; noncooperative game; chain store paradox

Superpositions of SU(3) coherent states via a nonlinear evolution

We show that a nonlinear Hamiltonian evolution can transform an SU(3) coherent state into a superposition of distinct SU(3) coherent states, with a superposition of two SU(2) coherent states presented as a special case. A phase space representation is depicted by projecting the multi-dimensional $Q$-symbol for the state to a spherical subdomain of the coset space. We discuss realizations of this nonlinear evolution in the contexts of nonlinear optics and Bose--Einstein condensates

Variational optimization of probability measure spaces resolves the chain store paradox

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game's expected payoff functionals. Optimizing such functionals requires generalized variational and functional optimization methods to locate novel equilibria. These variational methods can reconcile game theoretic prediction and observed human behaviours, as we illustrate by resolving the chain store paradox. Our generalized optimization analysis has significant implications for economics, artificial intelligence, complex system theory, neurobiology, and biological evolution and development.Comment: 11 pages, 5 figures. Replaced for minor notational correctio