1,246 research outputs found
Massive CP theory from a microscopic model for doped antiferromagnets
A path-integral for the t-J model in two dimensions is constructed based on
Dirac quantization, with an action found originally by Wiegmann (Phys. Rev.
Lett. {\bf 60}, 821 (1988); Nucl. Phys. B323, 311 (1989)). Concentrating on the
low doping limit, we assume short range antiferromagnetic order of the spin
degrees of freedom. Going over to a local spin quantization axis of the dopant
fermions, that follows the spin degree of freedom, staggered CP fields
result and the constraint against double occupancy can be resolved. The
staggered CP fields are split into slow and fast modes, such that after a
gradient expansion, and after integrating out the fast modes and the dopant
fermions, a CP field-theory with a massive gauge field is obtained that
describes generically incommensurate coplanar magnetic structures, as discussed
previously in the context of frustrated quantum antiferromagnets. Hence, the
possibility of deconfined spinons is opened by doping a colinear
antiferromagnet.Comment: 24 pages, no figure
On Foundation of the Generalized Nambu Mechanics
We outline the basic principles of canonical formalism for the Nambu
mechanics---a generalization of Hamiltonian mechanics proposed by Yoichiro
Nambu in 1973. It is based on the notion of Nambu bracket which generalizes the
Poisson bracket to the multiple operation of higher order on
classical observables and is described by Hambu-Hamilton equations of motion
given by Hamiltonians. We introduce the fundamental identity for the
Nambu bracket which replaces Jacobi identity as a consistency condition for the
dynamics. We show that Nambu structure of given order defines a family of
subordinated structures of lower order, including the Poisson structure,
satisfying certain matching conditions. We introduce analogs of action from and
principle of the least action for the Nambu mechanics and show how dynamics of
loops (-dimensional objects) naturally appears in this formalism. We
discuss several approaches to the quantization problem and present explicit
representation of Nambu-Heisenberg commutation relation for case. We
emphasize the role higher order algebraic operations and mathematical
structures related with them play in passing from Hamilton's to Nambu's
dynamical picture.Comment: 27 page
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