1,162 research outputs found
Holomorphic Supercurves and Supersymmetric Sigma Models
We introduce a natural generalisation of holomorphic curves to morphisms of
supermanifolds, referred to as holomorphic supercurves. More precisely,
supercurves are morphisms from a Riemann surface, endowed with the structure of
a supermanifold which is induced by a holomorphic line bundle, to an ordinary
almost complex manifold. They are called holomorphic if a generalised
Cauchy-Riemann condition is satisfied. We show, by means of an action identity,
that holomorphic supercurves are special extrema of a supersymmetric action
functional.Comment: 30 page
From Observed Action Identity to Social Affordances
Others' observed actions cause continuously changing retinal images, making it challenging to build neural representations of action identity. The monkey anterior intraparietal area (AIP) and its putative human homologue (phAIP) host neurons selective for observed manipulative actions (OMAs). The neuronal activity of both AIP and phAIP allows a stable readout of OMA identity across visual formats, but human neurons exhibit greater invariance and generalize from observed actions to action verbs. These properties stem from the convergence in AIP of superior temporal signals concerning: (i) observed body movements; and (ii) the changes in the body-object relationship. We propose that evolutionarily preserved mechanisms underlie the specification of observed-actions identity and the selection of motor responses afforded by them, thereby promoting social behavior
An Algebraic Construction of Generalized Coherent States for Shape-Invariant Potentials
Generalized coherent states for shape invariant potentials are constructed
using an algebraic approach based on supersymmetric quantum mechanics. We show
this generalized formalism is able to: a) supply the essential requirements
necessary to establish a connection between classical and quantum formulations
of a given system (continuity of labeling, resolution of unity, temporal
stability, and action identity); b) reproduce results already known for
shape-invariant systems, like harmonic oscillator, double anharmonic,
Poschl-Teller and self-similar potentials and; c) point to a formalism that
provides an unified description of the different kind of coherent states for
quantum systems.Comment: 14 pages of REVTE
Coherent states for continuous spectrum operators with non-normalizable fiducial states
The problem of building coherent states from non-normalizable fiducial states
is considered. We propose a way of constructing such coherent states by
regularizing the divergence of the fiducial state norm. Then, we successfully
apply the formalism to particular cases involving systems with a continuous
spectrum: coherent states for the free particle and for the inverted oscillator
are explicitly provided. Similar ideas can be used for other
systems having non-normalizable fiducial states.Comment: 17 pages, typos corrected, references adde
Some Physical Appearances of Vector Coherent States and CS Related to Degenerate Hamiltonians
In the spirit of some earlier work on the construction of vector coherent
states over matrix domains, we compute here such states associated to some
physical Hamiltonians. In particular, we construct vector coherent states of
the Gazeau-Klauder type. As a related problem, we also suggest a way to handle
degeneracies in the Hamiltonian for building coherent states. Specific physical
Hamiltonians studied include a single photon mode interacting with a pair of
fermions, a Hamiltonian involving a single boson and a single fermion, a
charged particle in a three dimensional harmonic force field and the case of a
two-dimensional electron placed in a constant magnetic field, orthogonal to the
plane which contains the electron. In this last example, an interesting modular
structure emerges for two underlying von Neumann algebras, related to opposite
directions of the magnetic field. This leads to the existence of coherent
states built out of KMS states for the system.Comment: 38 page
Ladder operators and coherent states for continuous spectra
The notion of ladder operators is introduced for systems with continuous
spectra. We identify two different kinds of annihilation operators allowing the
definition of coherent states as modified "eigenvectors" of these operators.
Axioms of Gazeau-Klauder are maintained throughout the construction.Comment: Typos correcte
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