Proper actions, fixed-point algebras and naturality in nonabelian duality

"Vegeu el resum a l'incici del document del fitxer adjunt."

Musical actions of dihedral groups

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor triads. We illustrate both geometrically and algebraically how these two actions are dual. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

Complex contact manifolds and S1 actions

We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.

Batalin-Vilkovisky analysis of covariant and noncovariant actions

The equivalence between the covariant and the noncovariant versions of a constrained system is shown to hold after quantization in the framework of the field-antifield formalism. Our study covers the cases of electromagnetism and Yang-Mills fields and sheds light on some aspects of the Faddeev-Popov method, for both the covariant and noncovariant approaches, which have not been fully clarified in the literature.

Gauge-invariant actions from constraint Hamiltonian dynamics

Dirac's constraint Hamiltonian formalism is used to construct a gauge-invariant action for the massive spin-one and -two fields.

Batalin-Vilkovisky analysis of covariant and noncovariant actions

The equivalence between the covariant and the noncovariant versions of a constrained system is shown to hold after quantization in the framework of the field-antifield formalism. Our study covers the cases of electromagnetism and Yang-Mills fields and sheds light on some aspects of the Faddeev-Popov method, for both the covariant and noncovariant approaches, which have not been fully clarified in the literature.

The contribution of real-time mirror reflections of motor actions on virtual body ownership in an immersive virtual environment

This paper reports an experiment that investigated people"s body ownership of an avatar that was observed in a virtual mirror. Twenty subjects were recruited in a within-groups study where 10 first experienced a virtual character that synchronously reflected their upper-body movements as seen in a virtual mirror, and then an asynchronous condition where the mirror avatar displayed prerecorded actions, unrelated to those of the participant. The other 10 subjects experienced the conditions in the opposite order. In both conditions the participant could carry out actions that led to elevation above ground level, as seen from their first person perspective and correspondingly in the mirror. A rotating virtual fan eventually descended to 2m above the ground. The hypothesis was that synchronous mirror reflection would result in higher subjective sense of ownership. A questionnaire analysis showed that the body ownership illusion was significantly greater for thesynchronous than asynchronous condition. Additionally participants in the synchronous condition avoided collision with the descending fan significantly more often than those in the asynchronous condition. The results of this experiment are put into context within similar experiments on multisensory correlation and body ownership within cognitive neuroscience.

Neural mechanisms underlying adaptive actions after slips

An increase in cognitive control has been systematically observed in responses produced immediately after the commission of an error. Such responses show a delay in reaction time (post-error slowing) and an increase in accuracy. To characterize the neurophysiological mechanism involved in the adaptation of cognitive control, we examined oscillatory electrical brain activity by electroencephalogram and its corresponding neural network by event-related functional magnetic resonance imaging in three experiments. We identified a new oscillatory thetabeta component related to the degree of post-error slowing in the correct responses following an erroneous trial. Additionally, we found that the activity of the right dorsolateral prefrontal cortex, the right inferior frontal cortex, and the right superior frontal cortex was correlated with the degree of caution shown in the trial following the commission of an error. Given the overlap between this brain network and the regions activated by the need to inhibit motor responses in a stop-signal manipulation, we conclude that the increase in cognitive control observed after the commission of an error is implemented through the participation of an inhibitory mechanism.