A problem on summation over histories in quantum mechanics

Transition amplitude corresponding to Dirac particle evaluated as sum over histories - quantum mechanic

Path-integrals in dynamics

Path integrals in dynamics - quantum mechanics and classical wave motion in one dimensio

Momentum operators in quantum mechanics

Momentum operators in quantum mechanic

On the fluidity of consonance and dissonance: The influence of musical context

The consonance/dissonance (C/D) level of a triadic chord is not a fixed or absolute value. Rather, it is fluid, since C/D depends both on a chord’s sonic characteristics and on the musical context in which it appears. To test the fluidity of C/D—the extent to which C/D perception is dependent on musical context—4 types of chords (major, minor, augmented, and diminished triads) were presented in isolation (“without musical context”) and as part of a short cadence (IV-V-I, “with musical context”). The C/D level of each chord was judged, as was the overall C/D and pleasantness/unpleasantness (P/U) level of the cadences. When isolated, major triads were considered most consonant, followed by minor and diminished triads, while augmented triads were judged most dissonant. In the context of a musical cadence, this rank order remained the same. However, evaluations of the dissonance of augmented and diminished chords varied depending on each chord’s functional position within the cadence. For instance, diminished triads were relatively consonant when on the subdominant, while augmented triads were relatively dissonant when on the tonic. These findings lend support to the hypotheses that: (a) the degree to which the harmonic function of a chord is familiar, and (b) the degree to which a chord’s stability (and hence also the listener’s expectation) is violated contribute to the perception of C/D

Full counting statistics of weak measurement

A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function for the moments of the output is provided. The outputs considered are not limited to the eigenstates of the pointer or of its conjugate variable, so that the results apply to any observable \Hat{o} of the probe. Furthermore, a family of well behaved complex quantities, the normal weak values, is introduced, in terms of which the statistics of the weak measurement can be described. It is shown that, within a good approximation, the whole statistics of weak measurement is described by a complex parameter, the weak value, and a real one.Comment: Expanded version: 9 pages, 3 Figs. Now the validity of the expansion for the moments is analysed. Introduced a one-parameter family of weak values, useful to express the correct characteristic function. More figures added. Thanks to Referee C of PRL for asking stimulating question

Windows Into Public Attitudes Towards Redistribution

redistribution, income taxation, public opinion

Celebrity capital in the political field: Russell Brand's migration from stand-up comedy to Newsnight

Our case study of charismatic celebrity comedian Russell Brand’s turn to political activism uses Bourdieu’s field theory to understand the process of celebrity migration across social fields. We investigate how Brand’s capital as a celebrity performer, storyteller and self-publicist translated from comedy to politics. To judge how this worked in practice, we analysed the comedic strategies used in his stand up show Messiah Complex and a Conversational Analysis of his notorious interview with Jeremy Paxman on the BBC’s flagship current affairs programme Newsnight . We argue that Brand was able to secure political legitimacy by creatively constituting himself as an authentic anti-austerity spokesperson for the disenfranchised left in UK. In order to do so he repurposed his celebrity capital to political ends and successfully deployed the cultural and social capital he had developed as a celebrity comedian to secure widespread engagement with his media performances

Catalyst optimisation for asymmetric synthesis by ligand chirality element addition - a perspective on stereochemical cooperativity

The concept of matched and mismatched stereochemical pairings has been utilised extensively in organic synthesis, with the cooperativity resulting from the former enabling many reactions to proceed with high stereoselectivity. This approach was first developed to improve the diastereoselectivity of a reaction by matching the configuration of an enantiopure reagent or catalyst with the configuration of an enantiopure substrate. It has been extended to the asymmetric transformation of prochiral substrates controlled by reagents and catalysts containing two or more stereogenic centres. Matched and mismatched pairings may again be identified, with the former resulting in higher product enantioselectivity. This Minireview examines stereochemical pairings within catalysts generated from the combination of a metal with an enantiopure ligand; specifically examples where the ligand diastereoisomers examined for cooperativity are formally the result of the addition of a chiral element to an existing enantiopure ligand. Comparison of all three ligands in each of the fifty-six examples examined reveals that in the majority of cases the added element of chirality increases and decreases the enantioselectivity with respect to the parent ligand. The iterative application of this effect offers a potentially powerful method for catalyst optimisation for use in asymmetric synthesis

Labour and the “Real” Constitution

Même si la constitution officielle du Canada ne fait aucunement mention du droit du travail ou de l’emploi, et quoique la jurisprudence ait depuis longtemps établi la prépondérance de la compétence provinciale dans ce domaine, les droits constitutionnels des syndicats et des travailleurs ont récemment fait l’objet de nombreux litiges et d’un examen approfondi dans la doctrine. Cet article passe en revue les tentatives de se servir des dispositions de la Charte canadienne des droits et libertés afin de protéger les intérêts des syndicats et des travailleurs et de faire progresser la cause de l’égalité en milieu de travail. Il explore ensuite la manière dont l’architecture constitutionnelle du Canada a eu tendance à contrecarrer les intérêts des syndicats et des travailleurs. En dernier lieu, il suggère que les intérêts des syndicats et des travailleurs seront tranchés en grande partie non pas par la constitution officielle mais bien par la « véritable constitution », soit la structure de son économie. Bien que la « véritable constitution » soit généralement défavorable aux droits et intérêts des syndicats et des travailleurs, à l’instar de la constitution officielle, elle est vague et laisse ample place à l’évolution et pour faire valoir des oppositions.While Canada’s formal constitution does not mention labour or employment law, and while jurisprudence has long established the primacy of provincial jurisdiction in this field, labour’s constitutional rights have been the subject of extensive recent litigation and scholarship. This article reviews attempts to use the provisions of the Canadian Charter of Rights and Freedoms to protect labour’s interests and to advance the cause of equality in the workplace. It then explores how Canada’s constitutional architecture has tended to frustrate the interests of unions and workers. And finally, it proposes that labour’s interests will largely be determined not by the formal constitution but by the “real constitution” — the structure of its economy. While the “real constitution” generally disfavours labour’s rights and interests, like the formal constitution it is vague and leaves ample room for challenge and for change