The possibility and significance of fractional angular momentum is discussed, and some simple physical realizations of it are mentioned. This leads naturally to consideration of the possibility of fractional quantum statistics, which is seen to be a possibility inherent in the kinematics of 2+1 dimensional quantum mechanics. Both sorts of fractionalization are intimately related to theories, and the classic considerations of Aharonov and Bohm on the significance of the vector potential in quantum mechanics. The meaning and importance of discrete gauge invariance in continuum theories is pointed out. Fractional statistics is shown to have a simple dynamical realization in the dynamics of charge-flux tube composites. Fractional statistics is shown to occur very naturally in the most geometrical quantum field theories in 2+1 dimensions, that is in the nonlinear sigma model and in quantum electrodynamics.
Frank WilczekRelated topics
angular dynamics field fractional meaning mechanics model momentum possibility quantum realization seen show significance simple statistics vector electrodynamicsRelated quotes
From the fundamental nature of the Philistine, it follows that, in regard to others, as he has no intellectual but only physical needs, he will seek those who are capable of satisfying the latter not the former. And so of all the demands he makes of others the very smallest will be that of any outstanding intellectual abilities. On the contrary, when he comes across these they will excite his antipathy and even hatred. For here he has a hateful feeling of inferiority and also a dull secret envy which he most carefully attempts to conceal even from himself; but in this way it grows sometimes into a feeling of secret rage and rancour. Therefore it will never occur to him to assess his own esteem and respect in accordance with such qualities, but they will remain exclusively reserved for rank and wealth, power and influence, as being in his eyes the only real advantages to excel in which is also his desire.
Arthur Schopenhauer
Yet why should an artist's way of looking at the world have any meaning for us? Why does it give us pleasure? Because, I believe, it increases our awareness of our own potentiality. Not of course our awareness of our potentiality as artists ourselves. But a way of looking at the world implies a certain relationship with the world, and every relationship implies action. The kind of actions implied vary a great deal. ... A work of art can, to some extent, increase an awareness of different potentialities in different people. The important point is that a valid work of art promises in some way or another the possibility of an increase, an improvement. Nor need the word be optimistic to achieve this; indeed, its subject may be tragic. For it is not the subject that makes the promise, it is the artist's way of viewing his subject. Goya's way of looking at a massacre amounts to the contention that we ought to be able to do without massacres.
John Berger
For, for aught we know, or for aught that the new science can say to the contrary, the gods which play the part of fate to the atoms of our brains may be our own minds. Through these atoms our minds may perchance affect the motions of our bodies and so the state of the world around us. To-day science can no longer shut the door on this possibility; she has no longer any unanswerable arguments to bring against our innate conviction of free-will. On the other hand, she gives no hint as to what absence of determinism or causation may mean. If we, and nature in general, do not respond in a unique way to external stimuli, what determines the course of events? If anything at all, we are thrown back on determinism and causation; if nothing at all, how can anything ever occur? As I see it, we are unlikely to reach any definite conclusions on these questions until we have a better understanding of the true nature of time.
James Jeans
Though the war ended forever the possibility of disunion, there still remain problems between State and Federal authority. There are divisions of interest, perhaps more apparent than real, among geographical sections or social groups. The seaboard thinks it has interests in maritime transportation and overseas commerce which differ greatly from those of the interior, which is peculiarly dependent upon railroads. Difference in climate and physical conditions throughout so great a territory tend to varied social habits and modes of living which react upon the economic and political attitudes. The industrial development of some sections contrasts with the agricultural character of others. Obviously, these differences give rise to many problems in government, which must always be recognized. But it is hardly conceivable that a really menacing contest between the sovereignty of the States and of the Union could ever again arise.
Calvin Coolidge
We are convinced that racial regeneration like individual regeneration, must come "from within." That is, it must be autonomous, self-directive, and not imposed from without. In other words, every potential parent, and especially every potential mother, must be brought to an acute realization of the primary and central importance of bringing children into this world. ... Not until the parents of the world are thus given control over their reproductive faculties will it ever be possible ... to improve the quality of the generations of the future, [or] even to maintain civilization even at its present level. ... An idealistic code of sexual ethics, imposed from above, a set of rules devised by high-minded theorists who fail to take into account the living conditions and desires of the submerged masses, can never be of the slightest value in effecting any changes in the mores of the people.
Margaret Sanger