By H. Weyl

TO MY buddy WALTER DALLENBACH FROM THE AUTHORS PREFACE TO the 1st GERMAN version the significance of the point of view afforded by way of the idea of teams for the invention of the overall legislation of quantum conception has of overdue develop into progressively more obvious. because i've got for a few years been deeply involved in the idea of the illustration of constant teams, it has appeared to me acceptable and critical to provide an account of the information gained through mathematicians operating during this box in a sort appropriate to the necessities of quantum physics. an extra impetus is to be present in the truth that, from the in basic terms mathematical point of view, it really is now not justifiable to attract such sharp differences among finite and non-stop teams in discussing the speculation in their representations as has been performed within the latest texts at the topic. My wish to convey how the ideas bobbing up within the conception of teams locate their software in physics via discussing yes of the extra vital examples has necessitated the inclusion of a brief account of the principles of quantum physics, for on the time the manuscript used to be written there existed no remedy of the topic to which i'll refer the reader. briefly this booklet, if it fulfills its function, should still permit the reader to benefit the necessities of the idea of teams and of quantum mechanics in addition to the rela tionships current among those matters the mathematical parts were written with the physicist in brain, and vice versa. i've got relatively emphasised the reciprocity M be tween the representations of the symmetric permutation crew and people of the total linear crew this reciprocity has as but been unduly missed within the actual literature, although it follows so much certainly from the conceptual constitution of quantum mechanics. vii viii the idea OF teams There exists, for my part, a it appears that evidently discernible parallelism among the newer advancements of arithmetic and physics. Occidental arithmetic has in earlier centuries damaged clear of the Greek view and a path which turns out to have originated in India and which has been transmitted, with additions, to us by means of the Arabs in it the concept that of quantity appears to be like as logically ahead of the ideas of geometry. the results of this has been that we've got utilized this systematically constructed quantity suggestion to all branches, without reference to if it is perfect for those specific purposes. however the current development in arithmetic is obviously towards a go back to the Greek perspective we now glance upon every one department of arithmetic as settling on its personal attribute area of amounts. The algebraist of the current day considers the continuum of actual or advanced numbers as in simple terms one box between many the new axiomatic origin of projective geometry could be regarded as the geometric counterpart of this view. This more recent arithmetic, together with the trendy concept of teams and summary algebra, is obviously prompted by means of a spirit various from that of classical arithmetic, which came across its maximum expression within the conception of services of a fancy variable. The continuum of actual numbers has retained its historic prerogative in physics for the expression of actual measurements, however it can justly be maintained that the essence of the hot Heisenberg-Schrodinger-Dirac quantum mechanics is to be present in the truth that there's linked to each one actual process a suite of amounts, constituting a non-commutative algebra within the technical mathematical experience, the weather of that are the actual amounts themselves. ZURICH, August, 1928 AUTHORS PREFACE TO the second one GERMAN variation throughout the educational 12 months 1928-29 I held a professorship in mathematical physics in Princeton University...