Application of distributions to the theory of elementary by Laurent Schwartz

By Laurent Schwartz

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If infinitesimal operators 6W, and 6Wac are defined similarly, the differential proper- ty (1,66) becomes the matrix equation from which we infer the operator equation 24 QUANTUM KINEMATICS AND DYNAMICS Thus the multiplicative composition law of transformation functions is expressed by an additive composition law for the infinitesimal operators 6W. 70), we learn that or which expresses the fixed numerical values of the. transformation function Indeed, the latter is not an independent condition on transformation functions but is implied by the composition property and the requirement that transformation functions, as matrices, be nonsingular.

34). If we perform an A-measureinent that does not distinguish between two (or more) states, there is a related additivity of the numbers p(a', b') , and, for the A-measurement that does not distinguish among any of the states, there appears 16 QUANTUM KINEMATICS AND DYNAMICS whence These properties qualify p(a', b 1 ) for the role of the probability that one observes the state a 1 in a, measurement performed on a system known to be in the state b 1 . But a probability is a real, non- negative number.

Compare P. A. M. Dirae, Be», Mad. Phys, 17, 19S (1945), where n<»n-Hermitian operators and complex "probabilities" are introduced. 8 The Null State Reconstruction of the Measurement Algebra Vector Algebra Wave Functions Unitary Transformations Infinitesimal Unitary Transformations Successive Unitary Transformations Unitary Transformation GroupsTranslations and Rotations 2 . 1 THE NULL STATE 29 32 35 37 40 44 46 48 53 54 56 62 The uncontrollable disturbance attendant upon a measurement implies that the act of measurement is indivisible.

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