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By S. L. Sobolev

ISBN-10: 0821815571

ISBN-13: 9780821815571

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Extra resources for Applications of Functional Analysis in Mathematical Physics (Translations of Mathematical Monographs, Vol 7)

Sample text

We can achieve this by introducing a charged test body at the point x and measuring the force exerted on it by the electric field (Fig. 1). The force exerted on the probe is determined from the change in the momentum of the latter. An exact measurement of the field component E1 is thus equivalent to an exact measurement of the momentum component p1 of the test body. As a result of this, the position of the test body will, according to Heisenberg's uncertainty principle, change in an uncontrollable way.

86) which has been studied in detail at the ISR storage rings at a center of mass energy of ~ 53 GeV. As can be seen in Fig. 87) The questions is: To what scattering angle in the center of mass system does this value of t correspond? yFi ---;- ~ 44 mrad ~ 2S. 58) by crossing. By this we mean processes in which one or more particles are replaced by their corresponding antiparticles, which then appear on the other side of the equation describing the reaction. 3 The Relativistic Kinematics of a Collision Between Two Particles 29 10~ • mb/GeV 2 10-3 10" 10-' do dT 1(j" 10-7 VS:53GeV ~ \ v--,......

An experiment of this type is sketched in Fig. 2. The spectral components of an electromagnetic wave are separated by a prism. Behind the prism the photons are detected by an array of counters which record the photons by means of the photoelectric effect. We now wish to investigate the question of the relationship between particles like the photon and the corresponding quantized field operator. In fact, the case of the electromagnetic field suffers from certain complications and will be dealt with in the second part of this book.

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Applications of Functional Analysis in Mathematical Physics (Translations of Mathematical Monographs, Vol 7) by S. L. Sobolev

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