By Armin Wachter (auth.)
Which difficulties do come up inside of relativistic improvements of the Schrödinger concept, specifically if one adheres to the standard one-particle interpretation, and to what volume can those difficulties be conquer? and what's the actual necessity of quantum box theories? in lots of books, solutions to those basic questions are given hugely insufficiently through treating the relativistic quantum mechanical one-particle idea very superficially and as an alternative introducing box quantization once attainable. in contrast, this monograph emphasizes relativistic quantum mechanics within the slender feel: it greatly discusses relativistic one-particle suggestions and divulges their difficulties and boundaries, for this reason motivating the need of quantized fields in a bodily understandable approach. the 1st chapters comprise a close presentation and comparability of the Klein-Gordon and Dirac idea, regularly in view of the non-relativistic concept. within the 3rd bankruptcy, we give some thought to relativistic scattering procedures and strengthen the Feynman principles from propagator options. this can be the place the impossibility to get round a quantum box theoretical reasoning is mentioned and easy quantum box theoretical suggestions are brought. This ebook addresses undergraduate and graduate physics scholars who're drawn to a basically prepared and dependent presentation of relativistic quantum mechanics within the "narrow experience" and its connection to quantum box theories. every one part features a brief precis and workouts with options. A mathematical appendix rounds up this glorious introductory booklet on relativistic quantum mechanics.
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Relativistic Description of Spin-0 Particles CT = R =⇒ P CT = P R . Since P and R are Lorentz-like, it follows that the P CT -transformation is Lorentz-like, too. 3, we are now in a position to complete the one-particle interpretation of the Klein-Gordon theory. 3, namely, [1] under which conditions is a decoupling of the Klein-Gordon theory into two one-particle theories possible, [2] which operators are appropriate for the one-particle concept and how can they be constructed, [3] how can physically meaningful and picture- as well as representationindependent one-particle expectation values be defined?
It turns a positive [negative] Klein-Gordon solution of charge +e [−e] into a negative [positive] Klein-Gordon solution of charge −e [+e]. • A positive Klein-Gordon solution φ(+) or ψ (+) represents a physical spin0 particle of charge +e within the potential Aμ , while the charge con(−) (−) jugate of the negative solution φC or ψC (and not the original negative solution) describes the physical antiparticle with opposite charge −e within the same potential Aμ . • The quantities Q, ρ, and j that are composed of φ(+) or ψ (+) [φ(−) or ψ (−) ] can be interpreted as the electric charge, charge density, and charge current density of the physical particle [antiparticle] (charge interpretation).
The second class is passive transformations. Here, not the physical state but the reference frame (or the basis system) is transformed, so that only the perspective changes, from which the same state is observed. These transformations are also called coordinate transformations as they always imply a 22 1. Relativistic Description of Spin-0 Particles change in the space-time coordinates. In this book we are dealing with relativistic theories, therefore the interesting transformations are the Lorentz transformations.