Abstract
It turns out that pip-space methods have many applications in physics, although they are seldom mentioned as such. To draw on a literary analogy, like Molière’s Monsieur Jourdain speaking in prose without knowing so, many authors have been using pip-space language without realizing it. In particular, chains or lattices of Hilbert spaces are quite common in many fields of mathematical physics. Some of these applications will be discussed at length in this chapter. To mention a few examples: quantum mechanics, in particular singular interactions (Section 7.1.3), scattering theory (Section 7.2), quantum field theory (Section 7.3), representations of Lie groups (Section 7.4), etc.
Keywords
- Hilbert Space
- Unitary Representation
- Dirac Formalism
- Gamow Vector
- Observable Vector
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 2009 Springer-Verlag Berlin Heidelberg
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Antoine, JP., Trapani, C. (2009). Applications in Mathematical Physics. In: Partial Inner Product Spaces. Lecture Notes in Mathematics(), vol 1986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05136-4_7
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DOI: https://doi.org/10.1007/978-3-642-05136-4_7
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05135-7
Online ISBN: 978-3-642-05136-4
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