Trace:

group_theory:notions:unitary_representations

This shows you the differences between two versions of the page.

Both sides previous revision Previous revision Next revision | Previous revision | ||

group_theory:notions:unitary_representations [2016/12/22 09:35] jakobadmin |
group_theory:notions:unitary_representations [2017/12/06 09:33] (current) |
||
---|---|---|---|

Line 7: | Line 7: | ||

To make sense of the probabilistic interpretation of quantum theory, we need to use unitary representations (see e.g. page 69 in [[http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf|Schwartz's book]]). Expressed differently, we are interested in representations of given groups on the Hilbert space in a quantum field theory. | To make sense of the probabilistic interpretation of quantum theory, we need to use unitary representations (see e.g. page 69 in [[http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf|Schwartz's book]]). Expressed differently, we are interested in representations of given groups on the Hilbert space in a quantum field theory. | ||

+ | Many important groups are non-compact (e.g. the Poincare group and the conformal group) and there is a theorem that tells us that all unitary representations of a non-compact group are infinite-dimensional. | ||

+ | "//The infinite-dimensional representations are | ||

+ | considered unphysical because we never see particle states in nature labelled by extra continuous | ||

+ | parameters.//" http://homepages.uc.edu/~argyrepc/cu661-gr-SUSY/susy2001.pdf | ||

+ | |||

+ | Thus it is often a non-trivial problem to find make sense of the unitary representations of such groups. | ||

===== Examples ===== | ===== Examples ===== |

group_theory/notions/unitary_representations.txt ยท Last modified: 2017/12/06 09:33 (external edit)