Maybe_Memorie:Maybe_Memorie said:This book discusses lots of different types of integrable models, both classical and quantum. As far as I'm aware this is the best intro book.
http://www.cambridge.org/ie/academi...e-scattering-method-and-correlation-functions
Now, it's really only spin chains I'm familiar with, but in this case the conserved quantities are given by taking the trace of the monodromy matrix on the auxiliary space. This defines the transfer matrix which generates a tower of commuting charges, one of which the is the Hamiltonian of the system. The one-dimensional spin chain with L sites and SU(2) symmetry has L degrees of freedom, whereas the transfer matrix only gives you L-1 conserved quantities. By adding a component of spin, say ##S^z##, we obtain the full set of commuting charges, and the system is integrable.
Conserved quantities refer to physical properties of a system that remain constant over time, even as the system undergoes changes. In an integrable quantum system, these quantities are related to symmetries of the system and can include energy, momentum, and angular momentum.
The conserved quantities of an integrable quantum system can be determined using mathematical techniques such as symmetry analysis, which involves identifying the symmetries of the system and deriving the corresponding conserved quantities.
Conserved quantities play a crucial role in integrable quantum systems as they provide a means to analyze and understand the behavior of the system. They also have practical applications, such as in predicting the outcomes of experiments and simulations.
Yes, the conserved quantities of an integrable quantum system are always constant. This is because the symmetries that give rise to these quantities are inherent properties of the system and remain unchanged throughout its evolution.
No, the conserved quantities of an integrable quantum system cannot be manipulated. This is because they are fundamental properties of the system and cannot be altered without breaking the underlying symmetries. However, the values of these quantities can be measured and used to make predictions about the behavior of the system.