The field of operator algebras has a strong connection with quantum theory and certainly is a necessary requirement for studying many literatures in modern Physics I list some of the books relating operator algebras and physics in the following:
S. Attal, A. Joye, C.A. Pillet, Editors, Open Quantum systems 1, the Hamiltonian approach. Springer, Lecture notes in mathematics, vol. 1880, (2006).
B. Blackadar, Operator algebras. Springer, Encyclopaedia of Mathematical Sciences, vol. 122, (2006).
O. Bratteli, D. W. Robinson, Operator algebras and quantum statistical mechanics 1, $C^*$- and $W^*$-algebras, symmetry groups, decomposition of states. Springer, Texts and monographs in physics, 2nd edition, 2nd printing, (2002).
Connes, A., Noncommutative geometry. Academic press, Inc. (1994).
Garcia-Bondia, J.M., Varilly, J.C., Figueroa, H., Elements of noncommutative geometry. Birkhauser Advanced Texts, Birkhauser, (2000).
N. P. Landsman, Mathematical topics between classical and quantum mechanics. Springer, Monographs in mathematics, (1998).
M. Takesaki, Theory of operator algebras I, II, II. Springer, Encyclopaedia of Mathematical Sciences, vol. 124, (2002).
N. Weaver, Mathematical quantization. Studies in advanced mathematics, Chapman and Hall/CRC, (2001).
In addition to the above books, for a more complete list of general references on $C^*$-algebras and operator algebras as well as for an easy reading for beginners see my lecture notes on $C^*$-algebras here.