Trotter formula

The Trotter formula is given by (Ref.1 Eq. 5):

$e^{-\beta (H_{0}+V)}=\lim _{n\rightarrow \infty }(e^{-\beta H_{0}/n}e^{-\beta V/n})^{n}$

where $H_{0}$ and $V$ are self-adjoint operators.

References

1. H. F. Trotter "On the Product of Semi-Groups of Operators", Proceedings of the American Mathematical Society 10 545-551 (1959)
2. Masuo Suzuki "Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems - Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations", Progress of Theoretical Physics 56 pp. 1454-1469 (1976)
3. Hans De Raedt and Bart De Raedt "Applications of the generalized Trotter formula", Physical Review A 28 3575-3580 (1983)
4. R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General 19 1551-1554 (1986)
5. Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)