Trotter formula

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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^{-\beta (H_0 + V)} = \lim_{n \rightarrow \infty} (e^{-\beta H_0 /n} e^{-\beta V/n})^n}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_0} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} are self-adjoint operators. This formula is used in the path integral formulation.

References

Related reading

• 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)
• Hans De Raedt and Bart De Raedt "Applications of the generalized Trotter formula", Physical Review A 28 3575-3580 (1983)
• R. Thieberger "On the convergence of the Trotter formula", Journal of Physics A: Mathematical and General 19 1551-1554 (1986)
• Masuo Suzuki "Improved Trotter-like formula", Physics Letters A 180 pp. 232-234 (1993)
• Oscar Bolina " Trotter formula and thermodynamic limits", arXiv:physics/0202003v1 (3 Feb 2002)