Creation operators are mathematical tools used in quantum mechanics and functional analysis to add particles to a quantum state or increase the degree of a given operator. In the context of free Brownian motion, they play a vital role in constructing Fock spaces and are essential for understanding the dynamics of non-interacting particles, which can be represented through stochastic processes. Creation operators allow for the manipulation of states in these spaces, enabling complex calculations and the development of theories around free processes.
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