Towards Hamiltonian Formalism for String Field Theory and Nonlocality
arXiv:2412.02577 · doi:10.1007/JHEP09(2025)119
Abstract
String field theories exhibit exponential suppression of interactions among the component fields at high energies due to infinite-derivative factors such as in the vertices. This nonlocality has hindered the development of a consistent Hamiltonian formalism, leading some to question whether such a formalism is even viable. To address this challenge, we introduce a toy model inspired by string field theory and construct its Hamiltonian formalism by demanding that it reproduce all correlation functions derived from the path-integral formalism. Within this framework, we demonstrate for this toy model that physical-state constraints can be imposed to eliminate negative-norm states, while zero-norm states decouple from the physical state space. This approach provides a novel perspective on the nonlocality inherent in string field theories.
66 pages, 1 figure; v2: minor corrections, reference added; v3: published version with additional clarifications on the model considered and the analytic continuation procedure
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