Hamiltonian Formalism for Space-time Non-commutative Theories

Abstract

Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to the evolution time. The Hamiltonian path integral quantization is considered and the Feynman rules in the Lagrangian formalism are derived. The case of non-commutative ϕ^3 theory is considered as an example.

6 pages, A new section is added with other comments and references. To appear in PRD

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• A Canonical Formalism For Lagrangians With Nonlocality Of Finite Extent
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• Energy Momentum Tensor and Marginal Deformations in Open String Field Theory
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• Dynamics and Stability of Light-Like Tachyon Condensation
• Initial value problem in string-inspired nonlocal field theory
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• Quantization of nonlocal fractional field theories via the extension problem
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
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• The Ostrogradskian Instability of Lagrangians with Nonlocality of Finite Extent
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• The Hamiltonian BRST quantization of a noncommutative nonabelian gauge theory and its Seiberg-Witten map
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• Towards Hamiltonian Formalism for String Field Theory and Nonlocality
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