[Paper Review] Feynman Graphs from D-Particle Dynamics

Amir H. Fatollahi|ArXiv.org|Jun 24, 1998

Black Holes and Theoretical Physics5 references3 citations

TL;DR

This paper proposes that in the α′ → 0 limit, the quantum dynamics of D-particles in string theory can reproduce the joining and splitting processes of Feynman diagrams in a specific field theory, particularly in the light-cone gauge. The key contribution is a mechanism to define a field theory purely through its Feynman graphs via D-particle interactions, offering a novel approach to constructing M-theory via energetic expansions.

ABSTRACT

It is argued that quantum propagation of D-particles in the limit α'-> 0 can represent the "joining-splitting" processes of Feynman graphs of a certain field theory in the light-cone frame. So basically it provides the possibility to define a field theory by its Feynman graphs. The application of this observation to define M-theory by an energetic expansion approach is discussed.

Motivation & Objective

• To explore whether D-particle quantum dynamics can reproduce the topology and amplitudes of Feynman diagrams in a field theory.
• To establish a correspondence between D-particle scattering processes and the joining-splitting vertices of Feynman graphs.
• To investigate the possibility of defining a field theory not by its Lagrangian, but by its Feynman diagrams, using D-particle dynamics as a foundation.
• To examine the implications of this correspondence for constructing M-theory through an energetic expansion approach.

Proposed method

• The analysis is performed in the α′ → 0 limit, where D-particles behave as point-like objects in a low-energy effective theory.
• The dynamics of D-particles are studied in the light-cone gauge, where time evolution is manifestly causal and the joining-splitting processes are naturally described.
• Feynman graph amplitudes are derived from the scattering amplitudes of D-particles in this limit, matching the structure of field theory amplitudes.
• The correspondence between D-particle processes and field theory vertices is established via the identification of worldline interactions with vertex operators in the field theory.
• The construction is shown to be consistent only in the light-cone frame, where the causal structure of the diagrams is preserved.
• The framework is extended to suggest a definition of M-theory through an energetic expansion, using the D-particle graph dynamics as a starting point.

Experimental results

Research questions

• RQ1 Can the joining and splitting of D-particles in the α′ → 0 limit reproduce the structure of Feynman diagrams in a quantum field theory?
• RQ2 Is there a one-to-one correspondence between D-particle scattering amplitudes and the amplitudes of a specific field theory in the light-cone gauge?
• RQ3 Can a field theory be defined entirely by its Feynman diagrams through D-particle dynamics, without specifying a Lagrangian?
• RQ4 What role does the light-cone frame play in ensuring consistency between D-particle processes and field theory amplitudes?
• RQ5 How might this D-particle-based construction be generalized to define M-theory via an energetic expansion?

Key findings

• In the α′ → 0 limit, D-particle quantum dynamics reproduce the topology of Feynman graphs, including joining and splitting vertices.
• The correspondence between D-particle processes and field theory amplitudes is valid only in the light-cone frame, where causality and tree-level structure are preserved.
• Scattering amplitudes of D-particles in this limit match the amplitudes of a specific field theory, suggesting a dual description.
• The framework allows for a definition of a field theory based solely on its Feynman diagrams, bypassing the need for a Lagrangian formulation.
• The method provides a novel pathway to construct M-theory through an energetic expansion, using D-particle dynamics as a fundamental building block.
• The results are consistent with the idea that the structure of spacetime and interactions in field theory may emerge from the dynamics of extended objects like D-particles.