Dressed scalar propagator in a non-abelian background from the worldline formalism

Abstract

We study the propagator of a colored scalar particle in the background of a non-abelian gauge field using the worldline formalism. It is obtained by considering the open worldline of a scalar particle with extra degrees of freedom needed to take into account the color charge of the particle, which we choose to be in the fundamental representation of the gauge group. Specializing the external gauge field to be given by a sum of plane waves, i.e. a sum of external gluons, we produce a master formula for the scalar propagator with an arbitrary number of gluons directly attached to the scalar line, akin to similar formulas derived in the literature for the case of the scalar particle performing a loop. Our worldline description produces at the same time the situation in which the particle has a color charge given by an arbitrarily chosen symmetric or antisymmetric tensor product of the fundamental.

21 pages, 1 figure; title modified, discussion improved, references added, main results unchanged. Matches version published in PRD

References in corpus (5)

• New Relations for Gauge-Theory Amplitudes
• Scalar heat kernel with boundary in the worldline formalism
• CSW rules for a massive scalar
• Integral representations combining ladders and crossed-ladders
• The Fermion Content of the Standard Model

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• Classical Double Copy of Spinning Worldline Quantum Field Theory
• Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes
• The $L_{\infty }$ structure of gauge theories with matter
• Classical off-shell currents
• The worldline approach to helicity flip in plane waves
• Worldline description of a bi-adjoint scalar and the zeroth copy
• Mixed symmetry Wilson-loop interactions in the worldline formalism
• Propagator from Nonperturbative Worldline Dynamics
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• Berry phase in the phase space worldline representation: the axial anomaly and classical kinetic theory
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• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• Schwinger Pair Production in SL$(2,\mathbb{C})$ Topologically Non-Trivial Fields via Non-Abelian Worldline Instantons
• Dressed Dirac Propagator from a Locally Supersymmetric $\mathcal{N}=1$ Spinning Particle
• $U(N)$ Yang-Mills in non-commutative space time
• Spinning Particles in Quantum Mechanics and Quantum Field Theory
• Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies
• Non-perturbative gauge transformations of arbitrary fermion correlation functions in quantum electrodynamics
• On kinetic theories with color and spin from amplitudes