Constructing phase space distributions with internal symmetries

Mueller, Niklas; Venugopalan, Raju

doi:10.1103/PhysRevD.99.056003

Title: Constructing phase space distributions with internal symmetries

Journal Article · Fri Mar 08 00:00:00 EST 2019 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.99.056003· OSTI ID:1498591

Mueller, Niklas; Venugopalan, Raju

We discuss an ab initio world-line approach to constructing phase space distributions in systems with internal symmetries. Starting from the Schwinger-Keldysh real-time path integral in quantum field theory, we derive the most general extension of the Wigner phase space distribution to include color and spin degrees of freedom in terms of dynamical Grassmann variables. The corresponding Liouville distribution for colored particles, which obey Wong’s equation, has only singlet and octet components, while higher moments are fully constrained by the Grassmann algebra. The extension of phase space dynamics to spin is represented by a generalization of the Pauli-Lubanski vector; its time evolution via the Bargmann-Michel-Telegdi equation also follows from the phase space trajectories of the underlying Grassmann coordinates. Our results for the Liouville phase space distribution in systems with both spin and color are of interest in fields as diverse as chiral fluids, finite temperature field theory and polarized parton distribution functions. We also comment on the role of the chiral anomaly in the phase space dynamics of spinning particles.

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Research Organization:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); German Research Foundation (DFG)

Grant/Contract Number:: SC0012704; 404640738

OSTI ID:: 1498591

Alternate ID(s):: OSTI ID: 1505106

Report Number(s):: BNL-211515-2019-JAAM; PRVDAQ; 056003

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 99 Journal Issue: 5; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 29 works

Citation information provided by
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
anomalies
many-body techniques
nonequilibrium statistical mechanics
path integrals
quantum field theory
quantum kinetic theory
relativistic heavy-ion collisions
relativistic kinetic theory
topology

Title: Constructing phase space distributions with internal symmetries

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