On analytic formulas of Feynman propagators in position space

ZHANG Hong-Hao; FENG Kai-Xi; QIU Si-Wei; ZHAO An; LI Xue-Song

doi:10.1088/1674-1137/34/10/005

Chinese Physics C> 2010, Vol. 34> Issue(10) : 1576-1582 DOI: 10.1088/1674-1137/34/10/005

On analytic formulas of Feynman propagators in position space

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Abstract：
We correct an inaccurate result of previous work on the Feynman propagator in position space of a free Dirac field in (3+1)-dimensional spacetime; we derive the generalized analytic formulas of both the scalar Feynman propagator and the spinor Feynman propagator in position space in arbitrary (D+1)-dimensional spacetime; and we further find a recurrence relation among the spinor Feynman propagator in (D+1)-dimensional spacetime and the scalar Feynman propagators in (D+1)-, (D-1)- and (D+3)-dimensional spacetimes.

References

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Zee A.Quantum Field Theory in a Nutshell.New Jersey:Princeton University Press,2003[2] Greiner W,Reinhardt J.Quantum Electrodynamics.Berlin:Springer,1992[3] Dewitt B S.Dynamical Theory of Groups and Fields.New York:Gordon Breach,1965[4] Peskin M E,Schroeder D V.An Introduction To Quantum Field Theory.New York:Addison-Wesley,1995[5] HUANG K.Quantum Field Theory:From Operators to Path Integrals.New Jersey:Wiley,1998[6] Bekenstein J D,Parker L,Phys.Rev.D,1981,23:2850[7] Mckay D W,Munczek H J.Phys.Rev.D,1997,55:2455.[8] Antonsen F,Bormann K.arXiv:hep-th/9608141[9] Di Sessa A.Phys.Rev.D,1974,9:2926[10] Gutzwiller M.Phys.Stat.Sol.B,2003,237:39[11] Birrell N D,Davies P C W.Quantum Fields In Curved Space.United Kingdom:Cambridge University Press,1982[12] Gradshteyn I S,Ryzhik I M.Tables of Integrals,Series,and Products.Trans.and ed.by Alan Jeffrey.Orlando,Florida:Academic Press,1980

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ZHANG Hong-Hao, FENG Kai-Xi, QIU Si-Wei, ZHAO An and LI Xue-Song. On analytic formulas of Feynman propagators in position space[J]. Chinese Physics C, 2010, 34(10): 1576-1582. doi: 10.1088/1674-1137/34/10/005

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Received: 2009-11-20
Revised: 2010-01-21

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沈阳化工大学材料科学与工程学院沈阳 110142

On analytic formulas of Feynman propagators in position space

Corresponding author: ZHANG Hong-Hao,

Received Date: 2009-11-20
Accepted Date: 2010-01-21
Available Online: 2010-10-05

Abstract:

We correct an inaccurate result of previous work on the Feynman propagator in position space of a free Dirac field in (3+1)-dimensional spacetime; we derive the generalized analytic formulas of both the scalar Feynman propagator and the spinor Feynman propagator in position space in arbitrary (D+1)-dimensional spacetime; and we further find a recurrence relation among the spinor Feynman propagator in (D+1)-dimensional spacetime and the scalar Feynman propagators in (D+1)-, (D-1)- and (D+3)-dimensional spacetimes.