RT Journal Article
T1 UV/IR mixing and the Goldstone theorem in noncommutative field theory
A1 Ruiz Ruiz, Fernando
AB Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, lambda(1) and lambda(2), associated to the two noncommutative extensions phi* star phi star phi* star phi and phi* star phi* star phi star phi of the interaction term \phi\(4) on commutative spacetime. It is shown that the symmetric phase is one loop renormalizable for all lambda(1) and lambda(2) compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if lambda(2) = 0, a condition required by the Ward identities for global U(I) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter theta.
PB Elsevier Science Bv
SN 0550-3213
YR 2002
FD 2002-08-19
LK https://hdl.handle.net/20.500.14352/58993
UL https://hdl.handle.net/20.500.14352/58993
LA eng
NO © 2002 Elsevier Science B.V. All rights reserved.The author is grateful to C.P. Martín formany illuminating conversations and for reading the manuscript. He also acknowledges financial support from CICyT, Spain through grant No. PB98-0842.
NO CICyT
DS Docta Complutense
RD 7 abr 2025