We study the perturbative unitarity of non-commutative quantum Yang-Mills theories, extending previous investigations on scalar field theories to the gauge case where non-locality mingles with the presence of unphysical states. We concentrate our e↵orts on two di↵erent aspects of the problem. We start by discussing the analytical structure of the vacuum polarization tensor, showing how Cutkoski’s rules and positivity of the spectral function are realized when non-commutativity does not a↵ect the temporal coordinate. When instead non-commutativity involves time, we find the presence of extra troublesome singularities on the p20-plane that seem to invalidate the perturbative unitarity of the theory. The existence of new tachyonic poles, with respect to the scalar case, is also uncovered. Then we turn our attention to a di↵erent unitarity check in the ordinary theories, namely time exponentiation of a Wilson loop. We perform a O(g4) generalization to the (spa- tial) non-commutative case of the familiar results in the usual Yang-Mills theory. We show that exponentiation persists at O(g4) in spite of the presence of Moyal phases reflecting non-commutativity and of the singular infrared behaviour induced by UV/IR mixing.

Nardelli, G., Bassetto, A., Griguolo, L., Vian, F., On the unitary of quantum gauge theories on non-commutative spaces, <<JOURNAL OF HIGH ENERGY PHYSICS>>, 2001; (0107): 1-8. [doi:10.1088/1126-6708/2001/07/008] [http://hdl.handle.net/10807/7693]

On the unitary of quantum gauge theories on non-commutative spaces

Nardelli, Giuseppe;Bassetto, Antonio;
2001

Abstract

We study the perturbative unitarity of non-commutative quantum Yang-Mills theories, extending previous investigations on scalar field theories to the gauge case where non-locality mingles with the presence of unphysical states. We concentrate our e↵orts on two di↵erent aspects of the problem. We start by discussing the analytical structure of the vacuum polarization tensor, showing how Cutkoski’s rules and positivity of the spectral function are realized when non-commutativity does not a↵ect the temporal coordinate. When instead non-commutativity involves time, we find the presence of extra troublesome singularities on the p20-plane that seem to invalidate the perturbative unitarity of the theory. The existence of new tachyonic poles, with respect to the scalar case, is also uncovered. Then we turn our attention to a di↵erent unitarity check in the ordinary theories, namely time exponentiation of a Wilson loop. We perform a O(g4) generalization to the (spa- tial) non-commutative case of the familiar results in the usual Yang-Mills theory. We show that exponentiation persists at O(g4) in spite of the presence of Moyal phases reflecting non-commutativity and of the singular infrared behaviour induced by UV/IR mixing.
2001
Inglese
Nardelli, G., Bassetto, A., Griguolo, L., Vian, F., On the unitary of quantum gauge theories on non-commutative spaces, <<JOURNAL OF HIGH ENERGY PHYSICS>>, 2001; (0107): 1-8. [doi:10.1088/1126-6708/2001/07/008] [http://hdl.handle.net/10807/7693]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/7693
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 29
social impact