We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.

Nonlocal scalar quantum field theory from causal sets / Belenchia, Alessio; Benincasa, Dionigi Maria Teofilo; Liberati, Stefano. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2015:3(2015), pp. 036.1-036.26. [10.1007/JHEP03(2015)036]

Nonlocal scalar quantum field theory from causal sets

Belenchia, Alessio;Benincasa, Dionigi Maria Teofilo;Liberati, Stefano
2015

Abstract

We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.
2015
3
1
26
36
10.1007/JHEP03(2015)036
https://link.springer.com/article/10.1007/JHEP03(2015)036
Belenchia, Alessio; Benincasa, Dionigi Maria Teofilo; Liberati, Stefano
File in questo prodotto:
File Dimensione Formato  
art%3A10.1007%2FJHEP03%282015%29036.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 587.99 kB
Formato Adobe PDF
587.99 kB Adobe PDF Visualizza/Apri

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: http://hdl.handle.net/20.500.11767/17049
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 41
  • ???jsp.display-item.citation.isi??? 37
social impact