Monopoles in Space‐Time Noncommutative Born‐Infeld Theory

Aschieri, Paolo

doi:10.1002/9783527610853.ch36

Cited by 1 publication

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The corresponding transformation property of multi-particle states (120) can be easily obtained by making use of co-associativity of the co-product (see for example [27,28]).…”

Section: Many-particle Statesmentioning

confidence: 99%

Thermal effective potential in two- and three-dimensional non-commutative spaces

Devi

Ghosh

Chakraborty

et al. 2013

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The issue of thermal correlation functions and the associated effective statistical potential in twodimensional Moyal space, arising in the twisted approach to implement rotational symmetry, has been revisited in an operatorial formulation where no explicit star product is used initially. The corresponding results using Moyal and Voros star products are then easily obtained by taking the corresponding overlap with Moyal and Voros bases. in contrast to the Moyal case where the concept of distance and, in particular, the relative separation between a pair of particles remain ambiguous when the Moyal star product is used, the Voros basis is more physical and the inter-particle distance can be introduced unambiguously. The forms of the correlation function and the effective potential are found to be same as the Moyal case except that the thermal wavelength undergoes a non-commutative deformation, ensuring that it has a lower bound of the order of √ θ. It is shown that in a suitable basis (called here quasi-commutative basis) in the multiparticle sector the thermal correlation function coincides with the commutative result both in the Moyal and Voros cases along with the restoration of the Pauli principle, except that in the Voros case the thermal wavelength, again, gets a non-commutative correction. Finally, we extend our result to three-dimensional non-commutative space and compute the correlation function and effective potential using both twisted and quasi-commutative bases in the Moyal and Voros cases. We find that there is SO(3) → SO(2) symmetry breaking in the effective potential, which also violates the Pauli principle, even for a pair of free particles, despite the fact that a deformed co-product is used to construct twisted symmetric/anti-symmetric basis. However, this SO(3) symmetry, along with Pauli principle, is restored once we use the quasi-commutative bases.

show abstract

“…The corresponding transformation property of multi-particle states (120) can be easily obtained by making use of co-associativity of the co-product (see for example [27,28]).…”

Section: Many-particle Statesmentioning

confidence: 99%