scholarly journals Covariant fields on anti-de Sitter spacetimes

2018 ◽  
Vol 33 (04) ◽  
pp. 1850026 ◽  
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Universal Covering ◽  
Positive Energy ◽  
De Sitter ◽  
Ladder Operators ◽  
Covariant Representations ◽  
Covering Group ◽  
Ads Spacetime ◽  
Casimir Operators ◽  
Free Fields ◽  
Covariant Field

The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.

scholarly journals Canonical quantization of the covariant fields on de Sitter space–times

2018 ◽  
Vol 33 (08) ◽  
pp. 1830007 ◽  
Author(s):  
Ion I. Cotaescu
Keyword(s):  
Isometry Group ◽  
Canonical Quantization ◽  
Principal Series ◽  
De Sitter Space ◽  
Fermion Mass ◽  
Dirac Field ◽  
De Sitter ◽  
Covariant Quantum ◽  
Covariant Representations ◽  
Casimir Operators

The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

scholarly journals Positive energy representations of Sobolev diffeomorphism groups of the circle

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Sebastiano Carpi ◽  
Simone Del Vecchio ◽  
Stefano Iovieno ◽  
Yoh Tanimoto
Keyword(s):  
Unitary Representation ◽  
Von Neumann Algebras ◽  
Universal Covering ◽  
Irreducible Representations ◽  
Positive Energy ◽  
Diffeomorphism Groups ◽  
Von Neumann ◽  
Direct Sum ◽  
Covering Groups

AbstractWe show that any positive energy projective unitary representation of $$\mathrm{Diff}_+(S^1)$$ Diff + ( S 1 ) extends to a strongly continuous projective unitary representation of the fractional Sobolev diffeomorphisms $$\mathcal {D}^s(S^1)$$ D s ( S 1 ) for any real $$s>3$$ s > 3 , and in particular to $$C^k$$ C k -diffeomorphisms $$\mathrm{Diff}_+^k(S^1)$$ Diff + k ( S 1 ) with $$k\ge 4$$ k ≥ 4 . A similar result holds for the universal covering groups provided that the representation is assumed to be a direct sum of irreducibles. As an application we show that a conformal net of von Neumann algebras on $$S^1$$ S 1 is covariant with respect to $$\mathcal {D}^s(S^1)$$ D s ( S 1 ) , $$s > 3$$ s > 3 . Moreover every direct sum of irreducible representations of a conformal net is also $$\mathcal {D}^s(S^1)$$ D s ( S 1 ) -covariant.

Sign in / Sign up

Export Citation Format

Share Document