Fetching the paper…
Reading the bibliography…
We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local.
V. Bargmann: On unitary ray representations of continuous groups. Ann. of Math
1954
Earlier work this paper cites.
E. Nelson: Analytic vectors. Ann. of Math
1959
Earlier work this paper cites.
H.J. Borchers and W. Zimmermann: On the self-adjointness of field operators. Nuovo Cimento
1963
Earlier work this paper cites.
L. Pukánzsky: The Plancherel formula for the universal covering group of SL(2, ℝ {\mathbb{R}} ). Math. Annalen
1964
Earlier work this paper cites.
D.B.A. Epstein: The simplicity of certain groups of homeomorphisms. Compositio Math
1970
Earlier work this paper cites.
M. Herman: Simplicité du groupe des difféomorphismes de classe C ∞ C^{\infty} , isotopes à l’identité, du tore de dimension n n . C.R. Acad. Sci. Paris Sér. A-B
1971
Earlier work this paper cites.
A. Connes: Une classification des facteurs de type III. Ann. Scient. Éc. Norm. Sup., 4 e 4^{e} série
1973
Earlier work this paper cites.
J.N. Mather: Simplicity of certain groups of diffeomorphisms. Bull. Amer. Math. Soc
1974
Earlier work this paper cites.
W. Thurston: Foliations and groups of diffeomorphisms. Bull. Amer. Math. Soc
1974
Earlier work this paper cites.
J. Bisognano, E. Wichmann: On the duality condition for a Hermitian scalar field. J. Math. Phys
1975
Earlier work this paper cites.
W. Driessler and J. Fröhlich: The reconstruction of local observables from the Euclidean Green’s functions of relativistic quantum field theory. Ann. Inst. H. Poincaré, Section A
1977
Earlier work this paper cites.
R. Longo: Notes on algebraic invariants for non-commutative dynamical systems. Commun. Math. Phys
1979
Earlier work this paper cites.
M. Reed and B. Simon: Methods of modern mathematical physics I. Functional analysis
1980
Earlier work this paper cites.
K. Fredenhagen and J. Hertel: Local algebras of observables and pointlike localized fields. Commun. Math. Phys
1981
Earlier work this paper cites.
S. Strătilă : Modular theory in operator algebras
1981
Earlier work this paper cites.
R.S. Hamilton: The inverse function theorem of Nash and Moser. Bull. Amer. Math. Soc
1982
Earlier work this paper cites.
V.F.R. Jones: Index of subfactors. Invent. Math
1983
Earlier work this paper cites.
S. Doplicher and R. Longo: Standard and split inclusions of von Neumann algebras. Invent. Math
1984
Earlier work this paper cites.
D.B.A. Epstein: Commutators of C ∞ C^{\infty} -diffeomorphisms. Appendix to “A curious remark concerning the geometric transfer map” by John N. Mather. Comment. Math. Helvetici
1984
Earlier work this paper cites.
D. Friedan, Z. Qiu and S. Shenker: Conformal invariance, unitarity and two dimensional critical exponents. Phys. Rev. Lett
1984
Earlier work this paper cites.
R. Goodman and N.R. Wallach: Structure and unitary cocycle representations of loop groups and the group od diffeomorphisms of the circle. J. Reine Angew. Math
1984
Earlier work this paper cites.
J. Milnor: Remarks on infinite-dimensional Lie groups. In B.S. De Witt and R. Stora Eds.: Relativity, groups and topology II
1984
Earlier work this paper cites.
R. Goodman and N.R. Wallach: Projective unitary positive-energy representations of Diff ( S 1 ) {\rm Diff}({S^{1}}) . J. Funct. Anal
1985
Earlier work this paper cites.
W. Driessler, S.J. Summers and E.H. Wichmann: On the connection between quantum fields and von Neumann algebras of local operators. Commun. Math. Phys
1986
Earlier work this paper cites.
D. Friedan, Z. Qiu and S. Shenker: Details of the non-unitarity proof for highest weight representations of the Virasoro algebra. Commun. Math. Phys
1986
Earlier work this paper cites.
P. Goddard, A. Kent and D. Olive: Unitary representations of the Virasoro and super-Virasoro algebra. Commun. Math. Phys
1986
Earlier work this paper cites.
A. Pressley and G. Segal: Loop groups
1986
Earlier work this paper cites.
O. Bratteli and D.W. Robinson: Operator algebras and quantum statistical mechanics 1
1987
Earlier work this paper cites.
J. Glimm and A. Jaffe: Quantum physics
1987
Earlier work this paper cites.
V.G. Kac and A. K. Raina: Bombay lectures on highest weight representations of infinite dimensional Lie algebras
1987
Earlier work this paper cites.
D. Buchholz, G. Mack and I.T. Todorov: The current algebra on the circle as a germ of local field theories. Nucl. Phys. B (Proc. Suppl.)
1988
Earlier work this paper cites.
R. Dijkgraaf, C. Vafa, E. Verlinde and H. Verlinde: The operator algebra of orbifold models. Commun. Math. Phys
1989
Earlier work this paper cites.
I.B. Frenkel, J. Lepowsky and A. Meurman: Vertex operator algebras and the monster
1989
Earlier work this paper cites.
P. Furlan, G. M. Sotkov and I.T. Todorov: Two-dimensional conformal quantum field theory. Riv. Nuovo Cimento
1989
Earlier work this paper cites.
R. Longo: Index of subfactors and statistics of quantum fields. I. Commun. Math. Phys
1989
Cited alongside, same era.
R.F. Streater and A.S. Wightman: PCT, spin and statistics and all that
1989
Cited alongside, same era.
H.J. Borchers and J. Yngvason: Positivity of Wightman functionals and the existence of local nets. Commun. Math. Phys
1990
Cited alongside, same era.
D. Buchholz: On quantum fields that generate local algebras. J. Math. Phys. 31
1990
Cited alongside, same era.
D. Buchholz and H. Schulz-Mirbach: Haag duality in conformal quantum field theory. Rev. Math. Phys
1990
Cited alongside, same era.
V.G. Kac: Infinite dimensional Lie algebras
1990
Cited alongside, same era.
S. Carpi: Classification of subsystems for the Haag-Kastler nets generated by c = 1 c=1 chiral current algebras. Lett. Math. Phys
1999
Later among the works it cites.
C. Dong and G. Mason: Quantum Galois theory for compact Lie groups. J. Algebra
1999
Later among the works it cites.
A. Hanaki, M. Miyamoto and D. Tambara: Quantum Galois theory for finite groups. Duke Math. J
1999
Later among the works it cites.
A. Matsuo and K. Nagatomo: On axioms for a vertex algebra and the locality of quantum fields
1999
Later among the works it cites.
V. Toledano Laredo: Integrating unitary representations of infinite-dimensional Lie groups, J. Funct. Anal
1999
Later among the works it cites.
F. Xu: Algebraic coset conformal field theory. Commun. Math. Phys
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
W. Rudin: Functional analysis
1991
Cited alongside, same era.
H.J. Borchers and J. Yngvason: From quantum fields to local von Neumann algebras. Rev. Math. Phys
1992
Cited alongside, same era.
R. Brunetti, D. Guido and R. Longo: Modular structure and duality in conformal quantum field theory. Commun. Math. Phys
1993
Cited alongside, same era.
I.B. Frenkel, Y.-Z. Huang and J. Lepowsky: On axiomatic approaches to vertex operator algebras and modules. Mem. Amer. Math. Soc
1993
Cited alongside, same era.
F. Gabbiani and J. Fröhlich: Operator algebras and conformal field theory. Commun. Math. Phys
1993
Cited alongside, same era.
H. Li: Symmetric invariant bilinear forms on vertex operator algebras. J. Pure Appl. Algebra
1994
Cited alongside, same era.
2000
Later among the works it cites.
H.J. Borchers, D. Buchholz and S. J. Summers: Polarization free generators and the S-matrix. Commun. Math. Phys
2001
Later among the works it cites.
C. D’Antoni, R. Longo and F. Radulescu: Conformal nets, maximal temperature and models from free probability. J. Operator Theory
2001
Later among the works it cites.
Y. Kawahigashi, R. Longo and M. Müger: Multi-interval subfactors and modularity of representations in conformal field theory. Commun. Math. Phys
2001
Later among the works it cites.
R. Brunetti, D. Guido and R. Longo: Modular localization and Wigner particles. Rev. Math. Phys
2002
Later among the works it cites.
R. Longo: Conformal subnets and intermediate subfactors. Commun. Math. Phys
2003
Later among the works it cites.
S. Carpi: On the representation theory of Virasoro nets. Commun. Math. Phys
2004
Later among the works it cites.
Y. Kawahigashi and R. Longo: Classification of local conformal nets. Case c < 1 c<1 . Ann of Math
2004
Later among the works it cites.
J. Lepowsky and H. Li: Introduction to vertex operator algebras and their representations
2004
Later among the works it cites.
M. Miyamoto: A new construction of the moonshine vertex operator algebra over the real number field. Ann. of Math
2004
Later among the works it cites.
M. Roitman: Invariant bilinear forms on a vertex algebra. J. Pure Appl. Algebra
2004
Later among the works it cites.
H. Bostelmann: Phase space properties and the short distance structure in quantum field theory. J. Math. Phys
2005
Later among the works it cites.
S. Carpi: Intersecting Jones projections. Int. J. Math
2005
Later among the works it cites.
S. Carpi and M. Weiner: On the uniqueness of diffeomorphism symmetry in conformal field theory. Commun. Math. Phys
2005
Later among the works it cites.
V.G. Kac, R. Longo and F. Xu: Solitons in affine and permutation orbifold. Commun. Math. Phys
2005
Later among the works it cites.
R. Longo and F. Xu: Topological sectors and a dichotomy in conformal field theory. Commun. Math. Phys
2005
Later among the works it cites.
A. Matsuo: 3-transposition groups of symplectic type and vertex operator algebras. J. Math. Soc. Japan
2005
Later among the works it cites.
M. Weiner: Conformal covariance and related properties of chiral QFT
2005
Later among the works it cites.
F. Xu: Strong additivity and conformal nets. Pacific J. Math
2005
Later among the works it cites.
B. Blackadar: Operator algebras
2006
Later among the works it cites.
C. Dong and F. Xu: Conformal nets associated with lattices and their orbifolds. Adv. Math
2006
Later among the works it cites.
Y. Kawahigashi and R. Longo: Local conformal nets arising from framed vertex operator algebras. Adv. Math
2006
Later among the works it cites.
S. Carpi, Y. Kawahigashi and R. Longo: Structure and classification of superconformal nets. Ann. H. Poincaré
2008
Later among the works it cites.
R. Longo: Real Hilbert subspaces, modular theory, SL(2, R) and CFT. In: Von Neumann algebras in Sibiu
2008
Later among the works it cites.
G. Höhn: The group of symmetries of the shorter Moonshine module. Abh. Math. Semin. Univ. Hambg
2010
Later among the works it cites.
M. Weiner: An algebraic version of Haag’s theorem. Commun. Math. Phys
2011
Later among the works it cites.
F. Xu: On examples of intermediate subfactors from conformal field theory. Commun. Math. Phys
2013
Later among the works it cites.
C. Dong and X. Lin: Unitary vertex operator algebras. J. Algebra
2014
Later among the works it cites.