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Pedro Lauridsen Ribeiro
Pedro Lauridsen Ribeiro
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Braided monoidal categories - more precisely, C-categories (i.e. categories enriched over the category of CC*-algebras)categories of such kind - are the basic mathematical tool to encode the structure of superselection sectors in low-dimensional (<4) QFT. The low dimensionality forces the braiding coming from permutation statistics to be non-trivial. There is a large literature on the subject, but two fundamental papers are the following:

  • K. Fredenhagen, K.-H. Rehren, B. Schroer, Superselection Sectors with Braid Group Statistics and Exchange Algebras. I. General Theory. Commun.Math.Phys. 125 (1989) 201-226;
  • K. Fredenhagen, K.-H. Rehren, B. Schroer, Superselection Sectors with Braid Group Statistics and Exchange Algebras. II. Geometric Aspects and Conformal Invariance. Rev.Math.Phys. Special Issue in honor of Rudolf Haag (1992) 113-157.

There is a recent, short review by Y. Kawahigashi on the subject, centered around chiral conformal QFT's on the circle (Conformal Field Theory, Tensor Categories and Operator Algebras, J.Phys. A Math. Theor. 48 (2015) 303001, arXiv:1503.05675 [math-ph], specially Section 3), which can be classified to a large extent using such methods.

Braided monoidal categories - more precisely, C-categories (i.e. categories enriched over the category of C-algebras) of such kind - are the basic mathematical tool to encode the structure of superselection sectors in low-dimensional (<4) QFT. The low dimensionality forces the braiding coming from permutation statistics to be non-trivial. There is a large literature on the subject, but two fundamental papers are the following:

  • K. Fredenhagen, K.-H. Rehren, B. Schroer, Superselection Sectors with Braid Group Statistics and Exchange Algebras. I. General Theory. Commun.Math.Phys. 125 (1989) 201-226;
  • K. Fredenhagen, K.-H. Rehren, B. Schroer, Superselection Sectors with Braid Group Statistics and Exchange Algebras. II. Geometric Aspects and Conformal Invariance. Rev.Math.Phys. Special Issue in honor of Rudolf Haag (1992) 113-157.

There is a recent, short review by Y. Kawahigashi on the subject, centered around chiral conformal QFT's on the circle (Conformal Field Theory, Tensor Categories and Operator Algebras, J.Phys. A Math. Theor. 48 (2015) 303001, arXiv:1503.05675 [math-ph], specially Section 3), which can be classified to a large extent using such methods.

Braided monoidal categories - more precisely, C*-categories of such kind - are the basic mathematical tool to encode the structure of superselection sectors in low-dimensional (<4) QFT. The low dimensionality forces the braiding coming from permutation statistics to be non-trivial. There is a large literature on the subject, but two fundamental papers are the following:

  • K. Fredenhagen, K.-H. Rehren, B. Schroer, Superselection Sectors with Braid Group Statistics and Exchange Algebras. I. General Theory. Commun.Math.Phys. 125 (1989) 201-226;
  • K. Fredenhagen, K.-H. Rehren, B. Schroer, Superselection Sectors with Braid Group Statistics and Exchange Algebras. II. Geometric Aspects and Conformal Invariance. Rev.Math.Phys. Special Issue in honor of Rudolf Haag (1992) 113-157.

There is a recent, short review by Y. Kawahigashi on the subject, centered around chiral conformal QFT's on the circle (Conformal Field Theory, Tensor Categories and Operator Algebras, J.Phys. A Math. Theor. 48 (2015) 303001, arXiv:1503.05675 [math-ph], specially Section 3), which can be classified to a large extent using such methods.

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Pedro Lauridsen Ribeiro
Pedro Lauridsen Ribeiro
  • 7.8k
  • 1
  • 35
  • 67

Braided monoidal categories - more precisely, C-categories (i.e. categories enriched over the category of C-algebras) of such kind - are the basic mathematical tool to encode the structure of superselection sectors in low-dimensional (<4) QFT. The low dimensionality forces the braiding coming from permutation statistics to be non-trivial. There is a large literature on the subject, but two fundamental papers are the following:

  • K. Fredenhagen, K.-H. Rehren, B. Schroer, Superselection Sectors with Braid Group Statistics and Exchange Algebras. I. General Theory. Commun.Math.Phys. 125 (1989) 201-226;
  • K. Fredenhagen, K.-H. Rehren, B. Schroer, Superselection Sectors with Braid Group Statistics and Exchange Algebras. II. Geometric Aspects and Conformal Invariance. Rev.Math.Phys. Special Issue in honor of Rudolf Haag (1992) 113-157.

There is a recent, short review by Y. Kawahigashi on the subject, centered around chiral conformal QFT's on the circle (Conformal Field Theory, Tensor Categories and Operator Algebras, J.Phys. A Math. Theor. 48 (2015) 303001, arXiv:1503.05675 [math-ph], specially Section 3), which can be classified to a large extent using such methods.