Special Issue "Quantum Symmetry"

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A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 January 2011)

Special Issue Editor

Guest Editor
Dr. Dean Rickles
Unit for History and Philosophy of Science, Faculty of Science, Sydney, NSW 2006, Australia
Website: http://www.usyd.edu.au/hps/staff/academic/Dean_Rickles.shtml
E-Mail: dean.rickles@sydney.edu.au
Phone: +61 2 9351 8552
Interests: philosophy of symmetry; quantum gravity; foundations of physics; spacetime physics; econophysics

Special Issue Information

Dear Colleagues,

There are several differences between classical and quantum theories that have an impact on the possible symmetries:
  • Physical states represented in Hilbert space rather than phase space.
  • Quantum mechanics defines symmetries as mappings between physical states that preserve transition amplitudes. (As Wigner proved, these symmetries can be represented in Hilbert space by unitary and anti-unitary operators.)
  • Quantum mechanics assigns complex numbers to these transition amplitudes.
  • The algebra of observables in quantum mechanics is non-commutative.
  • Quantum particles are indistinguishable.
  • Composite quantum systems are not represented by a Cartesian product structure, but by a linear tensor structure.
Quantum symmetries may also include gauge redundancies and dualities. Gauge redundancies can be understood as multiple representations of the same physical state. Dualities can be understood as isomorphisms holding between pairs of Hilbert spaces together with (canonical) operators. The possibilities for quantum symmetries are tightly constrained by the number of spacetime dimensions and by the dimensionality of the objects of the theory (including whether they are extensionless or structured). Quantum symmetries also refer to quantum groups, which aren't groups as such but algebras that reduce to groups in the limit as a deformation parameter (playing the part of Planck's constant) goes to 1 (returning multiplication to normal).

Contributions are invited on all aspects of quantum symmetries. Those that involve foundational issues or the intersection of theoretical physics and pure mathematics are especially welcomed. Possible themes (not ranked in order preference) include:

  • 2D Conformal Field Theory, Modular Invariance, Statistical Mechanics.
  • Dualities in Quantum Theories.
  • Mirror Symmetry in String Theory.
  • Emergent Quantum Symmetries, Symmetry Breaking, Effective Field Theory, Renormalization Group.
  • Hopf Algebras, Quantum Groups and Low Dimensional Physics.
  • Quantum Geometry (including Non-Commutative Geometry).
  • Spin-Statistics, Anyons, Fractional Quantum Hall Effect.
  • Connections between Quantum Symmetries and Spacetime/Object Dimensionality.
  • Quantum Symmetries in Computation.
  • Relationship between Classical and Quantum Symmetries.

Dr. Dean Rickles
Guest Editor

Keywords

  • quantum symmetry
  • S-duality
  • symmetry breaking
  • anyons
  • braid group
  • quantum groups
  • conformal field theory
  • modular invariance

Published Papers (7 papers)

Symmetry 2011, 3(3), 524-540; doi:10.3390/sym3030524
Received: 6 July 2011; Accepted: 17 July 2011 / Published: 27 July 2011
Show/Hide Abstract | Cited by 2 | PDF Full-text (322 KB)

Symmetry 2011, 3(3), 389-401; doi:10.3390/sym3030389
Received: 11 June 2011; Accepted: 21 June 2011 / Published: 29 June 2011
Show/Hide Abstract | PDF Full-text (266 KB)

Symmetry 2011, 3(2), 171-206; doi:10.3390/sym3020171
Received: 9 March 2011; in revised form: 6 April 2011 / Accepted: 12 April 2011 / Published: 27 April 2011
Show/Hide Abstract | Cited by 6 | PDF Full-text (658 KB)
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Symmetry 2011, 3(2), 134-154; doi:10.3390/sym3020134
Received: 21 February 2011; in revised form: 21 March 2011 / Accepted: 28 March 2011 / Published: 31 March 2011
Show/Hide Abstract | Cited by 3 | PDF Full-text (391 KB)

Symmetry 2011, 3(1), 16-36; doi:10.3390/sym3010016
Received: 6 January 2011; in revised form: 7 February 2011 / Accepted: 11 February 2011 / Published: 14 February 2011
Show/Hide Abstract | PDF Full-text (251 KB)
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Symmetry 2010, 2(4), 1945-1980; doi:10.3390/sym2041945
Received: 20 September 2010; in revised form: 26 October 2010 / Accepted: 11 November 2010 / Published: 19 November 2010
Show/Hide Abstract | Cited by 1 | PDF Full-text (418 KB)

Symmetry 2010, 2(4), 1810-1845; doi:10.3390/sym2041810
Received: 18 August 2010; in revised form: 14 September 2010 / Accepted: 8 October 2010 / Published: 1 November 2010
Show/Hide Abstract | Cited by 1 | PDF Full-text (286 KB)

Last update: 5 March 2014

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