Special Issue "Quantum Symmetry"

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

Deadline for manuscript submissions: 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:
Interests: philosophy of symmetry; quantum gravity; foundations of physics; spacetime physics; econophysics

Published Papers

Click here to see a list of 2 papers that have been published in this special issue.

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

Submission

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed Open Access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. For the first couple of issues the Article Processing Charge (APC) will be waived for well-prepared manuscripts. English correction and/or formatting fees of 250 CHF (Swiss Francs) will be charged in certain cases for those articles accepted for publication that require extensive additional formatting and/or English corrections.

Keywords

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

Planned Papers

Type of Paper: Review
Title: Lorentz and Squeeze Harmonics and Their Physical Applications
Authors: Y. S. Kim ¹ and Marilyn E. Noz ²
Affiliation: ¹ Center for Fundamental Physics, University of Maryland,College Park, Maryland 20742, USA; E-Mail: yskim@physics.umd.edu
² Department of Radiology, New York University,New York, New York 10016, USA; E-Mail: marilyne.noz@gmail.com
Abstract: Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac's light-cone coordinate system, Lorentz boosts are squeeze transformations. Thus the squeeze transformation is one of the fundamental transformations in Einstein's Lorentz-covariant world. It is possible to define a complete set of orthonormal functions defined for one Lorentz frame. It is shown that the same set can be used for other Lorentz frames. Transformation properties are discussed. Physical applications are discussed in both optics and high-energy physics. It is shown that the Lorentz harmonics provide the mathematical basis for squeezed states of light. It is shown also that the same set of harmonics can be used for understanding Lorentz-boosted hadrons in high-energy physics.

Last update: 8 October 2010

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