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Action Duality: A Constructive Principle for Quantum Foundations

Ken B. Wharton, David J. Miller, Huw Price
2011 Symmetry  
a corresponding model for its action-dual.  ...  If correct, this hypothesis would not only constrain realistic interpretations of quantum theory, but would also act as a constructive principle, allowing any realistic model of one experiment to generate  ...  KW gratefully acknowledges that much of this joint research was conducted during his tenure of a Visiting Fellowship at the Sydney Centre for the Foundations of Science, of the University of Sydney.  ... 
doi:10.3390/sym3030524 fatcat:foc2yxzucvhpla3eeavt5qvqbu

Equivariant Poincaré duality for quantum group actions [article]

Ryszard Nest, Christian Voigt
2009 arXiv   pre-print
We extend the notion of Poincar\'e duality in KK-theory to the setting of quantum group actions.  ...  Along the way we discuss general properties of equivariant KK-theory for locally compact quantum groups, including the construction of exterior products.  ...  An important guiding principle in all these constructions is equivariance with respect to the action of a quantum group.  ... 
arXiv:0902.3987v2 fatcat:ja663qfsffcbfmvkmvvaqelo5a

Equivariant Poincaré duality for quantum group actions

Ryszard Nest, Christian Voigt
2010 Journal of Functional Analysis  
We extend the notion of Poincaré duality in KK-theory to the setting of quantum group actions.  ...  Along the way we discuss general properties of equivariant KK-theory for locally compact quantum groups, including the construction of exterior products.  ...  An important guiding principle in all these constructions is equivariance with respect to the action of a quantum group.  ... 
doi:10.1016/j.jfa.2009.10.015 fatcat:wr2ixam5nfaihe6exc4e5gx5gu

Complexity-action duality of the shock wave geometry in a massive gravity theory

Yan-Gang Miao, Long Zhao
2018 Physical Review D  
On the holographic complexity dual to the bulk action, we investigate the action growth for a shock wave geometry in a massive gravity theory within the Wheeler-De Witt (WDW) patch at the late time limit  ...  For a global shock wave, the graviton mass does not affect the action growth in the bulk, i.e. the complexity on the boundary, showing that the action growth (complexity) is the same for both the Einstein  ...  Nicolini of Frankfurt Institute for Advanced Studies (FIAS) for kind hospitality. This work was supported in part by the National Natural Science Foundation of China under grant No.11675081.  ... 
doi:10.1103/physrevd.97.024035 fatcat:42awbtffkrd6jgq33ludsx744m

Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems [article]

Maxime Fairon
2021 arXiv   pre-print
We derive from our results a representation theoretic description of action-angle duality for several classical integrable systems.  ...  Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of algebras endowed with a (quasi-)Poisson bracket.  ...  The main tool needed to provide a precise construction of the action-angle duality maps is a study of morphisms of double (quasi-)Poisson algebras, which forms the core of this text.  ... 
arXiv:2008.01409v2 fatcat:x6uwl736avaxhnjrowb452jddu

QED Effective Actions in Space-Dependent Gauge and Electromagnetic Duality [article]

Sang Pyo Kim (Kunsan Nat'l Univ., Nat'l Taiwan Univ. and YITP, Kyoto Univ.)
2011 arXiv   pre-print
We develop the in-out formalism for one-loop effective actions in electromagnetic fields in the space-dependent gauge.  ...  We further advance a method using the inverse scattering matrix to calculate the effective actions in pure magnetic fields, find the effective actions in a constant magnetic field and a localized Sauter-type  ...  Page for early collaboration on Schwinger pair production in the spacedependent gauge, Hyun Kyu Lee and Yongsung Yoon for collaboration on QED effective action, W-Y.  ... 
arXiv:1105.4382v2 fatcat:uy2ykmwovrfmhbbwf2b6wfdc44

Commutative/Non-Commutative Dualities [article]

FG Scholtz, PH Williams, JN Kriel
2017 arXiv   pre-print
We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way.  ...  In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly  ...  Acknowledgements: This work was supported under a grant of the National Research Foundation of South Africa.  ... 
arXiv:1711.09236v1 fatcat:wbqqomrz3vff7llv7mz6f3kiyi

Commutative/Non-Commutative Dualities

F.G. Scholtz, P.H. Williams, J.N. Kriel
2019 Canadian journal of physics (Print)  
Acknowledgements: This work was supported under a grant of the National Research Foundation of South Africa.  ...  We show that it is in principle possible to construct dualities between commutative and noncommutative theories in a systematic way.  ...  In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly  ... 
doi:10.1139/cjp-2018-0887 fatcat:ewdf3zorpnfd7ab7udnem3jkqy

Dualities and emergent gravity: Gauge/gravity duality

Sebastian de Haro
2017 Studies in history and philosophy of modern physics  
Nevertheless, it is an interesting and potentially fruitful heuristic principle for quantum gravity theory construction.  ...  These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; and I argue that this exhausts the possibilities for combining dualities and  ...  I also thank Elena Castellani and Dean Rickles for organising a wonderful workshop and all of the participants for the helpful discussions.  ... 
doi:10.1016/j.shpsb.2015.08.004 fatcat:un5blp5uabh7dfcgqq5n6dirkq

Exact QED Path Integration of the Maxwell Action, with Gravitational Curvature and Boundary Terms, Using Pontryagin Duality [article]

Jay R. Yablon
2009 arXiv   pre-print
manifolds with sufficient symmetry to admit the application of Pontryagin duality as a form of harmonic analysis.  ...  We demonstrate how to explicitly calculate the QED path integral and associated Green functions, exactly, in curved spacetime, with retention of the boundary terms, to infinite order, for any and all spacetime  ...  As such, this may provide a necessary foundation for eventually resolving the Yang-Mills "mass gap.  ... 
arXiv:0911.1081v1 fatcat:agnfqnrqdnbxtc64uj3urmq4hy

Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems

Maxime Fairon
2022 Annales Henri Lebesgue  
We derive from our results a representation theoretic description of action-angle duality for several classical integrable systems.  ...  Double (quasi-)Poisson algebras were introduced by Van den Bergh as noncommutative analogues of algebras endowed with a (quasi-)Poisson bracket.  ...  Rubtsov for raising the question that motivated this work, and L. Fehér for useful comments.  ... 
doi:10.5802/ahl.121 fatcat:kogcnu5rwvfanaejdhcxbuwsjm

The Dynamics of Wave-Particle Duality

Adriano Orefice, Raffaele Giovanelli, Domenico Ditto
2018 Journal of Applied Mathematics and Physics  
Our approach reaches the double goal of a clear insight into the mechanism of wave-particle duality and of a reasonably simple computability.  ...  We faced then, as a typical example, the numerical solution of non-relativistic wave-mechanical equation systems in a number of numerical applications, showing that each particle turns out to "dances a  ...  Journal of Applied Mathematics and Physics representation, and reach (together with a reasonably simple computability) a clear insight into the mechanism of wave-particle duality.  ... 
doi:10.4236/jamp.2018.69157 fatcat:m6d7rv7d5rgo5jpnd4e2bnv7lm

Duality, quotients, and currents

Martin Roček, Erik Verlinde
1992 Nuclear Physics B  
This observation is used to clarify the interpretation of the generalized duality as a symmetry of conformal field theory. We extend these results to N=2 supersymmetric sigma models.  ...  We study the generalization of R→ 1/R duality to arbitrary conformally invariant sigma models with an isometry.  ...  Ginsparg, A. Giveon, E. Witten for discussions and M. Best for help with T E X. EV wishes to thank the Aspen Center  ... 
doi:10.1016/0550-3213(92)90269-h fatcat:7dcvo4wtcrfupnjkc4m6abesbe

Duality and Decoherence Free Subspaces [article]

David D. Song, Richard J. Szabo
2000 arXiv   pre-print
The notion of a generalized Dirac operator is introduced and used to naturally construct families of decoherence free subspaces for the encoding of quantum information.  ...  Quantum error avoiding codes are constructed by exploiting a geometric interpretation of the algebra of measurements of an open quantum system.  ...  Zanardi for very helpful comments on the manuscript. D.D.S. is grateful to P. Hayden for discussions.  ... 
arXiv:quant-ph/0011021v2 fatcat:tz4wh7ik5bejxohv2vcmcnkhau

Particle-unparticle duality in super-relativity [article]

Peter Leifer
2009 arXiv   pre-print
Initially, neither contradictable notion of quantum particle, nor space-time coordinates (that cannot be a priori attached to nothing) are used in this construction.  ...  Morphogenesis of the "field shell" of GCS and its dynamics have been studied for N=2 in DST.  ...  One may image some "elementary quantum states" (EAS) |ha > as a quantum motions with entire number a of the action quanta.  ... 
arXiv:0901.2694v1 fatcat:hqdwfr6sefccfdavtr2dr5arq4
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