Extension of the Poincaré Symmetry and Its Field Theoretical Implementation

Tanasă, Adrian

doi:10.3842/sigma.2006.056

Cited by 2 publications

(4 citation statements)

References 36 publications

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“…2. Note that a bosonic model with only the tr(X µ X ν X µ X ν ) term is not stable, 8 This new scaling was inspired in a crucial way by the work of Carrozza et al on the O(N ) 3 random tensor model [21]; see also [20]. 9 For example, if the interaction terms are all of the form tr(X µ X † µ ) s , then ≥ 4g as a consequence of Prop.…”

Section: The New Scalingmentioning

confidence: 99%

“…It is gratifying that the technology developed there can find an entirely different application, in providing interesting toy models for black holes. The original so-called "colored" tensor model of Gurau used by Witten admits more general uncolored versions [19] which can be further generalized along the lines of Tanasa et al [20] and Carrozza and Tanasa [21]. Witten's proposal was then extended using these works by Klebanov and Tarponolsky in [22].…”

Section: Introductionmentioning

confidence: 99%

“…This is unlike the case of tensor models with U(N ) 2 ×O(N ), which also appear naturally[20,22]. In the tensor context, the full symmetry group is gauged[27] 5.…”

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confidence: 99%

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The large $D$ limit of planar diagrams

Ferrari

2019

Ann. Inst. Henri Poincaré Comb. Phys. Interact.

103

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We show that in O(D) invariant matrix theories containing a large number D of complex or Hermitian matrices, one can define a D → ∞ limit for which the sum over planar diagrams truncates to a tractable, yet non-trivial, sum over melon diagrams. In particular, results obtained recently in SYK and tensor models can be generalized to traditional, string-inspired matrix quantum mechanical models of black holes.

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Section: The New Scalingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The large $D$ limit of planar diagrams

Ferrari

2019

Ann. Inst. Henri Poincaré Comb. Phys. Interact.

103

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“…From another direction, the Poincaré symmetry mechanism of special relativity can be extended to new algebraic systems [206]. In [167] in view of such extensions, are considered invariantfree Lagrangians and bosonic multiplets constituting a symmetry that interplays with (Abelian) U(1)-gauge symmetry that may possibly be described in categorical terms, in particular, within the notion of a cubical site [104].…”

Section: Graded 'Lie' Algebras and Superalgebrasmentioning

confidence: 99%

Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review

Bâianu¹

2009

SIGMA

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Abstract. A novel algebraic topology approach to supersymmetry (SUSY) and symmetry breaking in quantum field and quantum gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear fusion and other nuclear reaction studies in quantum chromodynamics, nonlinear physics at high energy densities, dynamic Jahn-Teller effects, superfluidity, high temperature superconductors, multiple scattering by molecular systems, molecular or atomic paracrystal structures, nanomaterials, ferromagnetism in glassy materials, spin glasses, quantum phase transitions and supergravity. This approach requires a unified conceptual framework that utilizes extended symmetries and quantum groupoid, algebroid and functorial representations of nonAbelian higher dimensional structures pertinent to quantized spacetime topology and state space geometry of quantum operator algebras. Fourier transforms, generalized FourierStieltjes transforms, and duality relations link, respectively, the quantum groups and quantum groupoids with their dual algebraic structures; quantum double constructions are also discussed in this context in relation to quasi-triangular, quasi-Hopf algebras, bialgebroids, Grassmann-Hopf algebras and higher dimensional algebra. On the one hand, this quantum algebraic approach is known to provide solutions to the quantum Yang-Baxter equation. On the other hand, our novel approach to extended quantum symmetries and their associated representations is shown to be relevant to locally covariant general relativity theories that are consistent with either nonlocal quantum field theories or local bosonic (spin) models with the extended quantum symmetry of entangled, 'string-net condensed' (ground) states. I.C. Baianu, J.F. Glazebrook and R. BrownKey words: extended quantum symmetries; groupoids and algebroids; quantum algebraic topology (QAT); algebraic topology of quantum systems; symmetry breaking, paracrystals, superfluids, spin networks and spin glasses; convolution algebras and quantum algebroids; nuclear Fréchet spaces and GNS representations of quantum state spaces (QSS); groupoid and functor representations in relation to extended quantum symmetries in QAT; quantization procedures; quantum algebras: von Neumann algebra factors; paragroups and Kac algebras; quantum groups and ring structures; Lie algebras; Lie algebroids; GrassmannHopf, weak C * -Hopf and graded Lie algebras; weak C * -Hopf algebroids; compact quantum groupoids; quantum groupoid C * -algebras; relativistic quantum gravity (RQG); supergravity and supersymmetry theories; fluctuating quantum spacetimes; intense gravitational fields; Hamiltonian algebroids in quantum gravity; Poisson-Lie manifolds and quantum gravity theories; quantum fundamental groupoids; tensor products of algebroids and categories; quantum double groupoids and algebroids; higher dimensional quantum symmetries; applications of generalized van Kampen theorem (GvKT) to quantum spacetime invariants

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Extension of the Poincaré Symmetry and Its Field Theoretical Implementation

Cited by 2 publications

References 36 publications

The large $D$ limit of planar diagrams

The large $D$ limit of planar diagrams

Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review

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