Annales Henri Poincaré, ISSN 1424-0637, 11/2016, Volume 17, Issue 11, pp. 3237 - 3254

The Jacobian Conjecture states that any locally invertible polynomial system in $${{\mathbb{C}}^n}$$ C n is globally invertible with polynomial inverse. Bass...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | RENORMALIZATION | PHYSICS, PARTICLES & FIELDS | Resveratrol

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | RENORMALIZATION | PHYSICS, PARTICLES & FIELDS | Resveratrol

Journal Article

Annals of Physics, ISSN 0003-4916, 03/2014, Volume 342, pp. 83 - 102

We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. The algebra would be large enough to capture...

Quantum resurgence | Quantisation deformation | Complex WKB method | Complex analysis | Complex topology | Zinn-Justin conjectures | PHYSICS, MULTIDISCIPLINARY | Zinn-justin conjectures | Algebra | Quantum physics | Deformation | Construction | Mathematical analysis | HYPERGEOMETRIC FUNCTIONS | QUANTUM COMPUTERS | QUANTIZATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DEFORMATION | ALGEBRA

Quantum resurgence | Quantisation deformation | Complex WKB method | Complex analysis | Complex topology | Zinn-Justin conjectures | PHYSICS, MULTIDISCIPLINARY | Zinn-justin conjectures | Algebra | Quantum physics | Deformation | Construction | Mathematical analysis | HYPERGEOMETRIC FUNCTIONS | QUANTUM COMPUTERS | QUANTIZATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DEFORMATION | ALGEBRA

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 12/2013, Volume 14, Issue 8, pp. 2025 - 2043

The noncommutative scalar theory with harmonic term (on the Moyal space) has a vanishing beta function. In this paper, we prove the renormalizability of the...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | NONCOMMUTATIVE FIELD-THEORY | INDUCED GAUGE-THEORY | SPACE | BETA-FUNCTION | PHYSICS, MULTIDISCIPLINARY | DUALITY | MODEL | PHYSICS, MATHEMATICAL | OSCILLATOR | PHI-THEORY | PHYSICS, PARTICLES & FIELDS

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | NONCOMMUTATIVE FIELD-THEORY | INDUCED GAUGE-THEORY | SPACE | BETA-FUNCTION | PHYSICS, MULTIDISCIPLINARY | DUALITY | MODEL | PHYSICS, MATHEMATICAL | OSCILLATOR | PHI-THEORY | PHYSICS, PARTICLES & FIELDS

Journal Article

The European Physical Journal C, ISSN 1434-6044, 8/2007, Volume 51, Issue 4, pp. 977 - 987

We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4-dimensional Moyal space and compute in position space the...

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | ALGEBRAS | MODELS | FIELD-THEORY | QUANTUM-MECHANICS | RENORMALIZATION | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Gauge theory | Harmonic oscillators

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | ALGEBRAS | MODELS | FIELD-THEORY | QUANTUM-MECHANICS | RENORMALIZATION | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Gauge theory | Harmonic oscillators

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2015, Volume 173, Issue 1, pp. 169 - 195

We introduce Frechet quantum supergroups and their representations. By using the universal deformation formula of the abelian supergroups R-m vertical bar n we...

Quantum group | Noncommutative supergeometry | Hopf algebra | Deformation quantization | Fréchet spaces | Multiplicative unitary | Frechet spaces | MATHEMATICS | quantum group | MULTIPLICATIVE UNITARIES | ALGEBRAS | deformation quantization | MANIFOLDS | noncommutative supergeometry | multiplicative unitary

Quantum group | Noncommutative supergeometry | Hopf algebra | Deformation quantization | Fréchet spaces | Multiplicative unitary | Frechet spaces | MATHEMATICS | quantum group | MULTIPLICATIVE UNITARIES | ALGEBRAS | deformation quantization | MANIFOLDS | noncommutative supergeometry | multiplicative unitary

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 02/2011, Volume 44, Issue 5, pp. 055401 - 12

We investigate symmetries of the scalar field theory with a harmonic term on the Moyal space with the Euclidean scalar product and general symplectic form. The...

DUALITY | ALGEBRAS | BETA-FUNCTION | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | RENORMALIZATION | Harmonics | Mathematical analysis | Scalars | Field theory | Orbits | Invariance | Invariants | Symmetry | Mathematics | Mathematical Physics | High Energy Physics - Theory | Physics

DUALITY | ALGEBRAS | BETA-FUNCTION | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | RENORMALIZATION | Harmonics | Mathematical analysis | Scalars | Field theory | Orbits | Invariance | Invariants | Symmetry | Mathematics | Mathematical Physics | High Energy Physics - Theory | Physics

Journal Article

Journal of Physics: Conference Series, ISSN 1742-6588, 04/2015, Volume 597, Issue 1

This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In...

Conference Proceeding

Journal of Functional Analysis, ISSN 0022-1236, 08/2012, Volume 263, Issue 3, pp. 549 - 603

We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of Rd....

Graded operator algebras | Deformation quantization | Heisenberg supergroup | Fréchet functional spaces | Harmonic analysis | Supermanifolds | Renormalization | INDUCED GAUGE-THEORY | MATHEMATICS | SPACES | Frechet functional spaces | MANIFOLDS | Analysis | Algebra | Operator Algebras | Quantum Algebra | Mathematics | Differential Geometry | Mathematical Physics

Graded operator algebras | Deformation quantization | Heisenberg supergroup | Fréchet functional spaces | Harmonic analysis | Supermanifolds | Renormalization | INDUCED GAUGE-THEORY | MATHEMATICS | SPACES | Frechet functional spaces | MANIFOLDS | Analysis | Algebra | Operator Algebras | Quantum Algebra | Mathematics | Differential Geometry | Mathematical Physics

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2010, Volume 6, p. 048

The harmonic term in the scalar field theory on the Moyal space removes the UV-IR mixing, so that the theory is renormalizable to all orders. In this paper, we...

Noncommutative QFT | Renormalization | Gauge theory | Heisenberg algebra | GAUGE-THEORY | ALGEBRAS | BETA-FUNCTION | renormalization | gauge theory | DUALITY | PARAMETRIC REPRESENTATION | PHYSICS, MATHEMATICAL | noncommutative QFT | Mathematics | Mathematical Physics | High Energy Physics - Theory | Physics

Noncommutative QFT | Renormalization | Gauge theory | Heisenberg algebra | GAUGE-THEORY | ALGEBRAS | BETA-FUNCTION | renormalization | gauge theory | DUALITY | PARAMETRIC REPRESENTATION | PHYSICS, MATHEMATICAL | noncommutative QFT | Mathematics | Mathematical Physics | High Energy Physics - Theory | Physics

Journal Article

Advances in Mathematics, ISSN 0001-8708, 03/2016, Volume 291, pp. 362 - 402

In this paper, we exhibit the non-formal star-exponential of the Lie group SL(2,R) realized geometrically on the curvature contraction of its one-sheeted...

Unitary representation | Orthogonality relation | Star-exponential | Deformation quantization | Bessel functions | Principal series | MATHEMATICS | ALGEBRA | Algebra

Unitary representation | Orthogonality relation | Star-exponential | Deformation quantization | Bessel functions | Principal series | MATHEMATICS | ALGEBRA | Algebra

Journal Article

The European Physical Journal C, ISSN 1434-6044, 2/2008, Volume 53, Issue 3, pp. 459 - 466

In this paper we find non-trivial vacuum states for the renormalizable non-commutative φ4 model. An associated linear sigma model is then considered. We...

Measurement Science, Instrumentation | Nuclear Physics, Heavy Ions, Hadrons | Physics | Physics beyond the Standard Model | Astronomy, Astrophysics and Cosmology | Elementary Particles, Quantum Field Theory | ALGEBRAS | BETA-FUNCTION | FIELD-THEORY | GOLDSTONE THEOREM | REPRESENTATION | R-4 | DUALITY | QUANTUM-MECHANICS | PHYSICS, PARTICLES & FIELDS | Broken symmetry

Measurement Science, Instrumentation | Nuclear Physics, Heavy Ions, Hadrons | Physics | Physics beyond the Standard Model | Astronomy, Astrophysics and Cosmology | Elementary Particles, Quantum Field Theory | ALGEBRAS | BETA-FUNCTION | FIELD-THEORY | GOLDSTONE THEOREM | REPRESENTATION | R-4 | DUALITY | QUANTUM-MECHANICS | PHYSICS, PARTICLES & FIELDS | Broken symmetry

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2012, Volume 6, Issue 2, pp. 343 - 387

We introduce the new notion of epsilon-graded associative algebras which takes its roots from the notion of commutation factors introduced in the context of...

ε-graded associative algebra | Derivation-based differential calculus | ε-derivations and connections | MATHEMATICS, APPLIED | FIELD-THEORY | CALCULUS | DIFFERENTIAL GEOMETRY | PHYSICS, MATHEMATICAL | DERIVATIONS | INDUCED GAUGE-THEORY | LIE-ALGEBRAS | MATHEMATICS | epsilon-derivations | epsilon-graded associative algebra | SPACE QUANTUM-MECHANICS | MATRIX ALGEBRAS | connections

ε-graded associative algebra | Derivation-based differential calculus | ε-derivations and connections | MATHEMATICS, APPLIED | FIELD-THEORY | CALCULUS | DIFFERENTIAL GEOMETRY | PHYSICS, MATHEMATICAL | DERIVATIONS | INDUCED GAUGE-THEORY | LIE-ALGEBRAS | MATHEMATICS | epsilon-derivations | epsilon-graded associative algebra | SPACE QUANTUM-MECHANICS | MATRIX ALGEBRAS | connections

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 08/2018

Journal Article

Journal of Physics: Conference Series, ISSN 1742-6596, 02/2008, Volume 103, Issue 1, p. 012010

J.Phys.Conf.Ser.103:012010,2008 We compute here the Yang-Mills effective action on Moyal space by integrating over the scalar fields in a noncommutative scalar...

Journal Article

10/2014

In this paper, we introduce the notion of multiplier of a Hilbert algebra. The space of bounded multipliers is a semifinite von Neumann algebra isomorphic to...

Journal Article

2013, ISBN 3034806442, Volume 61, 10

Reference

05/2011

Pacific Journal of Mathematics 273 (2015) 169-195 In this paper, we introduce Fr\'echet quantum supergroups and their representations. By using the universal...

Journal Article

01/2016

Numerous Lie supergroups do not admit superunitary representations except the trivial one, e.g., Heisenberg and orthosymplectic supergroups in mixed signature....

Journal Article

08/2011

Theta Ser. Adv. Math. 15 (2012) 61-73 We review recent works concerning deformation quantization of abelian supergroups. Indeed, we expose the construction of...

Journal Article

11/2013

Dev. Math. 37 (2014) 41-76, Springer We define and study a noncommutative Fourier transform on every homogeneous complex bounded domain. We then give an...

Journal Article

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