The Experts below are selected from a list of 12315 Experts worldwide ranked by ideXlab platform
Shahn Majid - One of the best experts on this subject based on the ideXlab platform.
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bicrossproduct structure of κ poincare Group and non commutative geometry
Physics Letters B, 1994Co-Authors: Shahn Majid, Henri RueggAbstract:Abstract We show that the κ-deformed Poincare quantum algebra proposed for particle physics has the structure of a Hopf algebra bicrossproduct U(so (1, 3)) T . The algebra is a semidirect product of the classical Lorentz Group so(1,3) acting in a formed way on the momentum sector T. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the κ-Poincare acts covariantly on a κ-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.
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bicrossproduct structure of kappa poincare Group and non commutative geometry
arXiv: High Energy Physics - Theory, 1994Co-Authors: Shahn Majid, Henri RueggAbstract:We show that the $\kappa$-deformed Poincar\'e quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct $U(so(1,3))\cobicross T$. The algebra is a semidirect product of the classical Lorentz Group $so(1,3)$ acting in a deformed way on the momentum sector $T$. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the $\kappa$-Poincar\'e acts covariantly on a $\kappa$-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.
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braided matrix structure of the sklyanin algebra and of the quantum Lorentz Group
Communications in Mathematical Physics, 1993Co-Authors: Shahn MajidAbstract:Braided Groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-Groups and super-matrices to the case of braid statistics. Here we construct braided Group versions of the standard quantum GroupsUq(g). They have the same FRT generatorsl± but a matrix braided-coproductΔL=L⊗L, whereL=l+Sl−, and are self-dual. As an application, the degenerate Sklyanin algebra is shown to be isomorphic to the braided matricesBMq(2); it is a braided-commutative bialgebra in a braided category. As a second application, we show that the quantum doubleD(Uq(sl2)) (also known as the “quantum Lorentz Group”) is the semidirect product as an algebra of two copies ofUq(sl2), and also a semidirect product as a coalgebra if we use braid statistics. We find various results of this type for the doubles of general quantum Groups and their semi-classical limits as doubles of the Lie algebras of Poisson Lie Groups.
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braided matrix structure of the sklyanin algebra and of the quantum Lorentz Group
arXiv: High Energy Physics - Theory, 1992Co-Authors: Shahn MajidAbstract:Braided Groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-Groups and super-matrices to the case of braid statistics. Here we construct braided Group versions of the standard quantum Groups $U_q(g)$. They have the same FRT generators $l^\pm$ but a matrix braided-coproduct $\und\Delta L=L\und\tens L$ where $L=l^+Sl^-$, and are self-dual. As an application, the degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices $BM_q(2)$; it is a braided-commutative bialgebra in a braided category. As a second application, we show that the quantum double $D(\usl)$ (also known as the `quantum Lorentz Group') is the semidirect product as an algebra of two copies of $\usl$, and also a semidirect product as a coalgebra if we use braid statistics. We find various results of this type for the doubles of general quantum Groups and their semi-classical limits as doubles of the Lie algebras of Poisson Lie Groups.
Andrew Strominger - One of the best experts on this subject based on the ideXlab platform.
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Gluon amplitudes as 2 d conformal correlators
Physical Review D, 2017Co-Authors: Sabrina Pasterski, Shuheng Shao, Andrew StromingerAbstract:Recently, spin-one wave functions in four dimensions that are conformal primaries of the Lorentz Group $SL(2,\mathbb{C})$ were constructed. We compute low-point, tree-level gluon scattering amplitudes in the space of these conformal primary wave functions. The answers have the same conformal covariance as correlators of spin-one primaries in a $2d$ CFT. The Britto--Cachazo--Feng--Witten (BCFW) recursion relation between three- and four-point gluon amplitudes is recast into this conformal basis.
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2d stress tensor for 4d gravity
Physical Review Letters, 2017Co-Authors: Daniel Kapec, Prahar Mitra, Anamaria Raclariu, Andrew StromingerAbstract:: We use the subleading soft-graviton theorem to construct an operator T_{zz} whose insertion in the four-dimensional tree-level quantum gravity S matrix obeys the Virasoro-Ward identities of the energy momentum tensor of a two-dimensional conformal field theory (CFT_{2}). The celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the CFT_{2}, with the Lorentz Group acting as the unbroken SL(2,C) subGroup.
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gluon amplitudes as 2d conformal correlators
Physical Review D, 2017Co-Authors: Sabrina Pasterski, Shuheng Shao, Andrew StromingerAbstract:Recently, spin-one wavefunctions in four dimensions that are conformal primaries of the Lorentz Group SL(2,C) were constructed. We compute low-point, tree-level gluon scattering amplitudes in the space of these conformal primary wavefunctions. The answers have the same conformal covariance as correlators of spin-one primaries in a 2d CFT. The BCFW recursion relation between three- and four-point gluon amplitudes is recast into this conformal basis.
Qinghai Wang - One of the best experts on this subject based on the ideXlab platform.
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wilson polynomials and the Lorentz transformation properties of the parity operator
Journal of Mathematical Physics, 2005Co-Authors: Carl M. Bender, Peter N Meisinger, Qinghai WangAbstract:The parity operator for a parity-symmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz Group. These representations are connected with Wilson polynomials.
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The C operator in PT-symmetric quantum field theory transforms as a Lorentz scalar
Physical Review D, 2005Co-Authors: Carl M. Bender, Sebastian F. Brandt, Jun Hua Chen, Qinghai WangAbstract:A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called C. It is shown here that C is the complex extension of the intrinsic parity operator and that the C operator transforms under the Lorentz Group as a scalar.
Giorgio Sarno - One of the best experts on this subject based on the ideXlab platform.
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numerical methods for eprl spin foam transition amplitudes and Lorentzian recoupling theory
General Relativity and Gravitation, 2018Co-Authors: Pietro Dona, Giorgio SarnoAbstract:The intricated combinatorial structure and the non-compactness of the Lorentz Group have always made the computation of \(SL(2,\mathbb {C})\) EPRL spin foam transition amplitudes a very hard and resource demanding task. With sl2cfoam we provide a C-coded library for the evaluation of the Lorentzian EPRL vertex amplitude. We provide a tool to compute the Lorentzian EPRL 4-simplex vertex amplitude in the intertwiner basis and some utilities to evaluate SU(2) invariants, booster functions and \(SL(2,\mathbb {C})\) Clebsch–Gordan coefficients. We discuss the data storage, parallelizations, time, and memory performances and possible future developments.
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numerical methods for eprl spin foam transition amplitudes and Lorentzian recoupling theory
arXiv: General Relativity and Quantum Cosmology, 2018Co-Authors: Pietro Dona, Giorgio SarnoAbstract:The intricated combinatorial structure and the non-compactness of the Lorentz Group have always made the computation of $SL(2,\mathbb{C})$ EPRL spin foam transition amplitudes a very hard and resource demanding task. With \texttt{sl2cfoam} we provide a C-coded library for the evaluation of the Lorentzian EPRL vertex amplitude. We provide a tool to compute the Lorentzian EPRL 4-simplex vertex amplitude in the intertwiner basis and some utilities to evaluate SU(2) invariants, booster functions and $SL(2,\mathbb{C})$ Clebsch-Gordan coefficients. We discuss the data storage, parallelizations, time, and memory performances and possible future developments.
Carl M. Bender - One of the best experts on this subject based on the ideXlab platform.
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wilson polynomials and the Lorentz transformation properties of the parity operator
Journal of Mathematical Physics, 2005Co-Authors: Carl M. Bender, Peter N Meisinger, Qinghai WangAbstract:The parity operator for a parity-symmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz Group. These representations are connected with Wilson polynomials.
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The C operator in PT-symmetric quantum field theory transforms as a Lorentz scalar
Physical Review D, 2005Co-Authors: Carl M. Bender, Sebastian F. Brandt, Jun Hua Chen, Qinghai WangAbstract:A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called C. It is shown here that C is the complex extension of the intrinsic parity operator and that the C operator transforms under the Lorentz Group as a scalar.
