The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Todd A. Brun - One of the best experts on this subject based on the ideXlab platform.
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Discrete spacetime, quantum walks, and relativistic wave equations
Physical Review A, 2018Co-Authors: Leonard Mlodinow, Todd A. BrunAbstract:It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper we define the 3D walk as a product of three coined one-dimensional walks. The factor corresponding to each one-dimensional walk involves two projection operators that act on an internal coin space, each projector is associated with either the "forward" or "backward" direction in that physical dimension. We show that the simple requirement that there is no preferred axis or direction along an axis---that is, that the walk be symmetric under parity transformations and rotations that swap the axes of the cubic lattice---leads to the requirement that the continuum limit of the walk is fully Lorentz invariant. We show further that, in the case of a massive particle, this simple symmetry requirement necessitates that inclusion of antimatter---the use of a four-dimensional internal space---and that the "coin flip" operation is generated by the parity transformation on the internal coin space, while the differences of the projection operators associated to each dimension must all Anticommute. Finally, we discuss the leading correction to the continuum limit, and the possibility of distinguishing through experiment between the discrete random walk and the continuum-based Dirac equation as a description of fermion dynamics.
Plyushchay, Mikhail S. - One of the best experts on this subject based on the ideXlab platform.
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On hidden broken nonlinear superconformal symmetry of conformal mechanics and nature of double nonlinear superconformal symmetry
'Elsevier BV', 2005Co-Authors: Correa Francisco, Del Olmo, Mariano A., Plyushchay, Mikhail S.Abstract:We show that for positive integer values $l$ of the parameter in the conformal mechanics model the system possesses a hidden nonlinear superconformal symmetry, in which reflection plays a role of the grading operator. In addition to the even $so(1,2)\oplus u(1)$-generators, the superalgebra includes $2l+1$ odd integrals, which form the pair of spin-$(l+{1/2})$ representations of the bosonic subalgebra and Anticommute for order $2l+1$ polynomials of the even generators. This hidden symmetry, however, is broken at the level of the states in such a way that the action of the odd generators violates the boundary condition at the origin. In the earlier observed double nonlinear superconformal symmetry, arising in the superconformal mechanics for certain values of the boson-fermion coupling constant, the higher order symmetry is of the same, broken nature.Comment: 8 pages; typos correcte
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On hidden broken nonlinear superconformal symmetry of conformal mechanics and nature of double nonlinear superconformal symmetry
2005Co-Authors: Correa F, Del Olmo M A, Plyushchay, Mikhail S.Abstract:We show that for positive integer values $l$ of the parameter in the conformal mechanics model the system possesses a hidden nonlinear superconformal symmetry, in which reflection plays a role of the grading operator. In addition to the even $so(1,2)\oplus u(1)$-generators, the superalgebra includes $2l+1$ odd integrals, which form the pair of spin-$(l+{1/2})$ representations of the bosonic subalgebra and Anticommute for order $2l+1$ polynomials of the even generators. This hidden symmetry, however, is broken at the level of the states in such a way that the action of the odd generators violates the boundary condition at the origin. In the earlier observed double nonlinear superconformal symmetry, arising in the superconformal mechanics for certain values of the boson-fermion coupling constant, the higher order symmetry is of the same, broken nature
Leonard Mlodinow - One of the best experts on this subject based on the ideXlab platform.
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Discrete spacetime, quantum walks, and relativistic wave equations
Physical Review A, 2018Co-Authors: Leonard Mlodinow, Todd A. BrunAbstract:It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper we define the 3D walk as a product of three coined one-dimensional walks. The factor corresponding to each one-dimensional walk involves two projection operators that act on an internal coin space, each projector is associated with either the "forward" or "backward" direction in that physical dimension. We show that the simple requirement that there is no preferred axis or direction along an axis---that is, that the walk be symmetric under parity transformations and rotations that swap the axes of the cubic lattice---leads to the requirement that the continuum limit of the walk is fully Lorentz invariant. We show further that, in the case of a massive particle, this simple symmetry requirement necessitates that inclusion of antimatter---the use of a four-dimensional internal space---and that the "coin flip" operation is generated by the parity transformation on the internal coin space, while the differences of the projection operators associated to each dimension must all Anticommute. Finally, we discuss the leading correction to the continuum limit, and the possibility of distinguishing through experiment between the discrete random walk and the continuum-based Dirac equation as a description of fermion dynamics.
P. Van Nieuwenhuizen - One of the best experts on this subject based on the ideXlab platform.
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N=4 superconformal symmetry for the covariant quantum superstring
Physics Letters B, 2005Co-Authors: Pietro Antonio Grassi, P. Van NieuwenhuizenAbstract:AbstractWe extend our formulation of the covariant quantum superstring as a WZNW model with N=2 superconformal symmetry to N=4. The two anticommuting BRST charges in the N=4 multiplet of charges are the usual BRST charge QS and a charge QV proposed by Dijkgraaf, Verlinde and Verlinde for topological models. Using our recent work on “gauging cosets”, we then construct a further charge QC which Anticommutes with QC+QV and which is intended for the definition of the physical spectrum
Alexander Yu. Vlasov - One of the best experts on this subject based on the ideXlab platform.
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Clifford algebras and universal sets of quantum gates
Physical Review A, 2001Co-Authors: Alexander Yu. VlasovAbstract:In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for n-qubit systems. It is based on the well-known application of Lie algebras together with the especially simple commutation law for Clifford algebras, which states that all basic elements either commute or Anticommute.