Supersymmetric extensions of Schr\"odinger-invariance

The set of dynamic symmetries of the scalar free Schr\"odinger equation in d space dimensions gives a realization of the Schr\"odinger algebra that may be extended into a representation of the conformal algebra in d+2 dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-1/2 L\'evy-Leblond equation. A N=2 supersymmetric extension of these equations leads, respectively, to a `super-Schr\"odinger' model and to the (3|2)-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras osp(2|2) *_s sh(2|2) and osp(2|4), respectively. The Schr\"odinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schr\"odinger-Neveu-Schwarz algebra sns^(N) with N supercharges. Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of osp(2|4). If one includes both N=2 supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values.Comment: Latex 2e, 46 pages, with 3 figures include

Supersymmetric extensions of Schr\"odinger-invariance

The set of dynamic symmetries of the scalar free Schr\"odinger equation in d space dimensions gives a realization of the Schr\"odinger algebra that may be extended into a representation of the conformal algebra in d+2 dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-1/2 L\'evy-Leblond equation. A N=2 supersymmetric extension of these equations leads, respectively, to a `super-Schr\"odinger' model and to the (3|2)-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras osp(2|2) *_s sh(2|2) and osp(2|4), respectively. The Schr\"odinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schr\"odinger-Neveu-Schwarz algebra sns^(N) with N supercharges. Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of osp(2|4). If one includes both N=2 supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values.Comment: Latex 2e, 46 pages, with 3 figures include

Supersymmetric extensions of Schr\"odinger-invariance

The set of dynamic symmetries of the scalar free Schr\"odinger equation in d space dimensions gives a realization of the Schr\"odinger algebra that may be extended into a representation of the conformal algebra in d+2 dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-1/2 L\'evy-Leblond equation. A N=2 supersymmetric extension of these equations leads, respectively, to a `super-Schr\"odinger' model and to the (3|2)-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras osp(2|2) *_s sh(2|2) and osp(2|4), respectively. The Schr\"odinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schr\"odinger-Neveu-Schwarz algebra sns^(N) with N supercharges. Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of osp(2|4). If one includes both N=2 supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values.Comment: Latex 2e, 46 pages, with 3 figures include

Programming an interpreter using molecular dynamics

PGA (ProGram Algebra) is an algebra of programs which concerns programs in their simplest form: sequences of instructions. Molecular dynamics is a simple model of computation developed in the setting of PGA, which bears on the use of dynamic data structures in programming. We consider the programming of an interpreter for a program notation that is close to existing assembly languages using PGA with the primitives of molecular dynamics as basic instructions. It happens that, although primarily meant for explaining programming language features relating to the use of dynamic data structures, the collection of primitives of molecular dynamics in itself is suited to our programming wants.Comment: 27 page