Wave and Dirac Operators, and Representations of the Conformal Group
نویسندگان
چکیده
Let M be the flat Minkowski space. The solutions of the ware equation, the Dirac equations, the Maxwell equations, or more generally the mass 0, spin s equations are invariant under a multiplier representation U, of the conformal group. We provide the space of distributions solutions of the mass 0, spin s equations with a Hilbert space structure H,5 , such that the representation U,$ will act unitarily on H, . We prove that the mass 0 equations give intertwining operators between representations of principal series. T$Te relate these representations to the Segal-Shale-Weil (or “ladder”) representation of U(2, 2).
منابع مشابه
Multiplets of representations, twisted Dirac operators and Vogan’s conjecture in affine setting
We extend classical results of Kostant and al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting an analogue of Vogan’s conjecture on infinitesimal characters of Harish–Chandra modules in terms of Dirac cohomology. For our calculations we use ...
متن کاملFermions and the Sch/nrcft Correspondence
We consider the problem of Dirac fermions propagating on a spacetime of Schrödinger isometry and the associated boundary Euclidean two-point function of fermionic scaling operators of the holographic dual non-relativistic conformal theory. Paying careful attention to the representations of the Schrödinger algebra that appear in this problem, we show carefully how the on-shell action is construc...
متن کاملIntertwining Differential Operators for $Mp(n, R)$ and $SU(n, n)$
For each of the two series of groups, three series of representations U,,, D,,, and H,, (n E Z) are considered. For each series of representations there is a differential operator with the property, that raised to the nth power (n > 0), it intertwines the representations indexed by n and n. The operators are generalizations of the d'Alembertian, the Diracoperator and a combination of the two. U...
متن کاملOn Conformal Powers of the Dirac Operator on Spin Manifolds
The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm w...
متن کاملConformal fields in the pp-wave limit
The pp-wave (Penrose limit) in conformal field theory can be viewed as a special contraction of the unitary representations of the conformal group. We study the kinematics of conformal fields in this limit in a geometric approach where the effect of the contraction can be visualized as an expansion of space-time. We discuss the two common models of space-time as carrier spaces for conformal fie...
متن کامل