The groups of Poincaré and Galilei in arbitrary dimensional spaces (original) (raw)
Related papers
Galilei-invariant equations for massive fields
Journal of Physics A: Mathematical and Theoretical, 2009
Galilei-invariant equations for massive fields with various spins have been found and classified. They have been derived directly, i.e., by using requirement of the Galilei invariance and various facts on representations of the Galilei group deduced in the paper written by de Montigny M, Niederle J and Nikitin A G, J. Phys. A 39, 1-21, 2006. A completed list of non-equivalent Galileiinvariant wave equations for vector and scalar fields is presented. It shows two things. First that the collection of such equations is very broad and describes many physically consistent systems. In particular it is possible to describe spin-orbit and Darwin couplings in frames of Galilei-invariant approach. Second, these Galilei-invariant equations can be obtained either via contraction of known relativistic equations or via contractions of quite new relativistic wave equations.
Reduction of the representations of the generalised Poincare algebra by the Galilei algebra
Journal of Physics A: Mathematical and General, 1980
The realisations of all classes of unitary irreducible representations of the generalised Poincaré group P (1, 4) have been found in a basis in which the Casimir operators of its important subgroup, i.e. the Galilei group, are of diagonal form. The exact form of the unitary operator which connects the canonical basis of the P (1, 4) group and the Galilei basis has been established. The paper of Fedorchuck [6] is devoted to the classification and the description of all subgroups of the P (1, 4) group. We will indicate the groups and the corresponding Lie algebras by the same indices.
On the Galilean-invariant equations for particles with arbitrary spin
1976
In our preceding paper [1] the equations of motion which are invariant under the Galilei group G have been obtained starting from the assumption that the Hamiltonian of a nonrelativistic particle has positive eigenvalues and negative ones. These nonrelativistic equations as well as the relativistic Dirac equation lead to the spin-orbit and to the Darwin interactions by the standard replacement p µ → π µ = p µ − eA µ . Previously it was generally accepted the hypothesis that the spin-orbit and the Darwin interactions are truly relativistic effects .
Galilei general relativistic quantum mechanics revisited
… e Outros Ensaios, AS Alves, FJ …, 1998
We review the recent advances in the generally covariant and geometrically intrinsic formulation of Galilei relativistic quantum mechanics. The main concepts used are Galilei-Newton space-time, Newtonian gravity and electromagnetism, space-time connection and cosymplectic form, quantum line bundle and quantum connection, Schrodinger equation and Hilbert bundle, quantisable functions and quantum operators. The paper contains a number of improvements and simplifications with respect to the already published or announced results.
Galilei general relativistic quantum mechanics
to appear, 1994
We present a general relativistic approach to quantum mechanics of a spinless charged particle, subject to external classical gravitational and electromagnetic fields in a curved space-time with absolute time. The scheme is also extended in order to treat the n-body quantum mechanics.
Class Quantum Gravity, 1995
In a preceding paper we developed a reformulation of Newtonian gravitation as a {\it gauge} theory of the extended Galilei group. In the present one we derive two true generalizations of Newton's theory (a {\it ten-fields} and an {\it eleven-fields} theory), in terms of an explicit Lagrangian realization of the {\it absolute time} dynamics of a Riemannian three-space. They turn out to be {\it gauge invariant} theories of the extended Galilei group in the same sense in which general relativity is said to be a {\it gauge} theory of the Poincar\'e group. The {\it ten-fields} theory provides a dynamical realization of some of the so-called ``Newtonian space-time structures'' which have been geometrically classified by K\"{u}nzle and Kucha\v{r}. The {\it eleven-fields} theory involves a {\it dilaton-like} scalar potential in addition to Newton's potential and, like general relativity, has a three-metric with {\it two} dynamical degrees of freedom. It is interesting to find that, within the linear approximation, such degrees of freedom show {\it graviton-like} features: they satisfy a wave equation and propagate with a velocity related to the scalar Newtonian potential.
On the new invariance algebras of relativistic equations for massless particles
Journal of Physics A: Mathematical and General, 1979
We show that the massless Dirac equation and Maxwell equations are invariant under a 23-dimensional Lie algebra, which is isomorphic to the Lie algebra of the group C4 ⊗ U (2) ⊗ U (2). It is also demonstrated that any Poincaré-invariant equation for a particle of zero mass and of discrete spin provide a unitary representation of the conformal group and that the conformal group generators may be expressed via the generators of the Poincaré group.