Andrzej Jakubiec

On the universality of linear Lagrangians for gravitational field

For a large class of purely metric, metric–affine, and purely affine theories of gravitation with nonlinear Lagrangians, it is proved that the theory is equivalent to the standard Einstein theory of gravitation interacting with additional matter fields.

On theories of gravitation with nonsymmetric connection

For a large class of theories of gravitation with nonsymmetric connection, based on general nonlinear Lagrangians, it is proved that the theory is equivalent to the standard Einstein theory of gravitation interacting with additional matter fields.

On interaction of the unified Maxwell-Einstein field with spinorial matter

Interaction of the unified Einstein-Maxwell field with the Dirac spinor field is investigated. A variational principle is found which is of a first differential order and, contrary to the standard variational derivation of the Dirac equation, does not lead to any second type of constraints. The present Letter follows [3] it its description of the Einstein-Maxwell field and [4] in its description of the Dirac field.

On the universality of Einstein equations

It is proved that a Lagrangian field theory based on a linear connection in space-time is equivalent to Einsteins general relativity interacting with additional matter fields.

Canonical variables for the Dirac theory

A new canonical structure for Diracs theory is proposed. The new configuration space A is a real, four-dimensional subbundle of the spinor bundle. A Lagrangian defined on Q describes a theory equivalent to the Dirac one. In this way we obtain a theory without second-type constraints.

On the Cauchy problem for the theory of gravitation with nonlinear Lagrangian

For a theory of gravitation with nonlinear Lagrangian it is shown that the Cauchy problem is well posed.

On local symmetries of the Schrödinger equation

Abstract The multi-symplectic approach to the Schrodinger equation with a potential V = V(t,xk) is given. The condition for a vector field X in the multi-symplectic space to be a symmetry field is found. For a spherically symmetrical potential all such symmetry fields are effectively found. The one-to-one correspondence between solutions of the free Schrodinger equation and solutions of the oscillator problem is given. This enables us to give a new geometric interpretation of the non-typical, given by A.O. Barut, symmetry of the Schrodinger equation.

A gauge-independent canonical formalism for the Dirac-Maxwell theory

Abstract The canonical structure of the space of Cauchy data for the Dirac-Maxwell theory is described. For so-called regular bispinors on a Cauchy surface Σ gauge-independent variables are found. The canonical structure of the Dirac field is determined by the canonical symplectic structure of the bundle cotangent to the manifold of all the orthonormal triads on Σ.

On a hydrodynamical description of the Dirac equation

A new form of the Dirac equation in curved spacetime (M, g) is given. It is based on the representation of a bispinor by means of an orthonormal vierbein eα and a complex number ϱ. In the geometrical language the Dirac equation obtained this way is equivalent to the system of second order equations for the vierbein. The function ϱ is uniquely determined by the vierbein field.