  General structure of classical reparametrization-invariant matter systems,
mainly the relativistic particle and its $d$-brane generalization, are studied.
The exposition is in close analogy with the relativistic particle in an
electromagnetic field as reparametrization-invariant system. The structure of a
diffeomorphism invariant Lagrangian action for an extended object ($d$-brane)
embedded in a bulk space M is discussed. Our construction uses first order
homogeneous Lagrangians to achieve general covariance in contrast to the
constructions that use scalar Lagrangians along with metric dependent
integration measure. The framework contains intrinsically the relativistic
point particle, string theory, and Dirac-Nambu-Goto Lagrangians. In a natural
way, the matter Lagrangian contains background interaction fields, such as a
1-form field, analogous to the electromagnetic vector potential, and a metric
tensor. The framework naturally suggests new classical interaction fields
beyond electromagnetism and gravity. Construction of aninteraction field
Lagrangian that is background free and consistent with the gauge symmetries
presented in the equations of motion for the matter is outlined.
  Keywords: diffeomorphism invariant systems, reparametrization-invariant
matter systems, matter Lagrangian, homogeneous singular Lagrangians,
relativistic particle, string theory, extended objects, d-branes, interaction
fields, classical forces beyond electromagnetism and gravity, generally
covariant theory, gauge symmetries, background free theories.
