No abstract

Few natural basic principles allow to extend Feynman integral over the paths to an integral over the surfaces so, that they coincide at long time scale, that is when the surface degenerates into a single particle world line. In the first approximation the loop Green functions have perimeter behavior. That corresponds to the case when free quarks interact through one gluon exchange. Quantum fluctuations of the surface generate the area low. Thus in this string theory asymptotic freedom and confinement can coexist.

We suggest an extension of the gauge principle which includes tensor gauge fields. The extended non-Abelian gauge transformations of the tensor gauge fields form a new large group. On this group one can define field strength tensors, which are transforming homogeneously with respect to the extended gauge transformations. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of tensor gauge fields of arbitrary large integer spin 1, 2, .... It does not contain higher derivatives of the tensor gauge fields, and all interactions take place through three-and four-particle exchanges with dimensionless coupling constant. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of tensor gauge bosons.We shall present a second invariant Lagrangian which can be constructed in terms of the above field strength tensors. The total Lagrangian is a sum of the two Lagrangians and exhibits enhanced local gauge invariance with double number of gauge parameters. This allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore three physical polarizations: two symmetric polarizations of helicity-two massless charged tensor gauge bosons and antisymmetric polarization of helicity-zero charged B field.

We suggest an infinite-dimensional extension of gauge transformations which includes non-Abelian tensor gauge fields. In this extension of the Yang–Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrarily large integer spins. The invariant Lagrangian does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with dimensionless coupling constant.