We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard formulation of gravity. In this formulation it is possible to couple arbitrary torsion to gauge fields without breaking the gauge invariance.

We study the effect of mass on geometric descriptions of gauge field theories. In an approach in which the massless theory resembles general relativity, the introduction of the mass entails non-zero torsion and the generalization to Einstein-Cartan-Sciama-Kibble theories. The relationships to pure torsion formulations (teleparallel gravity) and to higher gauge theories are also discussed.

The dynamics of the torsion-powered teleparallel theory are only viable because 36 multiplier fields disable all components Riemann-Cartan curvature. We generalize this suggestive approach by considering Poincar\'e gauge in which 60 such ``geometric multipliers'' can be invoked to any given irreducible part curvature, or indeed torsion. Torsion theories motivated a weak-field analysis frequentl...

Massless scalar and vector fields are coupled to Lyra geometry by means of Duffin-Kemmer-Petiau (DKP) theory. Using Schwinger Variational Principle, equations of motion, conservation laws and gauge symmetry are implemented. We find that the scalar field couples to the anholonomic part of the torsion tensor, and the gauge symmetry of the electromagnetic field is not breaking by the coupling with...

The geometry of supermanifolds provided with a Q-structure (i.e. with an odd vector field Q satisfying {Q, Q} = 0), a P -structure (odd symplectic structure ) and an S-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclass...

Twist knots form a family of special two–bridge knots which include the trefoil knot and the figure eight knot. The knot group of a two–bridge knot has a particularly nice presentation with only two generators and a single relation. One could find our interest in this family of knots in the following facts: first, twist knots except the trefoil knot are hyperbolic; and second, twist knots are n...

In the early seventies D. Ray and I. Singer [17] introduced the notion of zeta-regularized determinants. They used it to define the analytic version of Reidemeister torsion as an alternating product of determinants. One way to understand analytic torsion is to consider it as a ”multiplicative index” of an elliptic complex. By the L2-index theorem of M. Atiyah [1] this analogy suggests that one ...

The role of spin-torsion coupling to gravity is analyzed in the context of a model of chaotic inflation. The system of equations constructed from the Einstein-Cartan and inflaton field equations are studied and it is shown that spin-torsion interactions are effective only at the very first e-folds of inflation, becoming quickly negligible and, therefore, not affecting the standard inflationary ...

The approach of metric–affine field theory is to define spacetime as a real oriented 4-manifold equipped with a metric and an affine connection. The 10 independent components of the metric tensor and the 64 connection coefficients are the unknowns of the theory. We write the Yang–Mills action for the affine connection and vary it both with respect to the metric and the connection. We find a fam...

The problem of a rigorous theory of singularities in space-times with tor-sion is addressed. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors have done, because their definition of geodesics only involves the Christoffel connection, though studying theories with torsion. We propose a preliminary definition of singularities...