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We present a tetrad–affine approach to f ( Q ) gravity coupled to spinor fields of spin- 1 2 . After deriving the field equations, we derive the conservation law of the spin density, showing that the latter ensures the vanishing of the antisymmetric part of the Einstein-like equations, just as it happens in theories with torsion and metricity. We then focus on Bianchi type-I cosmological models proposing a general procedure to solve the corresponding field equations and providing analytical solutions in the case of gravitational Lagrangian functions of the kind f ( Q ) = α Q n . At late time such solutions are seen to isotropize and, depending on the value of the exponent n, they can undergo an accelerated expansion of the spatial scale factors.

Junction conditions are discussed within the framework of $f(R)$-gravity with torsion. After deriving general junction conditions, the cases of coupling to a Dirac field and a spin fluid are explicitly dealt with. The main differences with respect to Einstein--Cartan--Sciama--Kibble theory $\left(f(R)=R\right)$ are outlined., Comment: 13 pages

A gauge-independent formulation of the theory developed in J. Phys. A: Math. Gen. 36 8341 (2003) is proposed.

We construct a new geometrical framework for Yang–Mills Lagrangian field theories as an appropriate quotient space of the standard first jet-bundle and investigate the geometrical properties of the resulting mathematical setting. We deduce the field equations from a variational problem formulated through a regular Poincare–Cartan form, thus ensuring the kinematical admissibility of critical sections. We state a generalized Nother theorem and explicitly consider the case of the free Yang–Mills field.

A momentum representation for p-adic quantum mechanics is constructed. It uses a Fourier transform in the -space with respect to the p-adic Lebesgue distribution and a study of its properties. The momentum representation is used to investigate the spectral properties of the p-adic momentum operator and to study the (p-adic valued) Schrodinger equation for the p-adic harmonic oscillator.

We propose a physical interpretation for a p-adic picture of reality. According to this interpretation, p-adic numbers describe measurements with a finite accuracy (at the same time, real numbers describe measurements with an infinite accuracy). We consider the representation of the position operator in a p-adic Hilbert space and study the spectrum of this operator.

In this work we show how the Poincare-Cartan form can be used to describe the symmetries of Lagrangian supersymmetric (possibly p-adic) field theories. We show that the existence of the Poincare-Cartan form in supermanifold theory is ensured only in a relevant class of Lagrangian densities. Moreover, we give an abstract characterization of supersymmetric invariance based on the Poincare-Cartan form.

We present an analysis of the phase space of cosmological models based on a non minimal coupling between the geometry and a fermionic condensate. We obtain that the strong constraint coming from the Dirac equations allows a detailed design of the cosmology of these models and at the same time guarantees an evolution towards a state indistinguishable from General Relativistic cosmological models. In this light, we show how the use of some specific potentials is able to reproduce naturally two de Sitter phases separated by a power law expansion which could be an interesting model for the unification of an inflationary phase and a dark energy era., 25 pages, 4 figures, submitted to Classical and Quantum Gravity

The classical Frobenius theorem, both in its local and global formulations, is generalised to superanalytic supermanifolds. As an application, it is proved that a coset space G/H (where both G and H are super Lie groups) is a supermanifold. Existence and uniqueness of local flows of tangent vector fields is proved.

A mathematically consistent global theory of super fibre bundles is laid down. In this framework the authors perform, in a rigorous way, the analysis of the construction of super fibre bundles, connections, reduced bundles and reduced connections. Some bundles of physical interest, constructed over a supermanifold (the Lorentz bundle and the graded Poincare bundle), are analysed in detail. A criterion for the existence of a Lorentz bundle over a supermanifold is established. Some results about subgroups of super Lie groups are also given.