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We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological…
A coordinate-space representation for a charged scalar particle propagator in a constant magnetic field was obtained as a series over the Landau levels. Using the recently developed modified Fock-Schwinger method, an intermediate expression…
We derive a soft theorem for a massless scalar in an effective field theory with generic field content using the geometry of field space. This result extends the geometric soft theorem for scalar effective field theories by allowing the…
In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…
A generalised Amit-Roginsky vector model in flat space is obtained as the effective dynamics of pertubations around a classical solution of the Boulatov group field theory for 3d euclidean quantum gravity, extended to include additional…
We present in the most natural way, that is, in the context of the theory of vector and principal bundles and connections in them, fundamental geometrical concepts related to General Relativity and one of its extensions, the Einstein-Cartan…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We analyse the algebras generated by free component quantum fields together with the susy generators $Q,\bar Q$. Restricting to hermitian fields we first construct the scalar field algebra from which various scalar superfields can be…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…
We investigate cosmological density perturbations in a covariant and gauge-invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits…
One-dimensional free fermions are studied with emphasis on propagating fronts emerging from a step initial condition. The probability distribution of the number of particles at the edge of the front is determined exactly. It is found that…
We study the heredity of the classes of generalized metric spaces (for example, spaces with a $\sigma$-hereditarily closure-preserving $k$-network, spaces with a point-countable base, spaces with a base of countable order, spaces with a…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
Many homogeneous, four-dimensional space-time geometries can be considered within real projective geometry, which yields a mathematically well-defined framework for their deformations and limits without the appearance of singularities.…