Related papers: Gauge Formalism for General Relativity and Fermion…
We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$…
We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…
Gauge theories with finite gauge groups have applications to quantum simulation and quantum gravity. Recently, the exact number of gauge-invariant states was computed for pure gauge theories on arbitrary lattices. In this work, we…
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…
In this short article we introduce the mathematical framework of the principle of the fermionic projector and set up a variational principle in discrete space-time. The underlying physical principles are discussed. We outline the connection…
Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space…
We further explore the idea that physics takes place in Clifford space which should be considered as a generalization of spacetime. Following the old observation that spinors can be represented as members of left ideals of Clifford algebra,…
String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time…
The generalized connections of the (anti)-de Sitter space symmetry algebra, which are differential forms of arbitrary degree with values in any irreducible (spin)-tensor representation of the (anti)-de Sitter algebra, are studied. It is…
Gauge theories with and without matter are formulated in the derivative expansion. Amplitudues are derived as a power series in the energy scales; there are simplifications as compared with the usual loop expansion. The incorporation and…
The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is…
In this paper I offer an introduction to group field theory (GFT) and to some of the issues affecting the foundations of this approach to quantum gravity. I first introduce covariant GFT as the theory that one obtains by interpreting the…
Accounting for all the relativistic effects, we have developed the fully nonlinear gauge-invariant formalism for describing the cosmological observables and presented the second-order perturbative expressions associated with light…
A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on…
A description of motion is proposed, adapted to the composite bundle interpretation of Poincar\'e Gauge Theory. Reference frames, relative positions and time evolution are characterized in gauge-theoretical terms. The approach is…
This manuscript is devoted to introduce a gauge theory of the Lorentz Group based on the ambiguity emerging in dealing with isometric diffeo-morphism-induced Lorentz transformations. The behaviors under local transformations of fermion…
A broad class of contour gauges is shown to be determined by admissible contractions of the geometrical region considered and a suitable equivalence class of curves is defined. In the special case of magnetostatics, the relevant…
It is a review paper. General relativity (GR) is presented in the field theoretical form, where gravitational field (metric perturbations) together with other physical fields are propagated in an auxiliary arbitrary curved background…
We propose a graded classification of the entire field of multivector physics, including all alternative points of view. The (often tacit) postulates of different types of formulations are contrasted, summarizing their consequences.…
We present a short review of the spin curvatures that arise within the framework of one of the Infeld-van der Waerden formalisms for general relativity. All the spinor symmetries borne by the inner structure of general relativity are thus…