Related papers: A Geometric Representation for the Proca Model
We prove a formula which compares intersection numbers of conormal varieties of two projective varieties and their dual varieties. When one of them is linear, we can recover the usual Plucker formula for the degree of the dual variety. The…
For a theory with first and second class constraints, we propose a procedure for conversion of second class constraints based on deformation the structure of local symmetries of the Lagrangian formulation. It does not require extension or…
Any local field theory can be equivalently reformulated in the so-called unfolded form. General unfolded equations are non-Lagrangian even though the original theory is Lagrangian. Using the theory of a scalar field as a basic example, the…
The gauge fixed polygon model of 2+1 gravity with zero cosmological constant and arbitrary number of spinless point particles is reconstructed from the first order formalism of the theory in terms of the triad and the spin connection. The…
Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue…
We take as a starting point an expression for the quantum geometric tensor recently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of…
An outline of a proof of the local decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is briefly explained. We explicitly construct the gauge-invariant and…
The loop equations in the $U(N)$ lattice gauge theory are represented in the form of constraints imposed on a generating functional for the Wilson loop correlators. These constraints form a closed algebra with respect to commutation. This…
In this paper we give a geometric description of the Jacobi equations associated to a first-order Lagrangian field theory using a prolongation of the Lagrangian $L$ on a $k$-cosymplectic formulation. Moreover, using an appropriate…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling…
It is understood now that all projective (and conformal) invariants of Riemannian metrics can be found by a transparent construction based on representation theory. So this article with a partial and quite cumbersome construction of…
We examine a covariant quantization of electromagnetic fields by using an operator derived from a constant scalar that can be called extended Lorentz gauge. The quantization can avoid an inconsistency between Lorentz gauge and a commutation…
The relativistic theory of structure formation in cosmology is based mainly on linear perturbations about a homogeneous background. But we are now driven to understand the theory of higher-order perturbations in full detail, both from…
A simple Lagrangian is proposed that by the choice of the representation of SU(2), gives rise to field equations for arbitrary spin. In explicit examples it is shown, how the Klein-Gordon, the Dirac, and the Proca equation can be obtained…
It is shown that the currently studied ``string-inspired'' model for gravity on a line can be formulated as a gauge invariant theory based on the Poincar\'e group with central extension -- a formulation that complements and simplifies…
We introduce an algorithm to find possible constants of motion for a given replicator equation. The algorithm is inspired by Dirac geometry and a Hamiltonian description for the replicator equations with such constants of motion, up to a…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
Starting from matter lagrangean containing higher order derivative than the first, we construct the Poincare gauge theory by localising the Poincare symmetry of the matter theory. The construction is shown to follow the usual geometric…