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One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to…
We consider certain analytical features of a stochastic model that can explain among other things competition among species and simultaneous predation on the competing species from a geometric perspective which allows for a systematic…
A variational proof is provided of the existence and uniqueness of evolutions of regular Lagrangian systems.
GUP is a phenomenological model aimed for a description of a minimal length in quantum and classical systems. However, the analysis of problems in classical physics is usually approached preferring a different formalism than the one used…
We consider the canonical ensemble of $N$ particles admitting a strange Hamiltonian description. Each of the particles obeys a set of Newtonian equation of motion, which can also be described by the standard canonical Hamiltonian mechanics.…
Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back…
For a discrete mechanical system on a Lie group $G$ determined by a (reduced) Lagrangian $\ell$ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie algebra ${\mathfrak g}^*$ by the…
By means of an analogy with Classical Mechanics and Geometrical Optics, we are able to reduce Lagrangians to a kinetic term only. This form enables us to examine the extended solution set of field theories by finding the geodesics of this…
In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…
The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…
The construction of effective Lagrangians commonly involves the application of the `classical equation of motion' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in…
These lectures provide an introduction to effective theories concentrating on the basic ideas and providing some simple applications
Effective Lagrangians with dimension-six operators are widely used to analyse Higgs and other electroweak data. We show how to build a basis of operators such that each operator corresponds to a coupling which is well measured or will be in…
At the LHC, it will be possible to investigate scenarios for physics beyond the Standard Model in detail. We present precise total and differential cross section predictions, based on Prospino2.0 and SMadGraph. We also show to what degree…
Quantum corrections to Legendre transformations are shown to cancel to all orders in supersymmetric theories in path integral formalism. Using this result, lagrangians for auxiliary fields are generalized to non-quadratic forms. In…
We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such…
An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a…
We show the robustness of the structure of Legendre transform in thermodynamics against the replacement of the standard linear average with the Kolmogorov-Nagumo nonlinear average to evaluate the expectation values of the macroscopic…
The existence or not of pathologies in the context of Lagrangian theory is studied with the aid of Machine Learning algorithms. Using an example in the framework of classical mechanics, we make a proof of concept, that the construction of…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…