Related papers: Legendre transformations and Clairaut-type equatio…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…
The light-front Hamiltonian formulation for the scalar field theory contains a new ingredient in the form of a constraint equation. Renormalization of the two dimensional $\phi^{4}$ theory, described in the continuum, is discussed. The mass…
The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be…
The general framework of Legendre transformation is extended to the case of symplectic groupoids, using an appropriate generalization of the notion of generating function (of a Lagrangian submanifold).
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
We describe a new class of exact square integrable solutions of the Pauli and Dirac equation in rotating electromagnetic fields. Solutions obtained by putting equations in the stationary form with help of a coordinate transformation…
Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation…
We discuss some applications of the effective quantum field theory to the description of the physics beyond the Standard Model. We consider two different examples. In the first one we derive, at the one-loop level, an effective lagrangian…
The perturbative dynamics of quantum field theories is described by a recursive expansion similar to the well known loop expansion. The equivalent formulation based on low-energy dynamics via an expansion in derivatives is well known in the…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields. The simplest proposed theory is defined over arbitrary finite fields and loses the notion of unitaries. This makes such…
Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
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…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…
We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The usual functional Gamma does…