We review our recent work, hep-th/9803030, on the constraints imposed by global or local symmetries on perturbative quantum field theories. The analysis is performed in the Bogoliubov-Shirkov-Epstein-Glaser formulation of perturbative quantum field theory. In this formulation the S-matrix is constructed directly in the asymptotic Fock space with only input causality and Poincaré invariance. We ...

Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not c...

Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different ro...

The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework. The geometric meaning o...

Anomalies can be viewed as a breaking of some Noether symmetry through the effects of the vacuum. In relativistic quantum field theory (QFT), such a (classical) symmetry is broken by field quantization, cf. Refs [20, 7, 51] for recent reviews. This has important implications on such physical processes as the decay of the neutral π-meson [6], induced instanton effects [43], or underlies the post...

This article complements recent results of the papers [J. Math. Phys. 41 (2000), 480; 45 (2004), 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and Noether-type integration technique. It turned out that there exist nonlinear superposition principles for solutions of special second-order ordinary difference equati...

In a pilot-wave theory, an individual closed system is described by a wavefunction ψ(q) and configuration q. The evolution of the wavefunction and configuration are respectively determined by the Schrödinger equation and guidance equation. The guidance equation states that the velocity field for the configuration is given by the quantum current divided by the density |ψ(q)|2. We present the cur...