Related papers: Virial Theorem for Non-relativistic Quantum Fields…
It is considered, in the framework of constrained systems, the quantum dynamics of non-relativistic particles moving on a d-dimensional Riemannian manifold M isometrically embedded in $R^{d+n}$. This generalizes recent investigations where…
The recent progress in understanding the mathematics of complex stochastic quantization, as well as its application to quantum chromodynamics in situations that have a complex phase problem (e.g. finite quark density, real time), has opened…
The mathematical description of stable particle-like systems appearing in relativistic quantum field theory at large, respectively small scales or non-zero temperatures is discussed.
Jacobian conjectures (that nonsingular implies a global inverse) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The birational…
The worldline variational approach is extended beyond the quenched approximation, i.e. to include virtual pair production of heavy particles. This is achieved either by an expansion of the functional determinant to second order or by an…
A typical geometry extracted from the path integral of a quantum theory of gravity might be quite complicated in the UV region. Even if such a configuration is not physical, it may be of interest to understand the details of its nature,…
A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…
Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form,…
The development of a mechanics of non-differentiable paths suggested by Scale Relativity results in a foundation of Quantum Mechanics including Schr\"odinger's equation and all the other axioms under the assumption the path…
Jacobian conjectures (that nonsingular implies invertible) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The associated…
For a relativistic particle moving in the presence of mean scalar and vector fields, the energy at second order in the scalar field is shown to contain two contributions in general. One is a momentum-dependent repulsive interaction…
Observables of cosmic structures are usually not the underlying matter field but biased tracers of matter, such as galaxies or halos. We show how the bias found in Newtonian N-body simulations can be interpreted in terms of the weak-field…
Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus…
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a)…
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…
We derive a class of mesoscopic virial equations governing energy partition between conjugate position and momentum variables of individual degrees of freedom. They are shown to apply to a wide range of nonequilibrium steady states with…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
Linear-nonlinear transforms are interesting in vision science because they are key in modeling a number of perceptual experiences such as color, motion or spatial texture. Here we first show that a number of issues in vision may be…
We analyze, from a canonical quantum field theory perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in…
The Casimir effect is a quantum phenomenon rooted in the fact that vacuum fluctuations of quantum fields are affected by the presence of physical objects and boundaries. Since the energy spectrum of the vacuum fluctuations depends on…