Related papers: A Sommerfeld Explanation

We study the local existence and regularity of the density of the law of a functional on the Wiener space which satisfies a criterion that generalizes the H\"ormander condition of order one (that is, involving the first order Lie brackets)…

We study existence results for a fourth order problem describing single-component film models assuming initial data in Wiener spaces.

We review the continuous theory of dislocations from a mathematical point of view using mathematical tools, which were only partly available when the theory was developed several decades ago. We define a space of dislocation measures, which…

It is well known that the calculated cosmological constant, when regularized with a cutoff, differs hugely from the measured value. These calculations are made on the basis of a wave-vector cut-off that is usually set at the Planck scale.…

A discussion is given of the uncertainty principle in view of the introduction of a Gravitational Planck Constant. The need for such a gravitational constant is shown first. A reduced electromagnetic Planck constant and the analogous…

Given a compact Riemannian manifold, we prove a uniform Franks' lemma at second order for geodesic flows and apply the result in persistence theory.

Consider the semiclassical limit, as the Planck constant $\hbar\ri 0$, of bound states of a one-dimensional quantum particle in multiple potential wells separated by barriers. We show that, for each eigenvalue of the Schr\"odinger operator,…

We give new short proofs of Allard's regularity theorem for varifolds with bounded first variation and Brakke's regularity theorem for integral Brakke flows with bounded forcing. They are based on a decay of flatness, following from…

A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.

We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…

The blackbody is considered in the external general field. The additional coefficients of stimulated emission and absorption are introduced into the Einstein mechanism. Then, the generalized Planck formula is derived. The Einstein and Debye…

A remark on the proof that the Grothendieck constant satisfies $K_G < \pi/(2\ln(1+\sqrt{2}))$.

We argue that the discrepancy between the Planck mass scale and the observed value of the cosmological constant can be largely attenuated if those quantities are understood as a result of effective, and thus scale-dependent, couplings. We…

We clarify a point concerning the ultraviolet behaviour of the Quantum Field Theory of gravity, under the assumption of the existence of an ultraviolet Fixed Point. We explain why Newton's constant should to scale like the inverse of the…

It is shown that the Riemann-Silberstein vector, defined as ${\bf E} + i{\bf B}$, appears naturally in the $SL(2,C)$ algebraic representation of the electromagnetic field. Accordingly, a compact form of the Maxwell equations is obtained in…

Naive calculations in quantum field theory suggest that vacuum fluctuations should induce an enormous cosmological constant. What if these estimates are right? I argue that even a huge cosmological constant might be hidden in Planck scale…

We prove a conjecture of Stembridge concerning stability of Kronecker coefficients that vastly generalizes Murnaghan's theorem. The main idea is to identify the sequences of Kronecker coefficients in question with Hilbert functions of…

We establish the well-posedness of the Helmholtz equation with rough and compactly supported coefficients in Rd under sharp regularity assumptions. Using a paraproduct calculus in rescaled weighted Besov spaces, we rigorously define the…

Within the Sommerfeld atomic model the quantization of magnetic flux through the electronic orbits is investigated together with its dependency on additional sources of magnetic fields. These sources alter the magnetic flux through the…

Planck's formula and General Relativity indicate that potential energy influences spacetime. Using Einstein's Equivalence Principle and an extension of his Chock Hypothesis, an explicit description of this influence is derived. We present a…