Physical Interpreation of the Laplace Operator I am wondering if there is a physical interpretation of the Laplace operator (also known as Laplacian, Δ, ∇2, or ∇·∇). From my impression a gradient of a f
The supergravity/superstring and MGT gravitational field equations are formulated as sophisticated systems of nonlinear partial differential equations, PDEs. Various types of advanced analytic and numeric methods for constructing exact and approximate solutions of such equations have been explored. For GR, ...
There is no physical meaning of wave function as it is not a quantity which can be observed. Instead, it is complex. It is expressed as𝚿 (x, y, z, t) = a + ib and the complex conjugate of the wave function is expressed as𝚿 \[\times\](x, y, z, t) = a – ib. The...
Investigating the link between physical constraints like stability and causality with univalence, a mathematical limit, can provide valuable insights into the mathematical properties of the RH series and demonstrate the practical significance of these abstract limits. In this work, we explore the univalenc...
where we have expanded the unitary operator over a complete set of two-particle states (with no virtual particles) $$\begin{aligned} \hat{1} = \sum \limits _{f} |f\rangle \langle f| = \sum \limits _{f_e}\sum \limits _{f_{\gamma }}|f_e, f_{\gamma }\rangle \langle f_...
have a rather straightforward meaning: \(\zeta _2\) plays the role of the mass for the multiplet \(\phi _i\) , while all other couplings starting from \(\zeta _3\) are genuine interactions with which one can construct a perturbative expansion. specifically: \(\zeta _3\) is ...
Everything in the hole argument was correct up to the final conclusion. It has no physical content if, with respect to the same coordinate systemK, two different solutionsG(x) andG′(x) exist [see Section2.3]. To imagine two solutions simultaneously on the same manifold has no meaning, ...
situated out of the ground state, i.e., there is always a thermal cloud (depletion) that under typical experimental conditions could be neglected (see [38]). Moreover, notice that in the non-relativistic limit, the d’Alembertian operator in Eq. (10) becomes the Laplacian operator and ...
Observe, now, that we can use a well-known differential operator expression in a Riemannian manifold, div(𝜂gradΨ)=𝜂ΔΨ+〈grad𝜂,gradΨ〉, where Δ stands for the Laplacian operator. For further details, see, for instance, the work [22]. Thus, we shall have ∫Θ〈gradΨ...
essentially a product of the human mind and has no meaning apart from man, it owes its existence to the creative power of his intellect. There is more meaning in the statement that man gives laws to Nature than in its converse that Nature gives laws to man”, see [6]. It is a ...