Related papers: Gleason-type Theorems from Cauchy's Functional Equ…
The equations of time-dependent density functional theory are derived, via the expression for the quantum weak value, from ring polymer quantum theory using a symmetry between time and imaginary time. The imaginary time path integral…
We construct a stationary density functional for the partition function from a chosen set of one (boson) line irreducible Feynman diagrams. The construction does not proceed by the inversion of a Legendre transform. It is formulated for…
This note is intended for expanding the details on the derivation and properties of density functional theory, in hope to make them more systematic, better motivated, and step-by-step for readers new to the domain. The note starts with…
According to Born's rule quantum probabilities are given by the overlap between the system state and measurement states in a quite symmetrical way. This means that both contribute to any observed nonclassical effect that is usually…
The electron density $n(\rb,t)$, which is the central tool of time-dependent density functional theory, is presently considered to be derivable from a one-body time-dependent potential $V(\rb,t)$, via one-electron wave functions satisfying…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we formulate a…
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well…
We obtain density theorems for cuspidal automorphic representations of $\text{GL}_n$ over $\mathbb{Q}$ which fail the generalized Ramanujan conjecture at some place. We depart from previous approaches based on Kuznetsov-type trace formulae,…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
The Hohenberg-Kohn theorem of the density functional theory is extended by modifying the Levy constrained-search formulation. The new theorem allows us to choose arbitrary physical quantities as the basic variables which determine the…
The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the…
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…
Hybrid classical-quantum systems are of interest in numerous fields, from quantum chemistry to quantum information science. A fully quantum effective description of them is straightforward to formulate when the classical subsystem is…
A class of Clebsch-Gordan coefficients are derived from the properties of conditional probability using the binomial distribution. In particular, in the case of $l=l_1+l_2$ it is shown that $$[<l_1/2-k_1, l_2/2-k_2|l/2, k=k_1+k_2]>^2…
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…
From the viewpoint of the theory of orthomodular lattices of elementary propositions, Quantum Theories can be formulated in real, complex or quaternionic Hilbert spaces as established in Sol\'er's theorem. The said lattice eventually…
We present a new approach to absolute continuity of laws of Poisson functionals. The theoretical framework is that of local Dirichlet forms as a tool to study probability spaces. The method gives rise to a new explicit calculus that we show…
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure.…
We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge…
We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One…