Related papers: Theta Vectors and Quantum Theta Functions
The discriminant of a smooth plane cubic curve over the complex numbers can be written as a product of theta functions. This provides an important connection between algebraic and analytic objects. In this paper, we perform a new approach…
This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid [2020], is to interpret the phase…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
The Ermakov Lewis quantum invariant for the time dependent harmonic oscillator is expressed in terms of number and phase operators. The identification of these variables is made in accordance with the correspondence principle and the…
The quantum mechanical propagators of the linear automorphisms of the two-torus (cat maps) determine a projective unitary representation of the theta group, known as Weil's representation. We prove that there exists an appropriate choice of…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…
The original intent of the Koopman-von Neumann formalism was to put classical and quantum mechanics on the same footing by introducing an operator formalism into classical mechanics. Here we pursue their path the opposite way and examine…
The zeta-regularization allows to establish a connection between Feynman's path integral and Fourier integral operator zeta-functions. This fact can be utilized to perform the regularization of the vacuum expectation values in quantum field…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
Matrix elements of quantum intertwiner as well as the modified Q-operator for the quantum relativistic Toda chain at root of unity are constructed explicitly. Modified Q-operators make isospectrality transformations of quantum transfer…
In the Schroedinger formulation of non-Hermitian quantum theories a positive-definite metric operator $\eta\equiv e^{-Q}$ must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta…
In the second part of our work on observables we have shown that quantum observables in the sense of von Neumann, i.e.bounded selfadjoint operators in some von Neumann subalgebra $R$ of $L(H)$, can be represented as bounded continuous…
The $\Theta$-spherical functions generalize the spherical functions on Riemannian symmetric spaces and the spherical functions on non-compactly causal symmetric spaces. In this article we consider the case of even multiplicity functions. We…
Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…
We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide…
In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose…